Metrics for 0.5 * sqrt(2.0 * (sqrt(xre * xre + xim * xim) + xre))

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze109.0ms (2.1%)

Memory

38.6MiB live, 38.6MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	50%	50%	0%	0%	0%	0
0%	0%	50%	50%	0%	0%	0%	1
50%	25%	25%	50%	0%	0%	0%	2
50%	25%	25%	50%	0%	0%	0%	3
62.5%	31.2%	18.7%	50%	0%	0%	0%	4
62.5%	31.2%	18.7%	50%	0%	0%	0%	5
68.8%	34.3%	15.6%	50%	0%	0%	0%	6
68.8%	34.3%	15.6%	50%	0%	0%	0%	7
71.9%	35.9%	14%	50%	0%	0%	0%	8
71.9%	35.9%	14%	50%	0%	0%	0%	9
73.4%	36.7%	13.3%	50%	0%	0%	0%	10
73.4%	36.7%	13.3%	50%	0%	0%	0%	11
74.2%	37.1%	12.9%	50%	0%	0%	0%	12

Compiler

Compiled 31 to 20 computations (35.5% saved)

sample2.2s (43.1%)

Memory

181.5MiB live, 1 223.4MiB allocated

Samples

722.0ms	6 330×	0	valid
368.0ms	744×	2	valid
250.0ms	446×	3	valid
161.0ms	736×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.1s

ival-hypot: 356.0ms (33.7% of total)

ival-mult: 179.0ms (16.9% of total)

ival-<=: 143.0ms (13.5% of total)

ival-add: 132.0ms (12.5% of total)

ival-sqrt: 121.0ms (11.5% of total)

adjust: 68.0ms (6.4% of total)

ival-and: 31.0ms (2.9% of total)

exact: 23.0ms (2.2% of total)

ival-assert: 3.0ms (0.3% of total)

Bogosity

explain411.0ms (8%)

Memory

-69.3MiB live, 110.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
137	0	-	1	(1.1946407669880002e-243 1.8080992497830774e-158)	`(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))`
29	0	-	0	-	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`
25	1	(-1.7150547253791719e+162 2.4717060394964907e-242)	1	(-3.576005984519953e+252 4.875384630363744e-32)	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`
0	0	-	0	-	`(*.f64 xim xim)`
0	0	-	0	-	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`
0	0	-	0	-	`xre`
0	0	-	0	-	`#s(literal 2 binary64)`
0	0	-	0	-	`xim`
0	0	-	0	-	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))`
0	0	-	0	-	`#s(literal 1/2 binary64)`
0	0	-	0	-	`(+.f64 (.f64 xre xre) (.f64 xim xim))`
0	0	-	0	-	`(*.f64 xre xre)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))`	oflow-rescue	125	0
↳	`(+.f64 (.f64 xre xre) (.f64 xim xim))`	overflow	125
↳	`(*.f64 xim xim)`	overflow	74
↳	`(*.f64 xre xre)`	overflow	76
`+.f64`	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`	cancellation	29	0
`sqrt.f64`	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`	uflow-rescue	25	0
↳	`(*.f64 xim xim)`	underflow	55
↳	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`	underflow	33
↳	`(*.f64 xre xre)`	underflow	51
↳	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`	underflow	33
↳	`(+.f64 (.f64 xre xre) (.f64 xim xim))`	underflow	11
↳	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`	underflow	8
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))`	uflow-rescue	11	0
↳	`(+.f64 (.f64 xre xre) (.f64 xim xim))`	underflow	11
↳	`(*.f64 xim xim)`	underflow	55
↳	`(*.f64 xre xre)`	underflow	51

Confusion

	Predicted +	Predicted -
+	164	1
-	0	91

Precision

1.0

Recall

0.9939393939393939

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	164	0	1
-	0	0	91

Precision?

1.0

Recall?

0.9939393939393939

Freqs

test

number	freq
0	92
1	138
2	26

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Samples

59.0ms	392×	0	valid
13.0ms	44×	2	valid
12.0ms	30×	3	valid
9.0ms	46×	1	valid

Compiler

Compiled 169 to 40 computations (76.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 70.0ms

ival-hypot: 36.0ms (51.6% of total)

ival-mult: 16.0ms (23% of total)

ival-add: 7.0ms (10% of total)

ival-sqrt: 5.0ms (7.2% of total)

adjust: 4.0ms (5.7% of total)

exact: 1.0ms (1.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

preprocess27.0ms (0.5%)

Memory

5.7MiB live, 5.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	75
1	94	75
2	165	75
3	259	75
4	396	75
5	522	75
6	682	75
7	820	75
8	850	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (*.f64 xre xre) (*.f64 xim xim))) xre))))

(*.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Symmetry

(abs xim)

Compiler

Compiled 15 to 12 computations (20% saved)

eval0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.7%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))

Compiler

Compiled 15 to 12 computations (20% saved)

simplify3.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
cost-diff	1	(+.f64 (.f64 xre xre) (.f64 xim xim))
cost-diff	4	(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	75
0	20	75
1	30	75
2	32	75
0	32	49

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))
#s(literal 2 binary64)
(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)
(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))
(+.f64 (.f64 xre xre) (.f64 xim xim))
(*.f64 xre xre)
xre
(*.f64 xim xim)
xim

Outputs
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))
(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)
(+.f64 (hypot.f64 xim xre) xre)
(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))
(hypot.f64 xim xre)
(+.f64 (.f64 xre xre) (.f64 xim xim))
(fma.f64 xim xim (*.f64 xre xre))
(*.f64 xre xre)
xre
(*.f64 xim xim)
xim

localize47.0ms (0.9%)

Memory

19.4MiB live, 19.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0078125	(+.f64 (.f64 xre xre) (.f64 xim xim))
accuracy	5.6945493865729855	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
accuracy	6.517333692504556	(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)
accuracy	31.613181299280267	(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))

Samples

20.0ms	196×	0	valid
6.0ms	22×	2	valid
6.0ms	15×	3	valid
5.0ms	23×	1	valid

Compiler

Compiled 77 to 14 computations (81.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-hypot: 9.0ms (36.1% of total)

ival-mult: 8.0ms (32.1% of total)

ival-sqrt: 3.0ms (12% of total)

ival-add: 3.0ms (12% of total)

adjust: 2.0ms (8% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series17.0ms (0.3%)

Memory

6.0MiB live, 6.0MiB allocated

Counts

5 → 91

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))
(+.f64 (.f64 xre xre) (.f64 xim xim))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)

Outputs
xim
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(pow xim 2)
(+ (pow xim 2) (pow xre 2))
(* 1/2 (* (sqrt xim) (sqrt 2)))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(* (sqrt xim) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(+ xim xre)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(pow xre 2)
(* (pow xre 2) (+ 1 (/ (pow xim 2) (pow xre 2))))
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(* (sqrt xre) (pow (sqrt 2) 2))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* 2 xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 xre)
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(* -1/2 (/ (pow xim 2) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* (pow xim 2) (+ 1 (/ (pow xre 2) (pow xim 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ 1 (/ xre xim)))
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(* -1 xim)
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	xre	@	inf	((sqrt (+ (* xre xre) (* xim xim))) (+ (* xre xre) (* xim xim)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (+ (sqrt (+ (* xre xre) (* xim xim))) xre))
3.0ms	xre	@	-inf	((sqrt (+ (* xre xre) (* xim xim))) (+ (* xre xre) (* xim xim)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (+ (sqrt (+ (* xre xre) (* xim xim))) xre))
3.0ms	xim	@	inf	((sqrt (+ (* xre xre) (* xim xim))) (+ (* xre xre) (* xim xim)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (+ (sqrt (+ (* xre xre) (* xim xim))) xre))
3.0ms	xim	@	0	((sqrt (+ (* xre xre) (* xim xim))) (+ (* xre xre) (* xim xim)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (+ (sqrt (+ (* xre xre) (* xim xim))) xre))
2.0ms	xre	@	0	((sqrt (+ (* xre xre) (* xim xim))) (+ (* xre xre) (* xim xim)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (+ (sqrt (+ (* xre xre) (* xim xim))) xre))

simplify196.0ms (3.8%)

Memory

-29.0MiB live, 47.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	418	2518
1	1360	2346
2	5040	2328
0	8085	2192

Stop Event

1×	iter limit
1×	node limit

Counts

91 → 89

Calls

Call 1

Inputs
xim
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(pow xim 2)
(+ (pow xim 2) (pow xre 2))
(* 1/2 (* (sqrt xim) (sqrt 2)))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(* (sqrt xim) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(+ xim xre)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(pow xre 2)
(* (pow xre 2) (+ 1 (/ (pow xim 2) (pow xre 2))))
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(* (sqrt xre) (pow (sqrt 2) 2))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* 2 xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 xre)
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(* -1/2 (/ (pow xim 2) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* (pow xim 2) (+ 1 (/ (pow xre 2) (pow xim 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ 1 (/ xre xim)))
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(* -1 xim)
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))

Outputs
xim
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(fma.f64 (*.f64 #s(literal 1/2 binary64) xre) (/.f64 xre xim) xim)
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(fma.f64 (fma.f64 (.f64 xre (/.f64 xre (pow.f64 xim #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xim)) (.f64 xre xre) xim)
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(fma.f64 (pow.f64 xre #s(literal 4 binary64)) (fma.f64 (.f64 xre (/.f64 xre (pow.f64 xim #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xim #s(literal 3 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) xre) (/.f64 xre xim) xim))
(pow xim 2)
(*.f64 xim xim)
(+ (pow xim 2) (pow xre 2))
(fma.f64 xim xim (*.f64 xre xre))
(* 1/2 (* (sqrt xim) (sqrt 2)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(fma.f64 (.f64 xre #s(literal 1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim)))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))) xre (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim)))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(fma.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (.f64 #s(literal -1/32 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))))) xre)) xre (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim)))
(* (sqrt xim) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) xre (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))) xre)) xre (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(+ xim xre)
(+.f64 xim xre)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(fma.f64 (fma.f64 (/.f64 xre xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre xim)
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
(fma.f64 (fma.f64 (fma.f64 (*.f64 xre (/.f64 xre (pow.f64 xim #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xim)) xre #s(literal 1 binary64)) xre xim)
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(fma.f64 (/.f64 xre xre) (.f64 (/.f64 (.f64 xim xim) xre) #s(literal 1/2 binary64)) xre)
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(fma.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xre #s(literal 4 binary64)))) xre xre)
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xre #s(literal 4 binary64))))) xre xre)
(pow xre 2)
(*.f64 xre xre)
(* (pow xre 2) (+ 1 (/ (pow xim 2) (pow xre 2))))
(.f64 (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 1 binary64)) (.f64 xre xre))
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(sqrt.f64 xre)
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(.f64 (fma.f64 (.f64 (*.f64 xim xim) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))) xre)
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(.f64 (fma.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/32 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (.f64 (.f64 xim xim) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) xre)
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/32 binary64) (.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1/64 binary64))) (fma.f64 (.f64 (.f64 xim xim) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) xre)
(* (sqrt xre) (pow (sqrt 2) 2))
(*.f64 #s(literal 2 binary64) (sqrt.f64 xre))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64))) xre)
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(.f64 (fma.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64)))) xre)
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/16 binary64) (.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal -1/32 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64)))) xre)
(* 2 xre)
(*.f64 #s(literal 2 binary64) xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (/.f64 (.f64 xim xim) xre) #s(literal 2 binary64)) xre)
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (/.f64 (.f64 xim xim) xre) #s(literal 2 binary64))) xre)
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) #s(literal 2 binary64)) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (*.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 6 binary64))))) xre)
(* -1 xre)
(neg.f64 xre)
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xre #s(literal 4 binary64))))) xre xre))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 (.f64 #s(literal 1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/64 binary64) (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 xre)) (/.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 xim (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/32 binary64) (pow.f64 xim #s(literal 3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (fma.f64 #s(literal 1/512 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/32 binary64) (.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 xre)) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 (sqrt.f64 #s(literal -1 binary64)) xim)) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 xim #s(literal 3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (fma.f64 #s(literal 1/256 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(* -1/2 (/ (pow xim 2) xre))
(.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/8 binary64) xre))) (neg.f64 xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(/.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/8 binary64) xre) (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (/.f64 (.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 4 binary64))))) (neg.f64 xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(/.f64 (fma.f64 (.f64 (pow.f64 xim #s(literal 8 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 xre #s(literal 6 binary64)))) #s(literal -1/2 binary64) (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/8 binary64) xre) (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (/.f64 (*.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 4 binary64)))))) (neg.f64 xre))
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre)
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) xre)
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xim xim) (/.f64 #s(literal 1/2 binary64) xre)) (*.f64 xim xim) xre)
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(fma.f64 (.f64 (.f64 xim xim) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (sqrt.f64 xre))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(fma.f64 (fma.f64 (.f64 (.f64 xim xim) #s(literal -1/4 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/8 binary64))) (*.f64 xim xim) (sqrt.f64 xre))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim xim)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xre xre)) (/.f64 #s(literal 1/16 binary64) (pow.f64 xre #s(literal 5 binary64))))) #s(literal 1/4 binary64) (.f64 (.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) (.f64 xim xim) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/8 binary64))) (*.f64 xim xim) (sqrt.f64 xre))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (*.f64 #s(literal 2 binary64) (sqrt.f64 xre)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (.f64 xim xim)) (.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/4 binary64))) (.f64 xim xim) (.f64 #s(literal 2 binary64) (sqrt.f64 xre)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim xim)) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xre xre)) (/.f64 #s(literal 1/16 binary64) (pow.f64 xre #s(literal 5 binary64))))) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) (.f64 xim xim) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/4 binary64))) (.f64 xim xim) (.f64 #s(literal 2 binary64) (sqrt.f64 xre)))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(fma.f64 (/.f64 (.f64 xim xim) xre) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) (*.f64 #s(literal 2 binary64) xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xim xim) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) (.f64 #s(literal 2 binary64) xre))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 xre xre) xim) xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xre xre) xim) xim) #s(literal 1/2 binary64) #s(literal 1 binary64))) xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 6 binary64)) (pow.f64 xim #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 xre xim) #s(literal 1/2 binary64)) (/.f64 xre xim) (/.f64 (.f64 (pow.f64 xre #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xim #s(literal 4 binary64))))) xim xim)
(* (pow xim 2) (+ 1 (/ (pow xre 2) (pow xim 2))))
(.f64 (.f64 (fma.f64 (/.f64 xre xim) (/.f64 xre xim) #s(literal 1 binary64)) xim) xim)
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))) xim)
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))))) xim)
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (.f64 (.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))))) xim)
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))) xim)
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))) xim)
(* xim (+ 1 (/ xre xim)))
(fma.f64 (/.f64 xre xim) xim xim)
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(fma.f64 (fma.f64 (/.f64 (/.f64 (*.f64 xre xre) xim) xim) #s(literal 1/2 binary64) (/.f64 xre xim)) xim xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (*.f64 xre xre) xim) xim) #s(literal 1/2 binary64) (/.f64 xre xim))) xim xim)
(* -1 xim)
(neg.f64 xim)
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(.f64 (neg.f64 xim) (fma.f64 (/.f64 (/.f64 (.f64 xre xre) xim) xim) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(.f64 (neg.f64 xim) (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xre xre) xim) xim) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 6 binary64)) (pow.f64 xim #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 xre xim) #s(literal 1/2 binary64)) (/.f64 xre xim) (/.f64 (.f64 (pow.f64 xre #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xim #s(literal 4 binary64))))) xim xim))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 xim)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64))) (neg.f64 xim))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64)))) (neg.f64 xim))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64))) (.f64 (.f64 (.f64 xre (.f64 (sqrt.f64 #s(literal -1 binary64)) xre)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))) (/.f64 #s(literal 3/16 binary64) (pow.f64 xim #s(literal 3 binary64))))) (neg.f64 xim))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(.f64 (.f64 (neg.f64 (sqrt.f64 xim)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (neg.f64 xim))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/4 binary64) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64)))) (neg.f64 xim))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))) (.f64 (.f64 (.f64 xre (.f64 (sqrt.f64 #s(literal -1 binary64)) xre)) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))) (/.f64 #s(literal 3/8 binary64) (pow.f64 xim #s(literal 3 binary64))))) (neg.f64 xim))
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(fma.f64 (/.f64 xre xim) xim (neg.f64 xim))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(fma.f64 (/.f64 (fma.f64 #s(literal -1/2 binary64) (/.f64 (*.f64 xre xre) xim) xre) xim) xim (neg.f64 xim))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))
(fma.f64 (/.f64 (-.f64 xre (/.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) xim) (/.f64 #s(literal -1/8 binary64) xim) (.f64 (.f64 xre xre) #s(literal 1/2 binary64))) xim)) xim) xim (neg.f64 xim))

rewrite163.0ms (3.2%)

Memory

51.2MiB live, 51.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	53
0	20	53
1	61	53
2	398	53
3	4249	53
0	8367	31

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

5 → 237

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim)))
(+.f64 (.f64 xre xre) (.f64 xim xim))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)

Outputs
(*.f64 (sqrt.f64 (hypot.f64 xim xre)) (sqrt.f64 (hypot.f64 xim xre)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64)))) (pow.f64 (.f64 (-.f64 xre xim) (+.f64 xim xre)) #s(literal -1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 xim #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 (.f64 xim xre) #s(literal 2 binary64))) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/2 binary64)))
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(/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (pow.f64 (-.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)) (pow.f64 xre #s(literal 4 binary64))) (pow.f64 (hypot.f64 xim xre) #s(literal 4 binary64))))
(/.f64 (*.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 xre #s(literal 9 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 9 binary64))) (pow.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (pow.f64 (.f64 (hypot.f64 xim xre) xre) #s(literal 3 binary64))))
(/.f64 (*.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) #s(literal 2 binary64)) (pow.f64 (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) #s(literal 3 binary64)) (pow.f64 (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))))
(/.f64 (neg.f64 (-.f64 (*.f64 xre xre) (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))) (neg.f64 (-.f64 xre (hypot.f64 xim xre))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))))) (neg.f64 (neg.f64 (-.f64 (hypot.f64 xim xre) xre))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))))))
(/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 xre xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (-.f64 (hypot.f64 xim xre) xre)))
(/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (+.f64 (pow.f64 (*.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)) (pow.f64 xre #s(literal 4 binary64))) (pow.f64 (hypot.f64 xim xre) #s(literal 4 binary64))) (-.f64 (hypot.f64 xim xre) xre)))
(/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))) (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 xre #s(literal 9 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (pow.f64 (*.f64 (hypot.f64 xim xre) xre) #s(literal 3 binary64))) (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (.f64 (-.f64 (hypot.f64 xim xre) xre) (*.f64 xre xre))) (pow.f64 (-.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64))))
(/.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) (*.f64 (-.f64 (hypot.f64 xim xre) xre) (fma.f64 xre xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(/.f64 (-.f64 (*.f64 xre xre) (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (-.f64 xre (hypot.f64 xim xre)))
(/.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (.f64 (-.f64 (hypot.f64 xim xre) xre) (+.f64 (+.f64 (pow.f64 (.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)) (pow.f64 xre #s(literal 4 binary64))) (pow.f64 (hypot.f64 xim xre) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (*.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64)))))
(/.f64 (+.f64 (pow.f64 xre #s(literal 9 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 9 binary64))) (.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (-.f64 (+.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (pow.f64 (.f64 (hypot.f64 xim xre) xre) #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))) (neg.f64 (-.f64 (hypot.f64 xim xre) xre)))
(/.f64 (neg.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)))) (neg.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 xre (hypot.f64 xim xre)) (-.f64 (*.f64 xre xre) (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64)))
(/.f64 (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (-.f64 (hypot.f64 xim xre) xre))
(/.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64))) (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))))
(neg.f64 (/.f64 (neg.f64 (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))) (-.f64 (hypot.f64 xim xre) xre)))
(neg.f64 (/.f64 (neg.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)))) (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))))
(neg.f64 (/.f64 (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (neg.f64 (-.f64 (hypot.f64 xim xre) xre))))
(neg.f64 (/.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64))) (neg.f64 (fma.f64 (-.f64 xre (hypot.f64 xim xre)) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64)))) (fma.f64 xre (+.f64 (hypot.f64 xim xre) xre) (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64))) (neg.f64 (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (fma.f64 (neg.f64 xre) xre (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)))) (+.f64 (hypot.f64 xim xre) xre) (neg.f64 (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(fma.f64 (sqrt.f64 xre) (sqrt.f64 xre) (hypot.f64 xim xre))
(fma.f64 (sqrt.f64 (hypot.f64 xim xre)) (sqrt.f64 (hypot.f64 xim xre)) xre)
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64)))) (pow.f64 (*.f64 (-.f64 xre xim) (+.f64 xim xre)) #s(literal -1/2 binary64)) xre)
(fma.f64 (hypot.f64 (pow.f64 xim #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 (*.f64 xim xre) #s(literal 2 binary64))) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/2 binary64)) xre)
(fma.f64 (-.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) (/.f64 (pow.f64 (.f64 (-.f64 xre xim) (+.f64 xim xre)) #s(literal -1 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (neg.f64 (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(fma.f64 (+.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 (.f64 xim xre) #s(literal 2 binary64))) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (neg.f64 (.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(fma.f64 (hypot.f64 xim xre) (/.f64 (hypot.f64 xim xre) (-.f64 (hypot.f64 xim xre) xre)) (neg.f64 (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(fma.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (pow.f64 (-.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64)) (neg.f64 (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(-.f64 (/.f64 (*.f64 xre xre) (-.f64 xre (hypot.f64 xim xre))) (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 xre (hypot.f64 xim xre))))
(-.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre))))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (/.f64 (pow.f64 (hypot.f64 xim xre) #s(literal 2 binary64)) (-.f64 (hypot.f64 xim xre) xre)) (neg.f64 (*.f64 xre (/.f64 xre (-.f64 (hypot.f64 xim xre) xre)))))
(+.f64 (hypot.f64 xim xre) xre)
(+.f64 xre (hypot.f64 xim xre))

eval64.0ms (1.2%)

Memory: -46.2MiB live, 31.5MiB allocated
Compiler: Compiled 9 632 to 2 082 computations (78.4% saved)

prune14.0ms (0.3%)

Memory

16.7MiB live, 16.7MiB allocated

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	313	13	326
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	314	13	327

Accuracy

88.4%

Counts

327 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.3%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 xim xre) xre)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
▶	80.8%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	76.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 (hypot.f64 xim xre)) (sqrt.f64 (hypot.f64 xim xre)) xre))))
	79.3%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 xim xre)) #s(literal 2 binary64)) xre))))
▶	7.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
	6.7%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
	51.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (fma.f64 (fma.f64 (/.f64 xre xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre xim)))))
	12.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/8 binary64) xre))) (neg.f64 xre))))))
	53.8%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
	13.8%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))))))
▶	45.1%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
▶	50.9%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
▶	28.0%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Compiler

Compiled 546 to 406 computations (25.6% saved)

simplify85.0ms (1.7%)

Memory

16.1MiB live, 16.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score
cost-diff	0	(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
cost-diff	0	#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
cost-diff	0	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
cost-diff	3	(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
cost-diff	0	(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))
cost-diff	0	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
cost-diff	4	(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 2 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
cost-diff	0	#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
cost-diff	0	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
cost-diff	0	(sqrt.f64 xre)
cost-diff	0	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
cost-diff	0	(+.f64 (hypot.f64 xim xre) xre)
cost-diff	0	(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
cost-diff	0	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	441
0	83	391
1	141	391
2	245	391
3	574	383
4	1910	359
5	4058	359
6	6074	359
0	8035	355

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
(+.f64 (hypot.f64 xim xre) xre)
(hypot.f64 xim xre)
xim
xre
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(sqrt.f64 xre)
xre
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
#s(literal 1/2 binary64)
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 xim)
xim
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)))
(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))
#s(literal 2 binary64)
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)
#s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
(neg.f64 xre)
xre
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre)
(*.f64 #s(literal 1/2 binary64) xim)
xim
(/.f64 xim xre)
#s(literal 1 binary64)
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
#s(literal 1/2 binary64)
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
xre
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))
#s(literal 1 binary64)
(pow.f64 xim #s(literal 3 binary64))
xim
#s(literal 3 binary64)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) xim))
(/.f64 #s(literal 1 binary64) xim)

Outputs
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)))
(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
(*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))
(+.f64 (hypot.f64 xim xre) xre)
(+.f64 (hypot.f64 xre xim) xre)
(hypot.f64 xim xre)
(hypot.f64 xre xim)
xim
xre
#s(literal 2 binary64)
#s(literal 1/2 binary64)
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(sqrt.f64 xre)
xre
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
(.f64 #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 xim) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 xim) (sqrt.f64 #s(literal 2 binary64))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(*.f64 (sqrt.f64 xim) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
(sqrt.f64 xim)
xim
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
(.f64 (sqrt.f64 (.f64 (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre))) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)))
(sqrt.f64 (.f64 (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre))) xre) #s(literal 2 binary64)))
(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))
(.f64 (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre))) xre) #s(literal 2 binary64))
#s(literal 2 binary64)
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre))) xre)
#s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
#s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre)))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
(neg.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre))
(neg.f64 xre)
xre
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))
(fma.f64 (/.f64 xim xre) (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) #s(literal 1 binary64))
(/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre)
(*.f64 #s(literal 1/2 binary64) xim)
xim
(/.f64 xim xre)
#s(literal 1 binary64)
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
(.f64 #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xim) (fma.f64 (*.f64 #s(literal 1/2 binary64) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))) #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xim) (fma.f64 (*.f64 #s(literal 1/2 binary64) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xim) (fma.f64 (*.f64 #s(literal 1/2 binary64) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)
(sqrt.f64 #s(literal 2 binary64))
#s(literal 2 binary64)
xre
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))
(/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))
#s(literal 1 binary64)
(pow.f64 xim #s(literal 3 binary64))
xim
#s(literal 3 binary64)
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) xim))
(/.f64 #s(literal 1 binary64) xim)

localize155.0ms (3%)

Memory

-61.9MiB live, 51.1MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	2.4259547583364838	(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
accuracy	4.34212389320224	(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
accuracy	12.080439689233769	(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))
accuracy	15.995896267702326	#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
accuracy	0.0078125	(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)
accuracy	0.07650375976844201	(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))
accuracy	1.9084880086433706	(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
accuracy	34.20914354158534	#s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
accuracy	0.0	(sqrt.f64 xim)
accuracy	0.0	(sqrt.f64 #s(literal 2 binary64))
accuracy	0.20703125	(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
accuracy	16.141184982711714	#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
accuracy	0.0	(sqrt.f64 xre)
accuracy	16.593342573679838	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
accuracy	0.0	(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
accuracy	0.0	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
accuracy	0.00390625	(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
accuracy	0.0078125	(+.f64 (hypot.f64 xim xre) xre)

Samples

79.0ms	138×	0	valid
48.0ms	118×	0	invalid

Compiler

Compiled 341 to 40 computations (88.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-div: 43.0ms (41.1% of total)

ival-sqrt: 22.0ms (21% of total)

ival-mult: 19.0ms (18.2% of total)

ival-hypot: 10.0ms (9.6% of total)

ival-add: 5.0ms (4.8% of total)

ival-pow: 3.0ms (2.9% of total)

exact: 1.0ms (1% of total)

ival-neg: 1.0ms (1% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

series27.0ms (0.5%)

Memory

13.8MiB live, 13.8MiB allocated

Counts

23 → 138

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
(+.f64 (hypot.f64 xim xre) xre)
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(sqrt.f64 xre)
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(sqrt.f64 #s(literal 2 binary64))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)))
(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
(sqrt.f64 xim)
#s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))

Outputs
(* 1/2 (* (sqrt xim) (sqrt 2)))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(* (sqrt xim) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(* 2 xim)
(+ (* 2 xim) (* 2 xre))
(+ (* 2 xim) (* xre (+ 2 (/ xre xim))))
(+ (* 2 xim) (* xre (+ 2 (* xre (+ (* -1/4 (/ (pow xre 2) (pow xim 3))) (/ 1 xim))))))
xim
(+ xim xre)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
(sqrt xre)
(* -1/2 (/ (pow xim 2) xre))
(/ (+ (* -1 (pow xre 2)) (* -1/2 (pow xim 2))) xre)
(* (sqrt (/ 1 xim)) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(* 1/2 (/ (pow xim 2) (pow xre 2)))
(/ (+ (* 1/2 (pow xim 2)) (pow xre 2)) (pow xre 2))
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(* (sqrt xre) (pow (sqrt 2) 2))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* 4 xre)
(* xre (+ 4 (/ (pow xim 2) (pow xre 2))))
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (+ (* 1/8 (/ (pow xim 6) (pow xre 6))) (/ (pow xim 2) (pow xre 2))))))
(* 2 xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 xre)
(* xre (- (* -1/2 (/ (pow xim 2) (pow xre 2))) 1))
(* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2))))
(* xre (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))) (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))))
(* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2))))
(* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* (sqrt xim) (/ (sqrt 2) xre))))
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
1
(+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(* -1 (/ (pow xim 2) xre))
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (pow xim 2)) xre))
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2))) xre))
(* -1 (/ (+ (* -1 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(* -1 (* (sqrt xre) (pow (sqrt -1) 2)))
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* -1 (* xre (+ (* -1 (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))
(* -1 (* xre (+ (* -1 (* (sqrt xim) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 4 xre) (/ (pow xim 2) xre))
(+ (* 4 xre) (* (pow xim 2) (+ (* -1/4 (/ (pow xim 2) (pow xre 3))) (/ 1 xre))))
(+ (* 4 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/8 (/ (pow xim 2) (pow xre 5))) (* 1/4 (/ 1 (pow xre 3))))) (/ 1 xre))))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(+ (* -1 xre) (* -1/2 (/ (pow xim 2) xre)))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) (pow xim 2))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) xim)
(sqrt xim)
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(sqrt (/ 1 (pow xim 3)))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ 2 (* 2 (/ xre xim))))
(* xim (+ 2 (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 2 (+ (* -1/4 (/ (pow xre 4) (pow xim 4))) (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (/ xre xim)))
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(* (pow xim 2) (- (* -1 (/ xre (pow xim 2))) (* 1/2 (/ 1 xre))))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* (pow xim 2) (+ (/ 1 (pow xim 2)) (* 1/2 (/ 1 (pow xre 2)))))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -2 xim)
(* -1 (* xim (+ 2 (* -2 (/ xre xim)))))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (pow xre 2) xim)) (* 2 xre)) xim)))))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow xre 4) (pow xim 2))) (pow xre 2)) xim)) (* 2 xre)) xim)))))
(* -1 xim)
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))
(* -1 (* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2)))
(* -1 (* xim (+ (* -1 (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))))))
(* -1 (* (sqrt xim) (pow (sqrt -1) 2)))
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(* -1 (* (sqrt (/ 1 (pow xim 3))) (pow (sqrt -1) 2)))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	xre	@	-inf	((* (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (sqrt 2) (sqrt xim)) (sqrt 2) (* (neg xre) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)) (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) xim) (sqrt xim) (sqrt (+ (* xre xre) (* xim xim))) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1) (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (sqrt (/ 1 (pow xim 3))))
4.0ms	xim	@	-inf	((* (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (sqrt 2) (sqrt xim)) (sqrt 2) (* (neg xre) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)) (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) xim) (sqrt xim) (sqrt (+ (* xre xre) (* xim xim))) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1) (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (sqrt (/ 1 (pow xim 3))))
4.0ms	xre	@	inf	((* (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (sqrt 2) (sqrt xim)) (sqrt 2) (* (neg xre) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)) (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) xim) (sqrt xim) (sqrt (+ (* xre xre) (* xim xim))) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1) (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (sqrt (/ 1 (pow xim 3))))
4.0ms	xre	@	0	((* (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (sqrt 2) (sqrt xim)) (sqrt 2) (* (neg xre) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)) (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) xim) (sqrt xim) (sqrt (+ (* xre xre) (* xim xim))) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1) (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (sqrt (/ 1 (pow xim 3))))
4.0ms	xim	@	0	((* (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) 1/2) (sqrt (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2)) (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt xre) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (sqrt 2) (sqrt xim)) (sqrt 2) (* (neg xre) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1)) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)) (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (* (+ (* (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) xim) (sqrt xim) (sqrt (+ (* xre xre) (* xim xim))) (+ (* (/ (* 1/2 xim) xre) (/ xim xre)) 1) (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (sqrt (/ 1 (pow xim 3))))

simplify224.0ms (4.4%)

Memory

-25.1MiB live, 54.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	559	3225
1	1839	3024
2	6417	2883
0	8555	2716

Stop Event

1×	iter limit
1×	node limit

Counts

138 → 136

Calls

Call 1

Inputs
(* 1/2 (* (sqrt xim) (sqrt 2)))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(* (sqrt xim) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(* 2 xim)
(+ (* 2 xim) (* 2 xre))
(+ (* 2 xim) (* xre (+ 2 (/ xre xim))))
(+ (* 2 xim) (* xre (+ 2 (* xre (+ (* -1/4 (/ (pow xre 2) (pow xim 3))) (/ 1 xim))))))
xim
(+ xim xre)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
(sqrt xre)
(* -1/2 (/ (pow xim 2) xre))
(/ (+ (* -1 (pow xre 2)) (* -1/2 (pow xim 2))) xre)
(* (sqrt (/ 1 xim)) (sqrt 2))
(+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(* 1/2 (/ (pow xim 2) (pow xre 2)))
(/ (+ (* 1/2 (pow xim 2)) (pow xre 2)) (pow xre 2))
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(* (sqrt xre) (pow (sqrt 2) 2))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(* 4 xre)
(* xre (+ 4 (/ (pow xim 2) (pow xre 2))))
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (+ (* 1/8 (/ (pow xim 6) (pow xre 6))) (/ (pow xim 2) (pow xre 2))))))
(* 2 xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 xre)
(* xre (- (* -1/2 (/ (pow xim 2) (pow xre 2))) 1))
(* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2))))
(* xre (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))) (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))))
(* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2))))
(* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* (sqrt xim) (/ (sqrt 2) xre))))
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
1
(+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(* -1 (/ (pow xim 2) xre))
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (pow xim 2)) xre))
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2))) xre))
(* -1 (/ (+ (* -1 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(* -1 (* (sqrt xre) (pow (sqrt -1) 2)))
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(* -1 (* xre (+ (* -1 (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))
(* -1 (* xre (+ (* -1 (* (sqrt xim) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(+ (* 4 xre) (/ (pow xim 2) xre))
(+ (* 4 xre) (* (pow xim 2) (+ (* -1/4 (/ (pow xim 2) (pow xre 3))) (/ 1 xre))))
(+ (* 4 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/8 (/ (pow xim 2) (pow xre 5))) (* 1/4 (/ 1 (pow xre 3))))) (/ 1 xre))))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(+ (* -1 xre) (* -1/2 (/ (pow xim 2) xre)))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) (pow xim 2))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) xim)
(sqrt xim)
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(sqrt (/ 1 (pow xim 3)))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(* xim (+ 2 (* 2 (/ xre xim))))
(* xim (+ 2 (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 2 (+ (* -1/4 (/ (pow xre 4) (pow xim 4))) (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (/ xre xim)))
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(* (pow xim 2) (- (* -1 (/ xre (pow xim 2))) (* 1/2 (/ 1 xre))))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* (pow xim 2) (+ (/ 1 (pow xim 2)) (* 1/2 (/ 1 (pow xre 2)))))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(* -2 xim)
(* -1 (* xim (+ 2 (* -2 (/ xre xim)))))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (pow xre 2) xim)) (* 2 xre)) xim)))))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow xre 4) (pow xim 2))) (pow xre 2)) xim)) (* 2 xre)) xim)))))
(* -1 xim)
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))
(* -1 (* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))
(+ (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2))))
(* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2)))
(* -1 (* xim (+ (* -1 (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))))))
(* -1 (* (sqrt xim) (pow (sqrt -1) 2)))
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(* -1 (* (sqrt (/ 1 (pow xim 3))) (pow (sqrt -1) 2)))

Outputs
(* 1/2 (* (sqrt xim) (sqrt 2)))
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim))
(+ (* 1/4 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* 1/2 (* (sqrt xim) (sqrt 2))))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 xre (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (*.f64 #s(literal 1/2 binary64) (sqrt.f64 xim))))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) (fma.f64 xre (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim)))
(+ (* 1/2 (* (sqrt xim) (sqrt 2))) (* xre (+ (* 1/4 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/32 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/16 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 xre (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 xim))) (.f64 (.f64 xre xre) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) xre (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))))))
(* (sqrt xim) (sqrt 2))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(+ (* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2)))) (* (sqrt xim) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) xre (sqrt.f64 xim)))
(+ (* xre (+ (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))) (* (sqrt xim) (sqrt 2)))
(fma.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) (fma.f64 xre (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(+ (* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* xre (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* xre (sqrt 2)))) (* 1/8 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))) (* (sqrt xim) (sqrt 2)))
(fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) xre (sqrt.f64 xim)) (.f64 (.f64 xre xre) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) xre (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))))))
(* 2 xim)
(*.f64 #s(literal 2 binary64) xim)
(+ (* 2 xim) (* 2 xre))
(*.f64 #s(literal 2 binary64) (+.f64 xre xim))
(+ (* 2 xim) (* xre (+ 2 (/ xre xim))))
(fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim))
(+ (* 2 xim) (* xre (+ 2 (* xre (+ (* -1/4 (/ (pow xre 2) (pow xim 3))) (/ 1 xim))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 xre (/.f64 xre (pow.f64 xim #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) xim)) xre #s(literal 2 binary64)) xre (.f64 #s(literal 2 binary64) xim))
xim
(+ xim xre)
(+.f64 xre xim)
(+ xim (* xre (+ 1 (* 1/2 (/ xre xim)))))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) xim) xre #s(literal 1 binary64)) xre xim)
(+ xim (* xre (+ 1 (* xre (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 xre (/.f64 xre (pow.f64 xim #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) xim)) xre #s(literal 1 binary64)) xre xim)
(sqrt xre)
(sqrt.f64 xre)
(* -1/2 (/ (pow xim 2) xre))
(.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))
(/ (+ (* -1 (pow xre 2)) (* -1/2 (pow xim 2))) xre)
(/.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) xim) xim (.f64 (neg.f64 xre) xre)) xre)
(* (sqrt (/ 1 xim)) (sqrt 2))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))
(+ xim (* 1/2 (/ (pow xre 2) xim)))
(fma.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) xim) xre) xre xim)
(+ xim (* (pow xre 2) (+ (* -1/8 (/ (pow xre 2) (pow xim 3))) (* 1/2 (/ 1 xim)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 xre (/.f64 xre (pow.f64 xim #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) xim)) (.f64 xre xre) xim)
(+ xim (* (pow xre 2) (+ (* (pow xre 2) (- (* 1/16 (/ (pow xre 2) (pow xim 5))) (* 1/8 (/ 1 (pow xim 3))))) (* 1/2 (/ 1 xim)))))
(fma.f64 (pow.f64 xre #s(literal 4 binary64)) (fma.f64 (.f64 xre (/.f64 xre (pow.f64 xim #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xim #s(literal 3 binary64)))) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) xim) xre) xre xim))
(* 1/2 (/ (pow xim 2) (pow xre 2)))
(.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64))
(/ (+ (* 1/2 (pow xim 2)) (pow xre 2)) (pow xre 2))
(/.f64 (/.f64 (fma.f64 (.f64 xim xim) #s(literal 1/2 binary64) (.f64 xre xre)) xre) xre)
(* 1/2 (* (sqrt xre) (pow (sqrt 2) 2)))
(sqrt.f64 xre)
(* xre (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (*.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))) xre)
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(.f64 (fma.f64 (.f64 #s(literal -1/32 binary64) (pow.f64 xim #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) xre)
(* xre (+ (* -1/32 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/64 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 #s(literal -1/64 binary64) (/.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal 2 binary64)) (.f64 #s(literal -1/32 binary64) (pow.f64 xim #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) xre)
(* (sqrt xre) (pow (sqrt 2) 2))
(*.f64 (sqrt.f64 xre) #s(literal 2 binary64))
(* xre (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64))) xre)
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2)))))
(.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 xim #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64)))) xre)
(* xre (+ (* -1/16 (* (pow xim 4) (sqrt (/ 1 (pow xre 9))))) (+ (* -1/32 (* (/ (pow xim 4) (pow (sqrt 2) 2)) (sqrt (/ 1 (pow xre 9))))) (+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 5))))) (* (sqrt (/ 1 xre)) (pow (sqrt 2) 2))))))
(.f64 (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 9 binary64)))) (fma.f64 #s(literal -1/32 binary64) (/.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal 2 binary64)) (.f64 #s(literal -1/16 binary64) (pow.f64 xim #s(literal 4 binary64)))) (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 xim xim)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) #s(literal 2 binary64)))) xre)
(* 4 xre)
(*.f64 #s(literal 4 binary64) xre)
(* xre (+ 4 (/ (pow xim 2) (pow xre 2))))
(*.f64 (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64)) xre)
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (/ (pow xim 2) (pow xre 2)))))
(*.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64))) xre)
(* xre (+ 4 (+ (* -1/4 (/ (pow xim 4) (pow xre 4))) (+ (* 1/8 (/ (pow xim 6) (pow xre 6))) (/ (pow xim 2) (pow xre 2))))))
(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64))) (/.f64 (.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/8 binary64)) (pow.f64 xre #s(literal 6 binary64)))) xre)
(* 2 xre)
(*.f64 #s(literal 2 binary64) xre)
(* xre (+ 2 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 2 binary64)) xre)
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 2 binary64))) xre)
(* xre (+ 2 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(.f64 (+.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 6 binary64)))) xre)
(* -1 xre)
(neg.f64 xre)
(* xre (- (* -1/2 (/ (pow xim 2) (pow xre 2))) 1))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal -1/2 binary64) #s(literal -1 binary64)) xre)
(* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))
(* xre (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))) (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) xre))) xre)
(* 1/2 (* (sqrt (/ 1 xim)) (* xre (sqrt 2))))
(.f64 (.f64 #s(literal 1/2 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))
(* xre (+ (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))) (* (sqrt xim) (/ (sqrt 2) xre))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) #s(literal 1/2 binary64) (/.f64 (sqrt.f64 xim) xre))) xre)
xre
(* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre)
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64))) xre)
(* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xre #s(literal 4 binary64))))) xre xre)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))
(fma.f64 (/.f64 (/.f64 (*.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64))
(* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))
(+ (* 1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 (.f64 #s(literal 1/2 binary64) xim) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) (.f64 (.f64 #s(literal 1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/64 binary64) (.f64 (.f64 #s(literal -1/32 binary64) (sqrt.f64 xre)) (/.f64 (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(+ (* -1 (/ (+ (* -1/32 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/1024 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/64 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* 1/2 (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))))
(fma.f64 xim (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)))) #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/32 binary64) (pow.f64 xim #s(literal 3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (fma.f64 #s(literal 1/512 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/64 binary64) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre)))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(+ (* 1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 5))))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 5 binary64))))) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3)))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) #s(literal 1/32 binary64) (.f64 (.f64 #s(literal -1/16 binary64) (sqrt.f64 xre)) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(+ (* -1 (/ (+ (* -1/16 (* (/ (* (pow xim 3) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt xre))) (+ (* 1/512 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (pow (sqrt 1/2) 3)) (sqrt (/ 1 (pow xre 3))))) (* 1/32 (* (/ (* (pow xim 5) (* (sqrt -1) (sqrt 2))) (sqrt 1/2)) (sqrt (/ 1 (pow xre 3))))))) (pow xre 3))) (* (* xim (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))) (sqrt (/ 1 xre))))
(fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 xim (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64))) (/.f64 (fma.f64 (.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 xim #s(literal 3 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 xre) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (fma.f64 #s(literal 1/256 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (pow.f64 xim #s(literal 5 binary64))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 xim #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64))))))) (neg.f64 (pow.f64 xre #s(literal 3 binary64)))))
(* -1 (/ (pow xim 2) xre))
(/.f64 (*.f64 (neg.f64 xim) xim) xre)
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (pow xim 2)) xre))
(/.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/4 binary64) xre) (*.f64 xim xim)) (neg.f64 xre))
(* -1 (/ (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2))) xre))
(/.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/4 binary64) xre) (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal 1/8 binary64) (*.f64 xim xim))) (neg.f64 xre))
(* -1 (/ (+ (* -1 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/4 (/ (pow xim 4) (pow xre 2))) (+ (* 1/8 (/ (pow xim 6) (pow xre 4))) (pow xim 2)))) xre))
(/.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/4 binary64) xre) (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal 1/8 binary64) (.f64 xim xim))) (.f64 (pow.f64 xim #s(literal 8 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 xre #s(literal 6 binary64))))) (neg.f64 xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (* 1/2 (pow xim 2))) xre))
(/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (.f64 (/.f64 #s(literal -1/8 binary64) xre) (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre))) (neg.f64 xre))
(* -1 (/ (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2)))) xre))
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) xre) (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (/.f64 (.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 4 binary64))))) (neg.f64 xre))
(* -1 (/ (+ (* -1/2 (/ (+ (* 1/64 (pow xim 8)) (* 1/16 (pow xim 8))) (pow xre 6))) (+ (* -1/8 (/ (pow xim 4) (pow xre 2))) (+ (* 1/16 (/ (pow xim 6) (pow xre 4))) (* 1/2 (pow xim 2))))) xre))
(/.f64 (fma.f64 (.f64 (pow.f64 xim #s(literal 8 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 xre #s(literal 6 binary64)))) #s(literal -1/2 binary64) (fma.f64 (/.f64 #s(literal -1/8 binary64) xre) (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (/.f64 (*.f64 (pow.f64 xim #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 xre #s(literal 4 binary64)))))) (neg.f64 xre))
(* -1 (* (sqrt xre) (pow (sqrt -1) 2)))
(sqrt.f64 xre)
(* -1 (* xre (+ 1 (* 1/2 (/ (pow xim 2) (pow xre 2))))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64)) (neg.f64 xre))
(* -1 (* xre (+ (* -1 (* (sqrt (/ 1 xim)) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (sqrt 2))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) xre))) (neg.f64 xre))
(* -1 (* xre (+ (* -1 (* (sqrt xim) (/ (sqrt 2) xre))) (* -1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (-.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) #s(literal -1/2 binary64)) (/.f64 (sqrt.f64 xim) xre))) (neg.f64 xre))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (* 1/2 (/ (pow xim 2) (pow xre 2)))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) (pow.f64 xre #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64))) (neg.f64 xre))
(* -1 (* xre (+ 1 (+ (* -1/8 (/ (pow xim 4) (pow xre 4))) (+ (* 1/16 (/ (pow xim 6) (pow xre 6))) (* 1/2 (/ (pow xim 2) (pow xre 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 xim #s(literal 6 binary64)) (pow.f64 xre #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) (/.f64 (.f64 (pow.f64 xim #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xre #s(literal 4 binary64))))) xre xre))
(+ (* 1/8 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))))
(fma.f64 (.f64 (.f64 xim xim) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (sqrt.f64 xre))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* -1/4 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/8 (sqrt (/ 1 (pow xre 3)))))))
(fma.f64 (fma.f64 (.f64 (.f64 xim xim) #s(literal -1/4 binary64)) (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/8 binary64))) (*.f64 xim xim) (sqrt.f64 xre))
(+ (* 1/2 (* (sqrt xre) (pow (sqrt 2) 2))) (* (pow xim 2) (+ (* 1/8 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/4 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/4 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (fma.f64 (.f64 #s(literal 1/4 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xre xre)) (/.f64 #s(literal 1/16 binary64) (pow.f64 xre #s(literal 5 binary64))))) (.f64 xim xim) (.f64 #s(literal -1/4 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))))))) (.f64 xim xim) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/8 binary64))) (.f64 xim xim) (sqrt.f64 xre))
(+ (* 1/4 (* (pow xim 2) (sqrt (/ 1 (pow xre 3))))) (* (sqrt xre) (pow (sqrt 2) 2)))
(fma.f64 (.f64 (.f64 xim xim) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) (*.f64 (sqrt.f64 xre) #s(literal 2 binary64)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* -1/2 (* (* (pow xim 2) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3))))) (sqrt (/ 1 xre)))) (* 1/4 (sqrt (/ 1 (pow xre 3)))))))
(fma.f64 (fma.f64 (.f64 (.f64 (.f64 xim xim) #s(literal -1/2 binary64)) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/4 binary64))) (.f64 xim xim) (.f64 (sqrt.f64 xre) #s(literal 2 binary64)))
(+ (* (sqrt xre) (pow (sqrt 2) 2)) (* (pow xim 2) (+ (* 1/4 (sqrt (/ 1 (pow xre 3)))) (* (pow xim 2) (+ (* -1/2 (* (sqrt (/ 1 xre)) (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))))) (* 1/2 (* (* (pow xim 2) (- (* 1/16 (/ 1 (pow xre 5))) (* -1/4 (/ (+ (* 1/16 (/ 1 (* (pow xre 3) (pow (sqrt 2) 2)))) (* 1/8 (/ 1 (pow xre 3)))) (* (pow xre 2) (pow (sqrt 2) 2)))))) (sqrt (/ 1 xre)))))))))
(fma.f64 (fma.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xre)) (fma.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 #s(literal 1/8 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xre xre)) (/.f64 #s(literal 1/16 binary64) (pow.f64 xre #s(literal 5 binary64))))) (.f64 xim xim) (.f64 #s(literal -1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 xre #s(literal 3 binary64))) (/.f64 #s(literal 1/32 binary64) (pow.f64 xre #s(literal 3 binary64))))))) (.f64 xim xim) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xre #s(literal 3 binary64)))) #s(literal 1/4 binary64))) (.f64 xim xim) (*.f64 (sqrt.f64 xre) #s(literal 2 binary64)))
(+ (* 4 xre) (/ (pow xim 2) xre))
(fma.f64 #s(literal 4 binary64) xre (/.f64 (*.f64 xim xim) xre))
(+ (* 4 xre) (* (pow xim 2) (+ (* -1/4 (/ (pow xim 2) (pow xre 3))) (/ 1 xre))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/4 binary64) (/.f64 #s(literal 1 binary64) xre)) (.f64 xim xim) (*.f64 #s(literal 4 binary64) xre))
(+ (* 4 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/8 (/ (pow xim 2) (pow xre 5))) (* 1/4 (/ 1 (pow xre 3))))) (/ 1 xre))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 5 binary64)))) #s(literal 1/8 binary64) (/.f64 #s(literal -1/4 binary64) (pow.f64 xre #s(literal 3 binary64)))) (pow.f64 xim #s(literal 4 binary64)) (fma.f64 #s(literal 4 binary64) xre (/.f64 (.f64 xim xim) xre)))
(+ (* 1/2 (/ (pow xim 2) xre)) (* 2 xre))
(fma.f64 (/.f64 (.f64 xim xim) xre) #s(literal 1/2 binary64) (.f64 #s(literal 2 binary64) xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) (*.f64 #s(literal 2 binary64) xre))
(+ (* 2 xre) (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xim xim) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) (.f64 #s(literal 2 binary64) xre))
(+ (* -1 xre) (* -1/2 (/ (pow xim 2) xre)))
(fma.f64 (/.f64 (*.f64 xim xim) xre) #s(literal -1/2 binary64) (neg.f64 xre))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) (pow xim 2))
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 xim)) xre (sqrt.f64 (pow.f64 xim #s(literal 3 binary64))))) (*.f64 xim xim))
(/ (+ (* 1/2 (* (sqrt xim) (* xre (sqrt 2)))) (* (sqrt (pow xim 3)) (sqrt 2))) xim)
(/.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 xim)) xre (sqrt.f64 (pow.f64 xim #s(literal 3 binary64))))) xim)
(sqrt xim)
(sqrt.f64 xim)
(+ xre (* 1/2 (/ (pow xim 2) xre)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) xre) (*.f64 xim xim) xre)
(+ xre (* (pow xim 2) (+ (* -1/8 (/ (pow xim 2) (pow xre 3))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) xre)) (.f64 xim xim) xre)
(+ xre (* (pow xim 2) (+ (* (pow xim 2) (- (* 1/16 (/ (pow xim 2) (pow xre 5))) (* 1/8 (/ 1 (pow xre 3))))) (* 1/2 (/ 1 xre)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 xim (/.f64 xim (pow.f64 xre #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 xre #s(literal 3 binary64)))) (.f64 xim xim) (/.f64 #s(literal 1/2 binary64) xre)) (*.f64 xim xim) xre)
(sqrt (/ 1 (pow xim 3)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))) xim)
(* xim (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (.f64 xre xre)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (.f64 #s(literal 1/4 binary64) (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))))) xim)
(* xim (+ (* -1/16 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 xim)) (sqrt 2)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (.f64 (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) #s(literal 1/16 binary64))) xim)
(* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) xim)
(* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (.f64 xre xre))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))) xim)
(* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (sqrt 2)))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (sqrt 2)))) (* (sqrt (/ 1 xim)) (sqrt 2))))))
(.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (.f64 xre xre))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 #s(literal 2 binary64)) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))) xim)
(* xim (+ 2 (* 2 (/ xre xim))))
(*.f64 (fma.f64 (/.f64 xre xim) #s(literal 2 binary64) #s(literal 2 binary64)) xim)
(* xim (+ 2 (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2)))))
(*.f64 (fma.f64 (/.f64 xre xim) (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) xim)
(* xim (+ 2 (+ (* -1/4 (/ (pow xre 4) (pow xim 4))) (+ (* 2 (/ xre xim)) (/ (pow xre 2) (pow xim 2))))))
(*.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/4 binary64) (fma.f64 (/.f64 xre xim) (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64))) xim)
(* xim (+ 1 (/ xre xim)))
(fma.f64 (/.f64 xre xim) xim xim)
(* xim (+ 1 (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim))))
(fma.f64 (fma.f64 (/.f64 (*.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) (/.f64 xre xim)) xim xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/2 (/ (pow xre 2) (pow xim 2))) (/ xre xim)))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (*.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) (/.f64 xre xim))) xim xim)
(* (pow xim 2) (- (* -1 (/ xre (pow xim 2))) (* 1/2 (/ 1 xre))))
(.f64 (-.f64 (/.f64 #s(literal -1/2 binary64) xre) (/.f64 (/.f64 xre xim) xim)) (.f64 xim xim))
(* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2)))))
(.f64 (fma.f64 (/.f64 (.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) #s(literal 1 binary64))) xim)
(* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 6 binary64)) (pow.f64 xim #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xre xim) (/.f64 (.f64 (pow.f64 xre #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xim #s(literal 4 binary64))))) xim xim)
(* (pow xim 2) (+ (/ 1 (pow xim 2)) (* 1/2 (/ 1 (pow xre 2)))))
(fma.f64 (/.f64 (/.f64 (*.f64 xim xim) xre) xre) #s(literal 1/2 binary64) #s(literal 1 binary64))
(* -1/2 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 xim)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))
(* -1 (* xim (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (neg.f64 xim) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))))
(* -1 (* xim (+ (* -1/8 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(.f64 (neg.f64 xim) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64)))) (.f64 xre xre)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (.f64 (.f64 xre (sqrt.f64 #s(literal -1 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/4 binary64))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/16 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/4 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* 1/2 (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))))
(.f64 (neg.f64 xim) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))) (.f64 (neg.f64 (.f64 (.f64 (.f64 (sqrt.f64 xim) xre) xre) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))))) (/.f64 #s(literal 3/16 binary64) (pow.f64 xim #s(literal 3 binary64))))))
(* -1 (* (sqrt xim) (* (sqrt -1) (sqrt 2))))
(.f64 (.f64 (neg.f64 (sqrt.f64 xim)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* xim (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2))))))
(.f64 (neg.f64 xim) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))))
(* -1 (* xim (+ (* -1/4 (* (sqrt (/ 1 (pow xim 5))) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (neg.f64 xim) (fma.f64 (.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 5 binary64))))) (.f64 (.f64 xre xre) (sqrt.f64 #s(literal -1 binary64)))) (sqrt.f64 #s(literal 2 binary64)) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))))
(* -1 (* xim (+ (* -1 (/ (+ (* 1/8 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2))))) (* 1/4 (* (sqrt xim) (* (pow xre 2) (* (sqrt -1) (sqrt 2)))))) (pow xim 3))) (+ (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (sqrt -1) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (sqrt -1) (sqrt 2)))))))
(.f64 (neg.f64 xim) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))) (/.f64 (.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) xre) xre) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 xim) #s(literal 3/8 binary64))) (neg.f64 (pow.f64 xim #s(literal 3 binary64))))))
(* -2 xim)
(*.f64 #s(literal -2 binary64) xim)
(* -1 (* xim (+ 2 (* -2 (/ xre xim)))))
(*.f64 (neg.f64 xim) (fma.f64 #s(literal -2 binary64) (/.f64 xre xim) #s(literal 2 binary64)))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (pow xre 2) xim)) (* 2 xre)) xim)))))
(.f64 (neg.f64 xim) (-.f64 #s(literal 2 binary64) (/.f64 (.f64 xre (-.f64 #s(literal 2 binary64) (/.f64 xre xim))) xim)))
(* -1 (* xim (+ 2 (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (pow xre 4) (pow xim 2))) (pow xre 2)) xim)) (* 2 xre)) xim)))))
(.f64 (neg.f64 xim) (-.f64 #s(literal 2 binary64) (/.f64 (fma.f64 #s(literal 2 binary64) xre (/.f64 (fma.f64 (/.f64 #s(literal -1/4 binary64) xim) (/.f64 (pow.f64 xre #s(literal 4 binary64)) xim) (.f64 xre xre)) (neg.f64 xim))) xim)))
(* -1 xim)
(neg.f64 xim)
(* -1 (* xim (+ 1 (* -1 (/ xre xim)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 xre xim)) (neg.f64 xim))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1/2 (/ (pow xre 2) xim))) xim)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (.f64 (/.f64 xre xim) xre) #s(literal -1/2 binary64) xre) xim)) (neg.f64 xim))
(* -1 (* xim (+ 1 (* -1 (/ (+ xre (* -1 (/ (+ (* -1/8 (/ (pow xre 4) (pow xim 2))) (* 1/2 (pow xre 2))) xim))) xim)))))
(.f64 (-.f64 #s(literal 1 binary64) (/.f64 (-.f64 xre (/.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) xim) (/.f64 #s(literal -1/8 binary64) xim) (.f64 (*.f64 xre xre) #s(literal 1/2 binary64))) xim)) xim)) (neg.f64 xim))
(* -1 (* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2))))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)))
(+ (* -1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))) (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2))))
(.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))
(* (sqrt xim) (* (pow (sqrt -1) 2) (sqrt 2)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 xim))
(* -1 (* xim (+ (* -1 (* (sqrt (/ 1 xim)) (* (pow (sqrt -1) 2) (sqrt 2)))) (* 1/2 (* (sqrt (/ 1 (pow xim 3))) (* xre (* (pow (sqrt -1) 2) (sqrt 2))))))))
(.f64 (.f64 (neg.f64 (sqrt.f64 #s(literal 2 binary64))) (fma.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))) xre (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim))))) (neg.f64 xim))
(* -1 (* (sqrt xim) (pow (sqrt -1) 2)))
(sqrt.f64 xim)
(* -1 (* xim (+ 1 (* 1/2 (/ (pow xre 2) (pow xim 2))))))
(.f64 (neg.f64 xim) (fma.f64 (/.f64 (.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (* 1/2 (/ (pow xre 2) (pow xim 2)))))))
(.f64 (neg.f64 xim) (fma.f64 (/.f64 (pow.f64 xre #s(literal 4 binary64)) (pow.f64 xim #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 (/.f64 xre xim) xre) xim) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* xim (+ 1 (+ (* -1/8 (/ (pow xre 4) (pow xim 4))) (+ (* 1/16 (/ (pow xre 6) (pow xim 6))) (* 1/2 (/ (pow xre 2) (pow xim 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 xre #s(literal 6 binary64)) (pow.f64 xim #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xre xim) (/.f64 (.f64 (pow.f64 xre #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 xim #s(literal 4 binary64))))) xim xim))
(* -1 (* (sqrt (/ 1 (pow xim 3))) (pow (sqrt -1) 2)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))

rewrite152.0ms (3%)

Memory

56.2MiB live, 56.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	372
0	83	305
1	281	292
2	1650	285
0	8310	278

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

23 → 462

Calls

Call 1

Inputs
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64)))
(*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))
(+.f64 (hypot.f64 xim xre) xre)
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(sqrt.f64 xre)
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))
(sqrt.f64 #s(literal 2 binary64))
(.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)))
(.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))
(fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
#s(approx (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)
(sqrt.f64 xim)
#s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))))
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64))
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64))))

Outputs
(.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre))) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)))
(.f64 (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)) (.f64 (sqrt.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal 2 binary64)) (.f64 (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))))
(.f64 (pow.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)) #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)) (sqrt.f64 #s(literal 2 binary64)))
(*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)))
(pow.f64 (exp.f64 (log.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)) (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) (.f64 xre xre)) #s(literal 2 binary64))) (sqrt.f64 (-.f64 (hypot.f64 xre xim) xre)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 (pow.f64 (hypot.f64 xre xim) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))) #s(literal 2 binary64))) (sqrt.f64 (fma.f64 xre (-.f64 xre (hypot.f64 xre xim)) (pow.f64 (hypot.f64 xre xim) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) (.f64 xre xre)))) (sqrt.f64 (-.f64 (hypot.f64 xre xim) xre)))
(/.f64 (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (hypot.f64 xre xim) #s(literal 3 binary64)) (pow.f64 xre #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 xre (-.f64 xre (hypot.f64 xre xim)) (pow.f64 (hypot.f64 xre xim) #s(literal 2 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) (pow.f64 (.f64 #s(literal 2 binary64) xre) #s(literal 2 binary64)))) (sqrt.f64 (-.f64 (.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) xre))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 (hypot.f64 xre xim) #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 xre #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 #s(literal 2 binary64) xre) #s(literal 2 binary64)) (.f64 (.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) (.f64 #s(literal 2 binary64) xre))))))
(sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre)))
(exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))) #s(literal 1/2 binary64)))
(*.f64 #s(literal 2 binary64) (+.f64 (hypot.f64 xre xim) xre))
(*.f64 (+.f64 (hypot.f64 xre xim) xre) #s(literal 2 binary64))
(/.f64 (fma.f64 #s(literal 8 binary64) (pow.f64 xre #s(literal 3 binary64)) (.f64 #s(literal 8 binary64) (pow.f64 (hypot.f64 xre xim) #s(literal 3 binary64)))) (+.f64 (pow.f64 (.f64 #s(literal 2 binary64) xre) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (hypot.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 2 binary64) xre) (.f64 (hypot.f64 xre xim) #s(literal 2 binary64))))))
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(/.f64 (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 3 binary64))) (fma.f64 xre (-.f64 xre #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre)))) (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) xre) (-.f64 (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64)) (.f64 xre xre)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (fma.f64 xre (-.f64 xre #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre)))) (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64))) (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) xre) (-.f64 (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64)) (.f64 xre xre))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 xre (-.f64 xre #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre)))) (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64))) (+.f64 (pow.f64 xre #s(literal 3 binary64)) (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 3 binary64)))))
(-.f64 (/.f64 (.f64 xre xre) (-.f64 xre #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))))) (/.f64 (pow.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64)) (-.f64 xre #s(approx (sqrt (+ ( xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))))))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) #s(literal 2 binary64)) (-.f64 #s(approx (sqrt (+ ( xre xre) (* xim xim))) (.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) xre)) (/.f64 (.f64 xre xre) (-.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) xre)))
(+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))) xre)
(+.f64 xre #s(approx (sqrt (+ (* xre xre) (* xim xim))) (*.f64 (fma.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 xre xim) #s(literal -2 binary64)) #s(literal 1 binary64)) (neg.f64 xre))))
(*.f64 (sqrt.f64 (pow.f64 xim #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 xim #s(literal -3/2 binary64))))
(*.f64 (pow.f64 (pow.f64 xim #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 xim #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (pow.f64 (pow.f64 xim #s(literal -3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 xim #s(literal -3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 xim #s(literal 3/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 xim #s(literal 3/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 xim #s(literal -1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 xim #s(literal -1/4 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 xim #s(literal -3/4 binary64)) (pow.f64 xim #s(literal -3/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (pow.f64 xim #s(literal 3 binary64)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (pow.f64 xim #s(literal 3 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 xim #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 xim xim) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 xim #s(literal -1/2 binary64)) (pow.f64 xim #s(literal -1 binary64)))
(*.f64 (pow.f64 xim #s(literal -1 binary64)) (pow.f64 xim #s(literal -1/2 binary64)))
(*.f64 (pow.f64 xim #s(literal -3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)))
(*.f64 (pow.f64 xim #s(literal -3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 xim #s(literal -3/2 binary64)) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal -3/2 binary64)))
(pow.f64 (*.f64 (pow.f64 xim #s(literal -3 binary64)) (pow.f64 xim #s(literal -3 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 xim #s(literal -3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 xim #s(literal 3/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 xim #s(literal -1/2 binary64)) #s(literal 3 binary64))
(pow.f64 (pow.f64 xim #s(literal -1 binary64)) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 xim #s(literal -3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 xim #s(literal 3 binary64)) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 xim) #s(literal -3 binary64))
(pow.f64 (*.f64 xim xim) #s(literal -3/4 binary64))
(pow.f64 xim #s(literal -3/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (*.f64 (sqrt.f64 (neg.f64 xim)) xim)))
(/.f64 (sqrt.f64 (pow.f64 xim #s(literal -3/2 binary64))) (pow.f64 xim #s(literal 3/4 binary64)))
(/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (sqrt.f64 (neg.f64 xim)) #s(literal 3 binary64)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 (sqrt.f64 (neg.f64 xim)) xim))
(/.f64 #s(literal -1 binary64) (pow.f64 (neg.f64 (sqrt.f64 xim)) #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 xim #s(literal 3/2 binary64))))
(/.f64 (pow.f64 xim #s(literal -1/2 binary64)) xim)
(/.f64 (pow.f64 xim #s(literal -1 binary64)) (sqrt.f64 xim))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 xim #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (neg.f64 (pow.f64 xim #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 xim) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3/2 binary64)))
(sqrt.f64 (pow.f64 xim #s(literal -3 binary64)))
(fabs.f64 (pow.f64 xim #s(literal -3/2 binary64)))
(exp.f64 (neg.f64 (*.f64 (log.f64 xim) #s(literal 3/2 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 xim) #s(literal 3/2 binary64)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (neg.f64 (log.f64 xim)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 xim #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 xim) #s(literal 3 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 xim) #s(literal -3/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 xim #s(literal -1/2 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 xim)) #s(literal 1/2 binary64)))

eval95.0ms (1.9%)

Memory: -16.9MiB live, 60.4MiB allocated
Compiler: Compiled 23 731 to 3 578 computations (84.9% saved)

prune26.0ms (0.5%)

Memory

31.3MiB live, 31.3MiB allocated

Pruning

20 alts after pruning (17 fresh and 3 done)

	Pruned	Kept	Total
New	593	15	608
Fresh	6	2	8
Picked	2	3	5
Done	0	0	0
Total	601	20	621

Accuracy

88.5%

Counts

621 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.3%	(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
	76.6%	(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 xre xim)) (sqrt.f64 (hypot.f64 xre xim)) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
✓	80.8%	(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	53.8%	(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
	51.5%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64))
	13.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))
	51.4%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xre xim) (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) xim))) #s(literal 1/2 binary64))
	27.9%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64)) xre))) #s(literal 1/2 binary64))
	51.2%	(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
	79.3%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 xim xre)) #s(literal 2 binary64)) xre))))
✓	7.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
	6.7%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
	48.5%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (pow.f64 xim #s(literal -3/2 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) xim))) xim)))
	44.9%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))) xim)))
	50.7%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 xim))))
	47.6%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 xim) #s(literal 1/2 binary64))))))
	50.8%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
	47.5%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (exp.f64 (fma.f64 (log.f64 xim) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
	47.7%	(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) xim)) #s(literal 1/2 binary64)))))
✓	28.0%	#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Compiler

Compiled 1 140 to 555 computations (51.3% saved)

regimes44.0ms (0.9%)

Memory

-51.3MiB live, 27.7MiB allocated

Counts

29 → 2

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (fma.f64 (fma.f64 (/.f64 xre xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre xim)))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64)) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xre xim) (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))
(.f64 (sqrt.f64 (.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 xim xre) xre)) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 (+.f64 (hypot.f64 xre xim) xre)) (sqrt.f64 #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (pow.f64 xim #s(literal -3/2 binary64)) (.f64 (*.f64 (sqrt.f64 #s(literal 2 binary64)) xre) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 2 binary64) xim))) xim)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) xim) xim (.f64 (/.f64 (pow.f64 xim #s(literal 4 binary64)) xre) (/.f64 #s(literal -1/8 binary64) xre))) (neg.f64 xre))))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (exp.f64 (.f64 (log.f64 (.f64 #s(literal 2 binary64) xim)) #s(literal 1/2 binary64)))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (sqrt.f64 xim))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (sqrt.f64 #s(literal 2 binary64)) (exp.f64 (.f64 (log.f64 xim) #s(literal 1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (pow.f64 (sqrt.f64 (hypot.f64 xim xre)) #s(literal 2 binary64)) xre))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (fma.f64 (sqrt.f64 (hypot.f64 xim xre)) (sqrt.f64 (hypot.f64 xim xre)) xre))))
(.f64 (sqrt.f64 (.f64 (fma.f64 (sqrt.f64 (hypot.f64 xre xim)) (sqrt.f64 (hypot.f64 xre xim)) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (exp.f64 (fma.f64 (log.f64 xim) #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 2 binary64)) #s(literal 1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 2 binary64)) xre)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 xim #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (pow.f64 (pow.f64 #s(literal 2 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))) xim)))

Outputs

(*.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))

(*.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Calls

7 calls:

8.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)
6.0ms	xim
6.0ms	xre
6.0ms	(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))
6.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))

Results

Accuracy	Segments	Branch
82.6%	2	`xre`
80.8%	1	`xim`
85.6%	2	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))`
85.6%	2	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`
84.3%	2	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`
84.3%	2	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`
80.8%	1	`(*.f64 xim xim)`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes26.0ms (0.5%)

Memory

21.9MiB live, 21.9MiB allocated

Counts

15 → 4

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (fma.f64 (fma.f64 (/.f64 xre xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre xim)))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xim xre) (/.f64 xim xre) #s(literal 4 binary64)) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 (fma.f64 (/.f64 xre xim) (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) #s(literal 2 binary64)) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (.f64 (neg.f64 xre) (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) xim) xre) (/.f64 xim xre) #s(literal 1 binary64)))) xre))))

Outputs
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Calls

7 calls:

4.0ms	xim
3.0ms	xre
3.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
3.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
3.0ms	(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))

Results

Accuracy	Segments	Branch
63.1%	3	`xim`
63.1%	3	`(*.f64 xim xim)`
72.0%	4	`xre`
67.9%	3	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`
67.9%	3	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`
68.9%	3	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))`
68.9%	3	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`

Compiler

Compiled 55 to 45 computations (18.2% saved)

regimes4.0ms (0.1%)

Memory

3.1MiB live, 3.1MiB allocated

Counts

11 → 3

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (*.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (.f64 (/.f64 (.f64 xim xim) xre) #s(literal -1/2 binary64))))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (fma.f64 (fma.f64 (/.f64 xre xim) #s(literal 1/2 binary64) #s(literal 1 binary64)) xre xim)))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (.f64 #s(approx (+ ( (* 1/2 (* (sqrt 2) xre)) (sqrt (/ 1 (pow xim 3)))) (* (sqrt (/ 1 xim)) (sqrt 2))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) xim)) (sqrt.f64 #s(literal 2 binary64)))) xim)))

Outputs

(*.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (*.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))

#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Calls

1 calls:

3.0ms

xre

Results

Accuracy	Segments	Branch
70.0%	3	`xre`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes10.0ms (0.2%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

6 → 3

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))
(.f64 #s(literal 1/2 binary64) #s(approx (sqrt ( 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre))) (*.f64 (sqrt.f64 #s(literal 2 binary64)) (sqrt.f64 xim))))

Outputs

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre))))

(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (*.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))

#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Calls

5 calls:

2.0ms	xre
2.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
2.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
2.0ms	(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))
2.0ms	(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)

Results

Accuracy	Segments	Branch
53.8%	1	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`
53.8%	1	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`
53.8%	1	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))`
53.8%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`
65.7%	3	`xre`

Compiler

Compiled 51 to 40 computations (21.6% saved)

regimes2.0ms (0%)

Memory

2.0MiB live, 2.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))
(.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre)))))
(.f64 (sqrt.f64 (.f64 #s(approx (+ (sqrt (+ (* xim xim) (* xre xre))) xre) (+.f64 xre xim)) #s(literal 2 binary64))) #s(literal 1/2 binary64))

Outputs

(*.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (*.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64))

#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Calls

1 calls:

2.0ms

xre

Results

Accuracy	Segments	Branch
63.8%	2	`xre`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes8.0ms (0.1%)

Memory

9.6MiB live, 9.6MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Outputs
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Calls

7 calls:

1.0ms	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))
1.0ms	(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))
1.0ms	xre
1.0ms	(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))
1.0ms	xim

Results

Accuracy	Segments	Branch
28.0%	1	`(.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))))`
28.0%	1	`(sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre)))`
28.0%	1	`(.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (*.f64 xim xim))) xre))`
28.0%	1	`(+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)`
28.0%	1	`xim`
28.0%	1	`(*.f64 xim xim)`
28.0%	1	`xre`

Compiler

Compiled 55 to 45 computations (18.2% saved)

bsearch1.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.3269085229020487e-147

Compiler

Compiled 18 to 17 computations (5.6% saved)

bsearch189.0ms (3.7%)

Memory

-185.7MiB live, 27.1MiB allocated

Algorithm

3×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
147.0ms	1.1221053117115742e+86	7.184621420509988e+86
16.0ms	1.0462922708909144e-103	4.5943068755092025e-97
20.0ms	-1.6219224030935759e+74	-1.0481840565299877e+73

Samples

22.0ms	281×	0	valid
6.0ms	29×	2	valid
5.0ms	17×	3	valid
1.0ms	9×	1	valid

Compiler

Compiled 873 to 686 computations (21.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-hypot: 10.0ms (42.7% of total)

ival-mult: 5.0ms (21.3% of total)

ival-add: 3.0ms (12.8% of total)

ival-sqrt: 3.0ms (12.8% of total)

adjust: 1.0ms (4.3% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch6.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
4.0ms	1.1221053117115742e+86	7.184621420509988e+86
1.0ms	-1.6219224030935759e+74	-1.0481840565299877e+73

Samples

2.0ms

32×

valid

Compiler

Compiled 486 to 386 computations (20.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-hypot: 1.0ms (64.6% of total)

ival-true: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-mult: 0.0ms (0% of total)

ival-sqrt: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

bsearch21.0ms (0.4%)

Memory

5.9MiB live, 5.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	1.1221053117115742e+86	7.184621420509988e+86
18.0ms	-3.144785694375554e+148	-9.983002992542795e+147

Samples

6.0ms	21×	3	valid
4.0ms	20×	2	valid
2.0ms	14×	1	valid
2.0ms	25×	0	valid

Compiler

Compiled 425 to 344 computations (19.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-hypot: 5.0ms (44.6% of total)

ival-mult: 2.0ms (17.8% of total)

adjust: 1.0ms (8.9% of total)

ival-add: 1.0ms (8.9% of total)

ival-sqrt: 1.0ms (8.9% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

bsearch7.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	1.1221053117115742e+86	7.184621420509988e+86

Samples

3.0ms

48×

valid

Compiler

Compiled 240 to 200 computations (16.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-mult: 1.0ms (44.3% of total)

ival-hypot: 1.0ms (44.3% of total)

ival-true: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-sqrt: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

simplify109.0ms (2.1%)

Memory

15.7MiB live, 15.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	80	330
1	100	330
2	114	330
3	125	330
4	137	330
5	145	330
6	155	330
7	202	330
8	464	330
9	627	330
10	745	330
11	1041	330
12	1480	330
13	1839	330
14	2189	330
15	2434	330
16	2540	330
17	2878	330
18	3651	330
19	4778	330
20	6012	330

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))) #s(literal 0 binary64)) (.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(if (<=.f64 xre #s(literal -130000000000000002502206884884982926620860110534650344260666487942393364480 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 4531230712585365/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408 binary64)) (.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 270000000000000017753780405863343293231423331277507770907442856876618128672858465894400 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)))) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre)))))
(if (<=.f64 xre #s(literal -130000000000000002502206884884982926620860110534650344260666487942393364480 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 224999999999999996390160080111282644533503809992521935886578454942817626793984124780544 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ ( xre xre) (* xim xim))) xre) (+.f64 xim xre))))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))))
(if (<=.f64 xre #s(literal -17499999999999999437485831675276902038365910280529161893582458962909858125598687958135442165347019119912582706606965857471635063837966464864521027584 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre)))) (if (<=.f64 xre #s(literal 224999999999999996390160080111282644533503809992521935886578454942817626793984124780544 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre))))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))))
(if (<=.f64 xre #s(literal 189999999999999988976339400247098301014796443140233556360718105221488198882669713424384 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre)))
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

Outputs
(if (<=.f64 (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre))) #s(literal 0 binary64)) (.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (*.f64 (+.f64 (hypot.f64 xim xre) xre) #s(literal 2 binary64))) #s(literal 1/2 binary64)))
(if (<=.f64 xre #s(literal -130000000000000002502206884884982926620860110534650344260666487942393364480 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 4531230712585365/19701003098197239606139520050071806902539869635232723333974146702122860885748605305707133127442457820403313995153408 binary64)) (.f64 (sqrt.f64 #s(approx (* (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (fma.f64 (+.f64 (/.f64 xre xim) #s(literal 2 binary64)) xre (.f64 #s(literal 2 binary64) xim)))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 270000000000000017753780405863343293231423331277507770907442856876618128672858465894400 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 (sqrt.f64 (+.f64 (.f64 xre xre) (.f64 xim xim))) xre)))) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre)))))
(if (<=.f64 xre #s(literal -130000000000000002502206884884982926620860110534650344260666487942393364480 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (/.f64 (.f64 (neg.f64 xim) xim) xre))) #s(literal 1/2 binary64)) (if (<=.f64 xre #s(literal 224999999999999996390160080111282644533503809992521935886578454942817626793984124780544 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ ( xre xre) (* xim xim))) xre) (+.f64 xim xre))))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))))
(if (<=.f64 xre #s(literal -17499999999999999437485831675276902038365910280529161893582458962909858125598687958135442165347019119912582706606965857471635063837966464864521027584 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) (+.f64 #s(approx (sqrt (+ (* xre xre) (* xim xim))) (neg.f64 xre)) xre)))) (if (<=.f64 xre #s(literal 224999999999999996390160080111282644533503809992521935886578454942817626793984124780544 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 #s(literal 2 binary64) #s(approx (+ (sqrt (+ (* xre xre) (* xim xim))) xre) (+.f64 xim xre))))) #s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))))
(if (<=.f64 xre #s(literal 189999999999999988976339400247098301014796443140233556360718105221488198882669713424384 binary64)) (.f64 (sqrt.f64 #s(approx ( (+ (sqrt (+ (* xim xim) (* xre xre))) xre) 2) (.f64 #s(literal 2 binary64) xim))) #s(literal 1/2 binary64)) #s(approx ( 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre)))
#s(approx (* 1/2 (sqrt (* 2 (+ (sqrt (+ (* xre xre) (* xim xim))) xre)))) (sqrt.f64 xre))

soundness553.0ms (10.8%)

Memory

19.3MiB live, 19.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	418	2518
1	1360	2346
2	5040	2328
0	8085	2192
0	559	3225
1	1839	3024
2	6417	2883
0	8555	2716
0	12	53
0	20	53
1	61	53
2	398	53
3	4249	53
0	8367	31

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 741 to 289 computations (61% saved)

preprocess120.0ms (2.3%)

Memory: -67.6MiB live, 25.4MiB allocated
Remove: (abs xim)
Compiler: Compiled 786 to 252 computations (67.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	30	75
1	94	75
2	165	75
3	259	75
4	396	75
5	522	75
6	682	75
7	820	75
8	850	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10

Iter	Nodes	Cost
0	30	75
1	94	75
2	165	75
3	259	75
4	396	75
5	522	75
6	682	75
7	820	75
8	850	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10

start0.0ms (0%)

analyze109.0ms (2.1%)

sample2.2s (43.1%)

explain411.0ms (8%)

preprocess27.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize47.0ms (0.9%)

series17.0ms (0.3%)

simplify196.0ms (3.8%)

rewrite163.0ms (3.2%)

eval64.0ms (1.2%)

prune14.0ms (0.3%)

simplify85.0ms (1.7%)

localize155.0ms (3%)

series27.0ms (0.5%)

simplify224.0ms (4.4%)

rewrite152.0ms (3%)

eval95.0ms (1.9%)

prune26.0ms (0.5%)

regimes44.0ms (0.9%)

regimes26.0ms (0.5%)

regimes4.0ms (0.1%)

regimes10.0ms (0.2%)

regimes2.0ms (0%)

regimes8.0ms (0.1%)

bsearch1.0ms (0%)

bsearch189.0ms (3.7%)

bsearch6.0ms (0.1%)

bsearch21.0ms (0.4%)

bsearch7.0ms (0.1%)

simplify109.0ms (2.1%)

soundness553.0ms (10.8%)

preprocess120.0ms (2.3%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	30	75
1	94	75
2	165	75
3	259	75
4	396	75
5	522	75
6	682	75
7	820	75
8	850	75
0	12	15
0	20	15
1	30	15
2	32	15
0	32	10