Metrics for sqrt((sqrt(x*x+y*y)-x)/2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze164.0ms (3.4%)

Memory

-38.0MiB live, 41.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	24.7%	75.3%	0%	0%	0%	0
0%	0%	24.7%	75.3%	0%	0%	0%	1
50%	12.4%	12.4%	75.3%	0%	0%	0%	2
50%	12.4%	12.4%	75.3%	0%	0%	0%	3
50%	12.4%	12.4%	75.3%	0%	0%	0%	4
50%	12.4%	12.4%	75.3%	0%	0%	0%	5
56.3%	13.9%	10.8%	75.3%	0%	0%	0%	6
59.4%	14.7%	10%	75.3%	0%	0%	0%	7
64.1%	15.8%	8.9%	75.3%	0%	0%	0%	8
66.4%	16.4%	8.3%	75.3%	0%	0%	0%	9
69.1%	17.1%	7.6%	75.3%	0%	0%	0%	10
70.5%	17.4%	7.3%	75.3%	0%	0%	0%	11
72%	17.8%	6.9%	75.3%	0%	0%	0%	12

Compiler

Compiled 29 to 19 computations (34.5% saved)

sample1.8s (36.7%)

Memory

70.0MiB live, 801.0MiB allocated

Samples

587.0ms	6 324×	0	valid
302.0ms	906×	2	valid
150.0ms	985×	1	valid
12.0ms	41×	3	valid

Precisions

Click to see histograms. Total time spent on operations: 722.0ms

ival-hypot: 260.0ms (36% of total)

ival-div: 119.0ms (16.5% of total)

ival-<=: 95.0ms (13.2% of total)

ival-sqrt: 92.0ms (12.7% of total)

ival-sub: 59.0ms (8.2% of total)

adjust: 45.0ms (6.2% of total)

ival-and: 25.0ms (3.5% of total)

exact: 24.0ms (3.3% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain428.0ms (9%)

Memory

4.2MiB live, 220.6MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
61	-	3	(7.696381185387671e-162 7.273840672663935e-245)	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`
28	-	2	(1.4667047301611207e-39 1.0037301395928307e-180)	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`
26	-	0	-	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`#s(literal 2 binary64)`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	58	0
↳	`(*.f64 y y)`	underflow	129
↳	`(*.f64 x x)`	underflow	117
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	58
`sqrt.f64`	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`	uflow-rescue	26	0
↳	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`	underflow	26
↳	`(*.f64 y y)`	underflow	129
↳	`(*.f64 x x)`	underflow	117
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	58
↳	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`	underflow	26
`-.f64`	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`	cancellation	26	0

Confusion

	Predicted +	Predicted -
+	98	2
-	0	156

Precision

1.0

Recall

0.98

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	98	0	2
-	0	0	156

Precision?

1.0

Recall?

0.98

Freqs

test

number	freq
0	158
1	86
2	12

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

72.0ms	52×	2	valid
38.0ms	408×	0	valid
9.0ms	50×	1	valid
1.0ms	2×	3	valid

Compiler

Compiled 194 to 44 computations (77.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-hypot: 72.0ms (72.7% of total)

ival-mult: 8.0ms (8.1% of total)

ival-div: 5.0ms (5% of total)

ival-sqrt: 5.0ms (5% of total)

adjust: 3.0ms (3% of total)

ival-add: 3.0ms (3% of total)

ival-sub: 3.0ms (3% of total)

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

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

exact: 0.0ms (0% of total)

preprocess55.0ms (1.1%)

Memory

59.4MiB live, 59.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	69
1	64	67
2	129	67
3	241	67
4	385	67
5	502	67
6	594	67
7	713	67
8	829	67
9	854	67
0	10	13
0	17	13
1	23	13
2	30	13
3	43	13
4	66	13
5	90	13
6	144	13
7	215	13
8	316	13
9	397	13
10	463	13
11	477	13
12	496	13
13	518	13
14	548	13
15	590	13
16	604	13
17	606	13
0	606	8

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))

Outputs
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x)))

Symmetry

(abs y)

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.9%	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify70.0ms (1.5%)

Memory

-56.0MiB live, 16.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	384	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	59
0	17	59
1	23	59
2	30	59
3	43	59
4	66	59
5	90	59
6	144	59
7	215	59
8	316	59
9	397	59
10	463	59
11	477	59
12	496	59
13	518	59
14	548	59
15	590	59
16	604	59
17	606	59
0	606	38

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
#s(literal 2 binary64)

Outputs
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x)))
(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x))
(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
(-.f64 (hypot.f64 y x) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
(hypot.f64 y x)
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y
#s(literal 2 binary64)

localize38.0ms (0.8%)

Memory

13.8MiB live, 13.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	5.722523749332646	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
accuracy	6.418210236990898	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
accuracy	14.050368401503512	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Samples

18.0ms	204×	0	valid
6.0ms	26×	2	valid
4.0ms	25×	1	valid
0.0ms	1×	3	valid

Compiler

Compiled 120 to 22 computations (81.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-hypot: 7.0ms (36.2% of total)

ival-mult: 3.0ms (15.5% of total)

ival-div: 2.0ms (10.3% of total)

ival-sub: 2.0ms (10.3% of total)

ival-sqrt: 2.0ms (10.3% of total)

adjust: 1.0ms (5.2% of total)

ival-add: 1.0ms (5.2% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.3%)

Memory

5.5MiB live, 5.5MiB allocated

Counts

5 → 90

Calls

Call 1

Inputs
(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
(+.f64 (.f64 x x) (.f64 y y))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Outputs
(* 1/2 y)
(+ (* -1/2 x) (* 1/2 y))
(+ (* 1/2 y) (* x (- (* 1/4 (/ x y)) 1/2)))
(+ (* 1/2 y) (* x (- (* x (+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y)))) 1/2)))
(pow y 2)
(+ (pow x 2) (pow y 2))
(* (sqrt y) (sqrt 1/2))
(+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* 1/8 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* x (+ (* 1/16 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* 1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt 1/2))))))) (* (sqrt y) (sqrt 1/2)))
y
(+ y (* -1 x))
(+ y (* x (- (* 1/2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))) 1)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/4 (/ (pow y 2) x))
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (* 1/4 (pow y 2))) x)
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2)))) x)
(/ (+ (* -1/4 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2))))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* -1/512 (* (sqrt (/ 1 (pow x 9))) (/ (pow y 5) (pow (sqrt 1/2) 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))))
(* 1/2 (/ (pow y 2) x))
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (* 1/2 (pow y 2))) x)
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2)))) x)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2))))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/4 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (+ (* 1/32 (/ (pow y 6) (pow x 6))) (* 1/4 (/ (pow y 2) (pow x 2))))))))
(* -1 (* (sqrt x) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -2 x)
(* -1 (* x (+ 2 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* (pow y 2) (+ (* -1/16 (/ (pow y 2) (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/32 (/ (pow y 2) (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/256 (/ (pow y 2) (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* y (+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt x) (* (pow y 2) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))))))))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* (pow y 2) (+ (* -1/2 (* (sqrt x) (* (pow y 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))) (* (pow x 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow x 7))))))) (* 1/2 (* (sqrt x) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2)))))))))))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/128 (/ (pow y 2) (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/16 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2)))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))))
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))) (/ x y)))
(* y (- (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))) (/ x y)))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* 1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/2 x) (* -1/4 (/ (pow x 2) y))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (/ (pow x 4) (pow y 2))) (* 1/4 (pow x 2))) y)) (* -1/2 x)) y)))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (+ (* -1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y))) (* 1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 y)
(* -1 (* y (+ 1 (/ x y))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1/2 (/ (pow x 2) y)) x) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow x 4) (pow y 2))) (* 1/2 (pow x 2))) y)) x) y)))))
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* x x) (* y y)) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (sqrt (+ (* x x) (* y y))))
3.0ms	y	@	0	((/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* x x) (* y y)) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (sqrt (+ (* x x) (* y y))))
3.0ms	y	@	inf	((/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* x x) (* y y)) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (sqrt (+ (* x x) (* y y))))
2.0ms	x	@	-inf	((/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* x x) (* y y)) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (sqrt (+ (* x x) (* y y))))
2.0ms	x	@	0	((/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* x x) (* y y)) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (sqrt (+ (* x x) (* y y))))

simplify168.0ms (3.5%)

Memory

46.6MiB live, 46.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	449	2079
1	1416	2009
2	4934	2006
0	8272	1874

Stop Event

1×	iter limit
1×	node limit

Counts

90 → 88

Calls

Call 1

Inputs
(* 1/2 y)
(+ (* -1/2 x) (* 1/2 y))
(+ (* 1/2 y) (* x (- (* 1/4 (/ x y)) 1/2)))
(+ (* 1/2 y) (* x (- (* x (+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y)))) 1/2)))
(pow y 2)
(+ (pow x 2) (pow y 2))
(* (sqrt y) (sqrt 1/2))
(+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* 1/8 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* x (+ (* 1/16 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* 1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt 1/2))))))) (* (sqrt y) (sqrt 1/2)))
y
(+ y (* -1 x))
(+ y (* x (- (* 1/2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))) 1)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* 1/4 (/ (pow y 2) x))
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (* 1/4 (pow y 2))) x)
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2)))) x)
(/ (+ (* -1/4 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2))))) x)
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* -1/512 (* (sqrt (/ 1 (pow x 9))) (/ (pow y 5) (pow (sqrt 1/2) 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))))
(* 1/2 (/ (pow y 2) x))
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (* 1/2 (pow y 2))) x)
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2)))) x)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2))))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 x)
(* -1 (* x (+ 1 (* 1/4 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (+ (* 1/32 (/ (pow y 6) (pow x 6))) (* 1/4 (/ (pow y 2) (pow x 2))))))))
(* -1 (* (sqrt x) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -2 x)
(* -1 (* x (+ 2 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* (pow y 2) (+ (* -1/16 (/ (pow y 2) (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/32 (/ (pow y 2) (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/256 (/ (pow y 2) (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* y (+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt x) (* (pow y 2) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))))))))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* (pow y 2) (+ (* -1/2 (* (sqrt x) (* (pow y 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))) (* (pow x 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow x 7))))))) (* 1/2 (* (sqrt x) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2)))))))))))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/128 (/ (pow y 2) (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/16 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2)))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))))
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))) (/ x y)))
(* y (- (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))) (/ x y)))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* 1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/2 x) (* -1/4 (/ (pow x 2) y))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (/ (pow x 4) (pow y 2))) (* 1/4 (pow x 2))) y)) (* -1/2 x)) y)))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (+ (* -1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y))) (* 1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 y)
(* -1 (* y (+ 1 (/ x y))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1/2 (/ (pow x 2) y)) x) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow x 4) (pow y 2))) (* 1/2 (pow x 2))) y)) x) y)))))
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))

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

rewrite184.0ms (3.9%)

Memory

-28.3MiB live, 52.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	50
0	17	50
1	64	50
2	447	50
3	5120	50
0	8164	28

Stop Event

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

Counts

5 → 431

Calls

Call 1

Inputs
(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
(+.f64 (.f64 x x) (.f64 y y))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

Outputs
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (hypot.f64 y x)) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(.f64 (/.f64 (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (-.f64 (hypot.f64 y x) x))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (.f64 (+.f64 (hypot.f64 y x) x) x)))
(.f64 (/.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (+.f64 (pow.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) #s(literal 3 binary64)) (pow.f64 (hypot.f64 y x) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) (-.f64 (*.f64 (+.f64 (hypot.f64 y x) x) x) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (pow.f64 (hypot.f64 y x) #s(literal 4 binary64))))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 (hypot.f64 y x) x) #s(literal -1 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 x (hypot.f64 y x))) #s(literal -1/2 binary64))
(*.f64 (/.f64 (+.f64 (hypot.f64 y x) x) #s(literal 2 binary64)) (/.f64 (-.f64 (hypot.f64 y x) x) (+.f64 (hypot.f64 y x) x)))
(*.f64 (/.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)) (/.f64 (-.f64 (hypot.f64 y x) x) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(.f64 (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64)) (pow.f64 (+.f64 (hypot.f64 y x) x) #s(literal -1 binary64)))
(.f64 (.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64)) (pow.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64))) (pow.f64 (*.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) #s(literal -1 binary64)))
(*.f64 #s(literal -1/2 binary64) (-.f64 x (hypot.f64 y x)))
(.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64))) (pow.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 #s(literal 2 binary64) (hypot.f64 y x) (.f64 #s(literal -2 binary64) x)) #s(literal 1/4 binary64))
(.f64 #s(literal -1 binary64) (.f64 (-.f64 (hypot.f64 y x) x) #s(literal -1/2 binary64)))
(.f64 (+.f64 (hypot.f64 y x) x) (/.f64 (-.f64 (hypot.f64 y x) x) (.f64 (+.f64 (hypot.f64 y x) x) #s(literal 2 binary64))))
(*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (/.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)))
(*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (/.f64 (pow.f64 (+.f64 (hypot.f64 y x) x) #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (.f64 (pow.f64 (+.f64 (hypot.f64 y x) x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (pow.f64 (.f64 (+.f64 (hypot.f64 y x) x) #s(literal 2 binary64)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x)))
(.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (/.f64 (-.f64 (hypot.f64 y x) x) (.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64))))
(*.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1/2 binary64) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(*.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 (pow.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 2 binary64)))
(.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (pow.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)) #s(literal -1 binary64)))
(*.f64 (-.f64 x (hypot.f64 y x)) #s(literal -1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x))
(.f64 (sqrt.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x))) (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x))))
(.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x)) #s(literal 1 binary64))
(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
(pow.f64 (/.f64 (+.f64 (hypot.f64 y x) x) (*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (*.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64))) (-.f64 (.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (*.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 4 binary64) (fma.f64 #s(literal 2 binary64) (hypot.f64 y x) (*.f64 #s(literal -2 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal -2 binary64) (-.f64 x (hypot.f64 y x))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x))) #s(literal 2 binary64))
(pow.f64 (*.f64 #s(literal 1/2 binary64) (-.f64 (hypot.f64 y x) x)) #s(literal 1 binary64))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) #s(literal -1 binary64)) (+.f64 (hypot.f64 y x) x))
(/.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(/.f64 (*.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) #s(literal -1/2 binary64)) (+.f64 (hypot.f64 y x) x))
(/.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/2 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(/.f64 (*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1/2 binary64)) (neg.f64 (+.f64 (hypot.f64 y x) x)))
(/.f64 (*.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal -1/2 binary64)) (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 (*.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (+.f64 (hypot.f64 y x) x)))
(/.f64 (*.f64 (neg.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (+.f64 (hypot.f64 y x) x))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (*.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 #s(literal 2 binary64) (hypot.f64 y x) (.f64 #s(literal -2 binary64) x))) #s(literal 4 binary64))
(/.f64 (.f64 #s(literal 1 binary64) (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (.f64 (+.f64 (hypot.f64 y x) x) #s(literal 2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))) (neg.f64 (+.f64 (hypot.f64 y x) x)))
(/.f64 (*.f64 #s(literal 1/2 binary64) (neg.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 (*.f64 #s(literal 1 binary64) (-.f64 x (hypot.f64 y x))) #s(literal -2 binary64))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)) (pow.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64))) (-.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) (.f64 x #s(literal -1/2 binary64))))
(/.f64 (/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 2 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(/.f64 (/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 2 binary64)) (+.f64 (hypot.f64 y x) x))
(/.f64 (fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64) (pow.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 3 binary64))) (fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) #s(literal 1/4 binary64) (-.f64 (pow.f64 (.f64 x #s(literal -1/2 binary64)) #s(literal 2 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) (*.f64 x #s(literal -1/2 binary64))))))
(/.f64 (neg.f64 (*.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal 1/2 binary64))) (neg.f64 (+.f64 (hypot.f64 y x) x)))
(/.f64 (neg.f64 (*.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1/2 binary64))) (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)) (.f64 (.f64 x x) #s(literal 1/4 binary64)))) (neg.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x))))
(/.f64 (neg.f64 (-.f64 (.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/8 binary64)))) (neg.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/2 binary64) (+.f64 (hypot.f64 y x) x)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (hypot.f64 y x)) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (fma.f64 #s(literal 2 binary64) (hypot.f64 y x) (*.f64 #s(literal -2 binary64) x))) #s(literal -4 binary64))
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(/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (*.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (neg.f64 (+.f64 (hypot.f64 y x) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) (hypot.f64 y x)) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (-.f64 (hypot.f64 y x) x) #s(literal -1 binary64))))
(/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (neg.f64 (neg.f64 (+.f64 (hypot.f64 y x) x))))
(/.f64 (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (+.f64 (hypot.f64 y x) x))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) (hypot.f64 y x)) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (-.f64 (hypot.f64 y x) x) #s(literal -1 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (-.f64 (hypot.f64 y x) x) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 x x (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (*.f64 (neg.f64 x) (hypot.f64 y x)))))
(/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (neg.f64 (neg.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (neg.f64 x) (-.f64 (neg.f64 x) (hypot.f64 y x)) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(/.f64 (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))
(neg.f64 (-.f64 x (hypot.f64 y x)))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 4 binary64)) (pow.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) #s(literal 2 binary64)))) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (.f64 (+.f64 (hypot.f64 y x) x) x)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (+.f64 (pow.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) #s(literal 3 binary64)) (pow.f64 (hypot.f64 y x) #s(literal 6 binary64)))) (fma.f64 (.f64 (+.f64 (hypot.f64 y x) x) x) (-.f64 (*.f64 (+.f64 (hypot.f64 y x) x) x) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (pow.f64 (hypot.f64 y x) #s(literal 4 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (-.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (hypot.f64 y x)) (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) (neg.f64 (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (fma.f64 (neg.f64 x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (-.f64 (hypot.f64 y x) x) (neg.f64 (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 3/2 binary64)) (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 3/2 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (sqrt.f64 (hypot.f64 y x)) (sqrt.f64 (hypot.f64 y x)) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)) (neg.f64 x))
(fma.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)) (neg.f64 x))
(fma.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) (neg.f64 x))
(fma.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x (hypot.f64 y x))
(fma.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (/.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) (+.f64 (hypot.f64 y x) x)) (neg.f64 (.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (pow.f64 (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (hypot.f64 y x) x)) (neg.f64 (.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 (hypot.f64 y x) (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (hypot.f64 y x) (/.f64 (hypot.f64 y x) (+.f64 (hypot.f64 y x) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (/.f64 (hypot.f64 y x) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(fma.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (pow.f64 (+.f64 (hypot.f64 y x) x) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(fma.f64 x #s(literal -1 binary64) (hypot.f64 y x))
(-.f64 (+.f64 (hypot.f64 y x) #s(literal 0 binary64)) x)
(-.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (+.f64 (hypot.f64 y x) x)) (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x))))
(-.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 x (hypot.f64 y x)))
(-.f64 (hypot.f64 y x) x)
(exp.f64 (*.f64 (log.f64 (pow.f64 (-.f64 (hypot.f64 y x) x) #s(literal -1 binary64))) #s(literal -1 binary64)))
(+.f64 (neg.f64 (neg.f64 (hypot.f64 y x))) (neg.f64 x))
(+.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) (+.f64 (hypot.f64 y x) x)) (neg.f64 (*.f64 x (/.f64 x (+.f64 (hypot.f64 y x) x)))))
(+.f64 (/.f64 (pow.f64 (hypot.f64 y x) #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (+.f64 (hypot.f64 y x) x) x (pow.f64 (hypot.f64 y x) #s(literal 2 binary64))))))
(+.f64 (neg.f64 x) (hypot.f64 y x))
(+.f64 (hypot.f64 y x) (neg.f64 x))
(*.f64 (sqrt.f64 (hypot.f64 y x)) (sqrt.f64 (hypot.f64 y x)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) #s(literal -1 binary64))
(pow.f64 (sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 4 binary64)) #s(literal 2 binary64)) #s(literal 1/8 binary64))
(pow.f64 (sqrt.f64 (hypot.f64 y x)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 4 binary64)) #s(literal 1/4 binary64))
(pow.f64 (hypot.f64 y x) #s(literal 1 binary64))
(pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (.f64 y y) (.f64 x x)) (sqrt.f64 (fma.f64 y y (*.f64 (neg.f64 x) x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (-.f64 x y) (+.f64 y x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)) #s(literal -1 binary64))))
(sqrt.f64 (pow.f64 (hypot.f64 y x) #s(literal 2 binary64)))
(fabs.f64 (hypot.f64 y x))
(hypot.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 x)) y)
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 x)))
(hypot.f64 (exp.f64 (log.f64 y)) (neg.f64 x))
(hypot.f64 (exp.f64 (log.f64 y)) x)
(hypot.f64 (neg.f64 x) (exp.f64 (log.f64 y)))
(hypot.f64 (neg.f64 x) y)
(hypot.f64 y (exp.f64 (log.f64 x)))
(hypot.f64 y (neg.f64 x))
(hypot.f64 y x)
(hypot.f64 x (exp.f64 (log.f64 y)))
(hypot.f64 x y)
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (hypot.f64 y x))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (hypot.f64 y x) #s(literal 4 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (hypot.f64 y x)) #s(literal 1 binary64)))
(exp.f64 (log.f64 (hypot.f64 y x)))

eval68.0ms (1.4%)

Memory: -30.8MiB live, 45.0MiB allocated
Compiler: Compiled 12 810 to 2 376 computations (81.5% saved)

prune17.0ms (0.4%)

Memory

23.4MiB live, 23.4MiB allocated

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	504	14	518
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	505	14	519

Accuracy

99.9%

Counts

519 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.2%	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 y x) x)) (sqrt.f64 #s(literal 2 binary64)))
	79.2%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -2 binary64) (-.f64 x (hypot.f64 y x)))))
	63.9%	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (*.f64 x x))) x) #s(literal 2 binary64)))
▶	52.6%	(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
▶	80.7%	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
▶	53.0%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
	54.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
	54.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
	8.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
	7.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) x)) y) y)))
	31.1%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	51.1%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
▶	31.0%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
▶	22.4%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))

Compiler

Compiled 530 to 394 computations (25.7% saved)

simplify128.0ms (2.7%)

Memory

24.7MiB live, 24.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
cost-diff	0	(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
cost-diff	384	(/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64))
cost-diff	1024	(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
cost-diff	0	(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
cost-diff	0	(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
cost-diff	0	#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
cost-diff	0	(/.f64 #s(literal 1 binary64) x)
cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
cost-diff	0	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
cost-diff	0	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
cost-diff	0	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
cost-diff	0	(hypot.f64 y x)
cost-diff	0	(-.f64 (hypot.f64 y x) x)
cost-diff	0	(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
cost-diff	0	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	318
0	66	273
1	101	273
2	162	273
3	298	273
4	617	258
5	1178	258
6	2008	258
7	4039	258
8	5245	258
9	7000	258
0	8139	253

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
(-.f64 (hypot.f64 y x) x)
(hypot.f64 y x)
y
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
(/.f64 #s(literal 1/4 binary64) y)
#s(literal 1/4 binary64)
y
x
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
(/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64))
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(fma.f64 (/.f64 (*.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 x (/.f64 x y)) y)
(*.f64 x (/.f64 x y))
x
(/.f64 x y)
y
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)

Outputs
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
(sqrt.f64 (*.f64 (-.f64 x (hypot.f64 x y)) #s(literal -1/2 binary64)))
(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
(*.f64 (-.f64 x (hypot.f64 x y)) #s(literal -1/2 binary64))
(-.f64 (hypot.f64 y x) x)
(-.f64 (hypot.f64 x y) x)
(hypot.f64 y x)
(hypot.f64 x y)
y
x
#s(literal 1/2 binary64)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
(neg.f64 x)
x
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
#s(literal 1 binary64)
x
(*.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
y
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
(/.f64 #s(literal 1/4 binary64) y)
#s(literal 1/4 binary64)
y
x
#s(literal -1/2 binary64)
(*.f64 #s(literal 1/2 binary64) y)
#s(literal 1/2 binary64)
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (-.f64 #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y)) x) #s(literal 1/2 binary64)))
(/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64))
(.f64 (-.f64 #s(approx (sqrt (+ ( x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y)) x) #s(literal 1/2 binary64))
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y)) x)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))
#s(approx (sqrt (+ (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(fma.f64 (*.f64 (/.f64 x y) x) #s(literal 1/2 binary64) y)
(fma.f64 (/.f64 (*.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64))
(fma.f64 (/.f64 (*.f64 (/.f64 x y) x) y) #s(literal 1/2 binary64) #s(literal 1 binary64))
(/.f64 (*.f64 x (/.f64 x y)) y)
(/.f64 (*.f64 (/.f64 x y) x) y)
(*.f64 x (/.f64 x y))
(*.f64 (/.f64 x y) x)
x
(/.f64 x y)
y
#s(literal 1/2 binary64)
#s(literal 1 binary64)
#s(literal 2 binary64)

localize210.0ms (4.4%)

Memory

-50.4MiB live, 58.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	3.1350966155311712	(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
accuracy	5.718617499332646	(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
accuracy	6.406491486990898	(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
accuracy	12.543462985308791	#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))
accuracy	0.046875	(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
accuracy	0.07421875	(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
accuracy	6.406491486990898	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
accuracy	12.838442511222926	#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
accuracy	0.0	(*.f64 #s(literal 1/2 binary64) y)
accuracy	0.0625	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
accuracy	0.16796875	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
accuracy	14.124940758495029	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
accuracy	0.0	(neg.f64 x)
accuracy	6.406491486990898	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
accuracy	27.49797014340952	#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
accuracy	0.0	(hypot.f64 y x)
accuracy	0.0	(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
accuracy	5.718617499332646	(-.f64 (hypot.f64 y x) x)
accuracy	6.406491486990898	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))

Samples

49.0ms	26×	2	valid
34.0ms	142×	0	invalid
14.0ms	62×	0	valid
11.0ms	25×	1	valid
1.0ms	1×	3	valid

Compiler

Compiled 572 to 74 computations (87.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-mult: 45.0ms (52.4% of total)

ival-hypot: 12.0ms (14% of total)

ival-div: 9.0ms (10.5% of total)

ival-sqrt: 6.0ms (7% of total)

adjust: 4.0ms (4.7% of total)

ival-add: 4.0ms (4.7% of total)

ival-sub: 3.0ms (3.5% of total)

exact: 1.0ms (1.2% of total)

ival-neg: 1.0ms (1.2% of total)

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

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

series22.0ms (0.5%)

Memory

12.9MiB live, 12.9MiB allocated

Counts

21 → 108

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
(-.f64 (hypot.f64 y x) x)
(hypot.f64 y x)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
(neg.f64 x)
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
(*.f64 #s(literal 1/2 binary64) y)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))

Outputs
(* (sqrt y) (sqrt 1/2))
(+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* 1/8 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* x (+ (* 1/16 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* 1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt 1/2))))))) (* (sqrt y) (sqrt 1/2)))
(* 1/2 y)
(+ (* -1/2 x) (* 1/2 y))
(+ (* 1/2 y) (* x (- (* 1/4 (/ x y)) 1/2)))
(+ (* 1/2 y) (* x (- (* x (+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y)))) 1/2)))
y
(+ y (* -1 x))
(+ y (* x (- (* 1/2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))) 1)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 x)
(* 1/2 (* (sqrt (/ 1 x)) y))
(sqrt (/ 1 x))
(/ 1 x)
-1/2
(- (* 1/4 (/ x y)) 1/2)
(* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* -1/512 (* (sqrt (/ 1 (pow x 9))) (/ (pow y 5) (pow (sqrt 1/2) 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))))
(* 1/4 (/ (pow y 2) x))
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (* 1/4 (pow y 2))) x)
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2)))) x)
(/ (+ (* -1/4 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2))))) x)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (* 1/2 (pow y 2))) x)
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2)))) x)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2))))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* 1/4 (/ (pow x 2) y))
(* (pow x 2) (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* 1/2 (/ y (pow x 2))) (* 1/4 (/ 1 y))) (* 1/2 (/ 1 x))))
(* 1/4 (/ x y))
(* x (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* -1 (* (sqrt x) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ 1 (* 1/4 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (+ (* 1/32 (/ (pow y 6) (pow x 6))) (* 1/4 (/ (pow y 2) (pow x 2))))))))
(* -2 x)
(* -1 (* x (+ 2 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* 1/2 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* -1/2 (/ y x))) x)) (* 1/4 (/ 1 y))))
(* -1 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 y)))))
(* y (+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt x) (* (pow y 2) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))))))))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* (pow y 2) (+ (* -1/2 (* (sqrt x) (* (pow y 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))) (* (pow x 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow x 7))))))) (* 1/2 (* (sqrt x) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2)))))))))))))
(* (pow y 2) (+ (* -1/16 (/ (pow y 2) (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/32 (/ (pow y 2) (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/256 (/ (pow y 2) (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/128 (/ (pow y 2) (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))) y)
(/ (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/2 y)))) y)
(/ (+ (* -1/2 y) (* 1/4 x)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2)))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/16 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))) (/ x y)))
(* y (- (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))) (/ x y)))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (+ (* -1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y))) (* 1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* 1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/2 x) (* -1/4 (/ (pow x 2) y))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (/ (pow x 4) (pow y 2))) (* 1/4 (pow x 2))) y)) (* -1/2 x)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (/ x y))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1/2 (/ (pow x 2) y)) x) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow x 4) (pow y 2))) (* 1/2 (pow x 2))) y)) x) y)))))
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ (* -1/2 x) (* 1/4 (/ (pow x 2) y))) y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
5.0ms	y	@	0	((sqrt (* (- (sqrt (+ (* y y) (* x x))) x) 1/2)) (* (- (sqrt (+ (* y y) (* x x))) x) 1/2) (- (sqrt (+ (* y y) (* x x))) x) (sqrt (+ (* y y) (* x x))) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (* (sqrt (/ 1 x)) (* 1/2 y)) (sqrt (/ 1 x)) (/ 1 x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (+ (* (/ 1/4 y) x) -1/2) (* (+ (* (/ (* x (/ x y)) y) 1/2) 1) y) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (* 1/2 y) (sqrt (+ (* x x) (* y y))))
3.0ms	x	@	-inf	((sqrt (* (- (sqrt (+ (* y y) (* x x))) x) 1/2)) (* (- (sqrt (+ (* y y) (* x x))) x) 1/2) (- (sqrt (+ (* y y) (* x x))) x) (sqrt (+ (* y y) (* x x))) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (* (sqrt (/ 1 x)) (* 1/2 y)) (sqrt (/ 1 x)) (/ 1 x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (+ (* (/ 1/4 y) x) -1/2) (* (+ (* (/ (* x (/ x y)) y) 1/2) 1) y) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (* 1/2 y) (sqrt (+ (* x x) (* y y))))
3.0ms	y	@	inf	((sqrt (* (- (sqrt (+ (* y y) (* x x))) x) 1/2)) (* (- (sqrt (+ (* y y) (* x x))) x) 1/2) (- (sqrt (+ (* y y) (* x x))) x) (sqrt (+ (* y y) (* x x))) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (* (sqrt (/ 1 x)) (* 1/2 y)) (sqrt (/ 1 x)) (/ 1 x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (+ (* (/ 1/4 y) x) -1/2) (* (+ (* (/ (* x (/ x y)) y) 1/2) 1) y) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (* 1/2 y) (sqrt (+ (* x x) (* y y))))
3.0ms	x	@	inf	((sqrt (* (- (sqrt (+ (* y y) (* x x))) x) 1/2)) (* (- (sqrt (+ (* y y) (* x x))) x) 1/2) (- (sqrt (+ (* y y) (* x x))) x) (sqrt (+ (* y y) (* x x))) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (* (sqrt (/ 1 x)) (* 1/2 y)) (sqrt (/ 1 x)) (/ 1 x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (+ (* (/ 1/4 y) x) -1/2) (* (+ (* (/ (* x (/ x y)) y) 1/2) 1) y) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (* 1/2 y) (sqrt (+ (* x x) (* y y))))
3.0ms	x	@	0	((sqrt (* (- (sqrt (+ (* y y) (* x x))) x) 1/2)) (* (- (sqrt (+ (* y y) (* x x))) x) 1/2) (- (sqrt (+ (* y y) (* x x))) x) (sqrt (+ (* y y) (* x x))) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (* (sqrt (/ 1 x)) (* 1/2 y)) (sqrt (/ 1 x)) (/ 1 x) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (+ (* (/ 1/4 y) x) -1/2) (* (+ (* (/ (* x (/ x y)) y) 1/2) 1) y) (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (- (sqrt (+ (* x x) (* y y))) x) (* 1/2 y) (sqrt (+ (* x x) (* y y))))

simplify216.0ms (4.5%)

Memory

-31.6MiB live, 49.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	2274
1	1538	2196
2	5312	2191
0	8649	2051

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 106

Calls

Call 1

Inputs
(* (sqrt y) (sqrt 1/2))
(+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* 1/8 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt 1/2)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* x (+ (* 1/16 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* 1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt 1/2))))))) (* (sqrt y) (sqrt 1/2)))
(* 1/2 y)
(+ (* -1/2 x) (* 1/2 y))
(+ (* 1/2 y) (* x (- (* 1/4 (/ x y)) 1/2)))
(+ (* 1/2 y) (* x (- (* x (+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y)))) 1/2)))
y
(+ y (* -1 x))
(+ y (* x (- (* 1/2 (/ x y)) 1)))
(+ y (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))) 1)))
(+ y (* 1/2 (/ (pow x 2) y)))
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* -1 x)
(* 1/2 (* (sqrt (/ 1 x)) y))
(sqrt (/ 1 x))
(/ 1 x)
-1/2
(- (* 1/4 (/ x y)) 1/2)
(* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* -1/512 (* (sqrt (/ 1 (pow x 9))) (/ (pow y 5) (pow (sqrt 1/2) 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))))
(* 1/4 (/ (pow y 2) x))
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (* 1/4 (pow y 2))) x)
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2)))) x)
(/ (+ (* -1/4 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2))))) x)
(* 1/2 (/ (pow y 2) x))
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (* 1/2 (pow y 2))) x)
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2)))) x)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2))))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* 1/4 (/ (pow x 2) y))
(* (pow x 2) (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(* (pow x 2) (- (+ (* 1/2 (/ y (pow x 2))) (* 1/4 (/ 1 y))) (* 1/2 (/ 1 x))))
(* 1/4 (/ x y))
(* x (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(* 1/2 (/ (pow x 2) y))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(* -1 (* (sqrt x) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(* -1 (* x (+ 1 (* 1/4 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (+ (* 1/32 (/ (pow y 6) (pow x 6))) (* 1/4 (/ (pow y 2) (pow x 2))))))))
(* -2 x)
(* -1 (* x (+ 2 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(* 1/2 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* -1/2 (/ y x))) x)) (* 1/4 (/ 1 y))))
(* -1 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 y)))))
(* y (+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt x) (* (pow y 2) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))))))))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* (pow y 2) (+ (* -1/2 (* (sqrt x) (* (pow y 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))) (* (pow x 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow x 7))))))) (* 1/2 (* (sqrt x) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2)))))))))))))
(* (pow y 2) (+ (* -1/16 (/ (pow y 2) (pow x 3))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/32 (/ (pow y 2) (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/256 (/ (pow y 2) (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/128 (/ (pow y 2) (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(+ x (* 1/2 (/ (pow y 2) x)))
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(/ (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))) y)
(/ (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/2 y)))) y)
(/ (+ (* -1/2 y) (* 1/4 x)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2)))))
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))))
(* y (+ 1/2 (* -1/2 (/ x y))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/16 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(* y (+ 1 (* -1 (/ x y))))
(* y (- (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))) (/ x y)))
(* y (- (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))) (/ x y)))
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (+ (* -1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y))) (* 1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(* -1/2 y)
(* -1 (* y (+ 1/2 (* 1/2 (/ x y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/2 x) (* -1/4 (/ (pow x 2) y))) y)))))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (/ (pow x 4) (pow y 2))) (* 1/4 (pow x 2))) y)) (* -1/2 x)) y)))))
(* -1 y)
(* -1 (* y (+ 1 (/ x y))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1/2 (/ (pow x 2) y)) x) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow x 4) (pow y 2))) (* 1/2 (pow x 2))) y)) x) y)))))
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(* -1 (* y (- (* -1 (/ (+ (* -1/2 x) (* 1/4 (/ (pow x 2) y))) y)) 1/2)))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))

Outputs
(* (sqrt y) (sqrt 1/2))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 y))
(+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 y)))) (* (sqrt y) (sqrt 1/2)))
(fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 y)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* 1/8 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))))) (* (sqrt y) (sqrt 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)))) x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 y)))
(+ (* x (+ (* -1/2 (* (sqrt (/ 1 y)) (sqrt 1/2))) (* x (+ (* 1/16 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* 1/8 (* (sqrt (/ 1 (pow y 3))) (sqrt 1/2))))))) (* (sqrt y) (sqrt 1/2)))
(fma.f64 (fma.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (.f64 (fma.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))))) x)) x (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 y)))
(* 1/2 y)
(*.f64 #s(literal 1/2 binary64) y)
(+ (* -1/2 x) (* 1/2 y))
(fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 y) (* x (- (* 1/4 (/ x y)) 1/2)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
(+ (* 1/2 y) (* x (- (* x (+ (* -1/16 (/ (pow x 2) (pow y 3))) (* 1/4 (/ 1 y)))) 1/2)))
(fma.f64 (fma.f64 (fma.f64 (.f64 x (/.f64 x (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) y)) x #s(literal -1/2 binary64)) x (.f64 #s(literal 1/2 binary64) y))
y
(+ y (* -1 x))
(-.f64 y x)
(+ y (* x (- (* 1/2 (/ x y)) 1)))
(fma.f64 (fma.f64 (/.f64 x y) #s(literal 1/2 binary64) #s(literal -1 binary64)) x y)
(+ y (* x (- (* x (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))) 1)))
(fma.f64 (fma.f64 (fma.f64 #s(literal -1/8 binary64) (*.f64 x (/.f64 x (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) y)) x #s(literal -1 binary64)) x y)
(+ y (* 1/2 (/ (pow x 2) y)))
(fma.f64 (*.f64 x (/.f64 x y)) #s(literal 1/2 binary64) y)
(+ y (* (pow x 2) (+ (* -1/8 (/ (pow x 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (fma.f64 #s(literal -1/8 binary64) (.f64 x (/.f64 x (pow.f64 y #s(literal 3 binary64)))) (/.f64 #s(literal 1/2 binary64) y)) (.f64 x x) y)
(+ y (* (pow x 2) (+ (* (pow x 2) (- (* 1/16 (/ (pow x 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (.f64 x (/.f64 x (pow.f64 y #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 x (/.f64 x y)) #s(literal 1/2 binary64) y))
(* -1 x)
(neg.f64 x)
(* 1/2 (* (sqrt (/ 1 x)) y))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
-1/2
#s(literal -1/2 binary64)
(- (* 1/4 (/ x y)) 1/2)
(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
(* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y) (.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2)))))
(fma.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y) (.f64 (.f64 #s(literal 1/32 binary64) (pow.f64 y #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64)))))))
(+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 3))) (+ (* -1/512 (* (sqrt (/ 1 (pow x 9))) (/ (pow y 5) (pow (sqrt 1/2) 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 9))) (pow y 5))) (* (sqrt (/ 1 x)) (* y (pow (sqrt 1/2) 2))))))
(fma.f64 (.f64 #s(literal -1/512 binary64) (/.f64 (pow.f64 y #s(literal 5 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64)))) (fma.f64 (.f64 #s(literal -1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y) (.f64 (*.f64 #s(literal 1/32 binary64) (pow.f64 y #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 9 binary64))))))))
(* 1/4 (/ (pow y 2) x))
(.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (* 1/4 (pow y 2))) x)
(/.f64 (fma.f64 (.f64 #s(literal 1/4 binary64) y) y (.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal -1/16 binary64) x))) x)
(/ (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2)))) x)
(/.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal -1/16 binary64) x) (fma.f64 (.f64 #s(literal 1/4 binary64) y) y (/.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/32 binary64)) (pow.f64 x #s(literal 4 binary64))))) x)
(/ (+ (* -1/4 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/16 (/ (pow y 4) (pow x 2))) (+ (* 1/32 (/ (pow y 6) (pow x 4))) (* 1/4 (pow y 2))))) x)
(/.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 8 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1/4 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (/.f64 #s(literal -1/16 binary64) x) (fma.f64 (.f64 #s(literal 1/4 binary64) y) y (/.f64 (*.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/32 binary64)) (pow.f64 x #s(literal 4 binary64)))))) x)
(* 1/2 (/ (pow y 2) x))
(.f64 (/.f64 (.f64 y y) x) #s(literal 1/2 binary64))
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (* 1/2 (pow y 2))) x)
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (.f64 (.f64 y y) #s(literal 1/2 binary64))) x)
(/ (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2)))) x)
(/.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 (.f64 y y) #s(literal 1/2 binary64)))) x)
(/ (+ (* -1/2 (/ (+ (* 1/64 (pow y 8)) (* 1/16 (pow y 8))) (pow x 6))) (+ (* -1/8 (/ (pow y 4) (pow x 2))) (+ (* 1/16 (/ (pow y 6) (pow x 4))) (* 1/2 (pow y 2))))) x)
(/.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 8 binary64)) (/.f64 #s(literal 5/64 binary64) (pow.f64 x #s(literal 6 binary64)))) #s(literal -1/2 binary64) (fma.f64 (/.f64 #s(literal -1/8 binary64) x) (/.f64 (pow.f64 y #s(literal 4 binary64)) x) (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal 1/16 binary64) (.f64 (*.f64 y y) #s(literal 1/2 binary64))))) x)
x
(* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64))) x)
(* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) (/.f64 y x) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x)
(* 1/4 (/ (pow x 2) y))
(.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) x) x)
(* (pow x 2) (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) (.f64 x x))
(* (pow x 2) (- (+ (* 1/2 (/ y (pow x 2))) (* 1/4 (/ 1 y))) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 (/.f64 y x) (/.f64 #s(literal 1/2 binary64) x) (-.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 #s(literal 1/2 binary64) x))) (.f64 x x))
(* 1/4 (/ x y))
(*.f64 (/.f64 #s(literal 1/4 binary64) y) x)
(* x (- (* 1/4 (/ 1 y)) (* 1/2 (/ 1 x))))
(*.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 #s(literal 1/2 binary64) x)) x)
(* 1/2 (/ (pow x 2) y))
(.f64 (.f64 x (/.f64 x y)) #s(literal 1/2 binary64))
(* (pow x 2) (+ (* 1/2 (/ 1 y)) (/ y (pow x 2))))
(.f64 (.f64 (+.f64 (/.f64 y (*.f64 x x)) (/.f64 #s(literal 1/2 binary64) y)) x) x)
(* -1 (* (sqrt x) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))
(.f64 (.f64 (neg.f64 (sqrt.f64 x)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64)))) (sqrt.f64 #s(literal 2 binary64)))
(* -1 (* x (+ (* -1/4 (* (sqrt (/ 1 (pow x 5))) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 #s(literal -1/4 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 y y)) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 y #s(literal 4 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal -1/16 binary64) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (*.f64 y y)) (sqrt.f64 #s(literal 2 binary64))))) (neg.f64 (pow.f64 x #s(literal 3 binary64))))))
(* -1 (* x (+ (* -1 (/ (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))) (+ (* 1/32 (* (sqrt (/ 1 (pow x 3))) (/ (* (pow y 4) (* (sqrt -1) (sqrt 1/2))) (pow (sqrt 2) 3)))) (* 1/4 (* (sqrt x) (/ (* (pow y 2) (* (sqrt -1) (sqrt 1/2))) (sqrt 2)))))) (pow x 3))) (* (sqrt (/ 1 x)) (* (sqrt -1) (* (sqrt 1/2) (sqrt 2)))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 #s(literal 2 binary64))) (sqrt.f64 #s(literal 1/2 binary64)) (/.f64 (fma.f64 (.f64 #s(literal -1/16 binary64) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (pow.f64 y #s(literal 4 binary64))) (sqrt.f64 #s(literal 2 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3 binary64)))) (pow.f64 y #s(literal 4 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 2 binary64)))) #s(literal 1/64 binary64) (.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 #s(literal 1/2 binary64))) (.f64 y y)) (sqrt.f64 #s(literal 2 binary64)))))) (neg.f64 (pow.f64 x #s(literal 3 binary64))))))
(* -1 (* x (+ 1 (* 1/4 (/ (pow y 2) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (* 1/4 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/16 binary64) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/16 (/ (pow y 4) (pow x 4))) (+ (* 1/32 (/ (pow y 6) (pow x 6))) (* 1/4 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/32 binary64) (fma.f64 (/.f64 (.f64 #s(literal 1/4 binary64) y) x) (/.f64 y x) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))
(* -2 x)
(*.f64 #s(literal -2 binary64) x)
(* -1 (* x (+ 2 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal 2 binary64)))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal 2 binary64))))
(* -1 (* x (+ 2 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(.f64 (neg.f64 x) (+.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 y y) x) #s(literal 2 binary64))) (/.f64 (*.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))
(* -1 (* x (+ 1 (* 1/2 (/ (pow y 2) (pow x 2))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (* 1/2 (/ (pow y 2) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow y 4) (pow x 4))) (+ (* 1/16 (/ (pow y 6) (pow x 6))) (* 1/2 (/ (pow y 2) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (.f64 (/.f64 y x) #s(literal 1/2 binary64)) (/.f64 y x) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))
(* 1/2 (* (sqrt (/ 1 x)) (* y (pow (sqrt -1) 2))))
(.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) y) #s(literal -1/2 binary64))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (pow x 2) (+ (* -1 (/ (+ 1/2 (* -1/2 (/ y x))) x)) (* 1/4 (/ 1 y))))
(.f64 (.f64 (-.f64 (/.f64 #s(literal 1/4 binary64) y) (/.f64 (fma.f64 (/.f64 y x) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) x)) x) x)
(* -1 (* x (- (* 1/2 (/ 1 x)) (* 1/4 (/ 1 y)))))
(*.f64 (fma.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/4 binary64) y) (/.f64 #s(literal -1/2 binary64) x)) x)
(* y (+ (* -1/16 (* (sqrt (/ 1 (pow x 5))) (pow y 2))) (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y) (.f64 (*.f64 #s(literal -1/16 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (* (sqrt x) (* (pow y 2) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))))))))))
(fma.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 y y)) (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/128 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/16 binary64))) (pow.f64 y #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(* y (+ (* (sqrt (/ 1 x)) (pow (sqrt 1/2) 2)) (* (pow y 2) (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* (pow y 2) (+ (* -1/2 (* (sqrt x) (* (pow y 2) (+ (* -1/16 (/ (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2))))) (* (pow x 2) (pow (sqrt 1/2) 2)))) (* 5/128 (/ 1 (pow x 7))))))) (* 1/2 (* (sqrt x) (- (* 1/16 (/ 1 (pow x 5))) (* 1/256 (/ 1 (* (pow x 5) (pow (sqrt 1/2) 2)))))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/128 binary64) (pow.f64 x #s(literal 5 binary64))))) (sqrt.f64 x) (.f64 (.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 y y)) (fma.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/128 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 x x)) #s(literal -1/8 binary64) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 7 binary64)))))) (.f64 y y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/16 binary64))) (pow.f64 y #s(literal 3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(* (pow y 2) (+ (* -1/16 (/ (pow y 2) (pow x 3))) (* 1/4 (/ 1 x))))
(.f64 (.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) x)) y) y)
(* (pow y 2) (+ (* (pow y 2) (- (* 1/32 (/ (pow y 2) (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/32 binary64) (pow.f64 x #s(literal 5 binary64))) y) y (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/4 binary64) x)) (.f64 y y))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/256 (/ (pow y 2) (pow x 7))) (* 1/32 (/ 1 (pow x 5))))) (* 1/16 (/ 1 (pow x 3))))) (* 1/4 (/ 1 x))))
(.f64 (fma.f64 (fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 7 binary64)))) #s(literal -5/256 binary64) (/.f64 #s(literal 1/32 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y) (/.f64 #s(literal -1/16 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/4 binary64) x)) (*.f64 y y))
(* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y))
(* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) y) y (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y))
(* (pow y 2) (+ (* (pow y 2) (- (* (pow y 2) (+ (* -5/128 (/ (pow y 2) (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 (fma.f64 (fma.f64 (fma.f64 #s(literal -5/128 binary64) (.f64 y (/.f64 y (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))) (.f64 y y) (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y))
(+ x (* 1/2 (/ (pow y 2) x)))
(fma.f64 (/.f64 #s(literal 1/2 binary64) x) (*.f64 y y) x)
(+ x (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow x 3))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (.f64 y y) x)
(+ x (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64))) y) y (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 3 binary64)))) (.f64 y y) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 y y) x)
(/ (+ (* -1/2 (* x y)) (* 1/4 (pow x 2))) y)
(/.f64 (fma.f64 (.f64 x y) #s(literal -1/2 binary64) (.f64 (*.f64 x x) #s(literal 1/4 binary64))) y)
(/ (+ (* 1/4 (pow x 2)) (* y (+ (* -1/2 x) (* 1/2 y)))) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y)) y)) y)
(/ (+ (* -1/2 y) (* 1/4 x)) y)
(/.f64 (fma.f64 #s(literal 1/4 binary64) x (*.f64 #s(literal -1/2 binary64) y)) y)
(/ (+ (* 1/2 (pow x 2)) (pow y 2)) y)
(/.f64 (fma.f64 (.f64 x x) #s(literal 1/2 binary64) (.f64 y y)) y)
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))
(.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal 1/2 binary64)))) y)
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2)))))
(.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) #s(literal 1/4 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal 1/2 binary64))))) y)
(* y (+ (* -1/2 (* (* x (sqrt 1/2)) (sqrt (/ 1 (pow y 3))))) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/4 (* (* (pow x 2) (sqrt 1/2)) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (sqrt 1/2))))))
(.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) #s(literal -1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/2 binary64)) x) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64))))) #s(literal 1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal 1/2 binary64))))) y)
(* y (+ 1/2 (* -1/2 (/ x y))))
(*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (* 1/4 (/ (pow x 2) (pow y 2))))))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/4 binary64) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) y)
(* y (+ 1/2 (+ (* -1/2 (/ x y)) (+ (* -1/16 (/ (pow x 4) (pow y 4))) (* 1/4 (/ (pow x 2) (pow y 2)))))))
(.f64 (+.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/4 binary64) y) x) (/.f64 x y) (/.f64 (*.f64 (pow.f64 x #s(literal 4 binary64)) #s(literal -1/16 binary64)) (pow.f64 y #s(literal 4 binary64)))) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64))) y)
(* y (+ 1 (* -1 (/ x y))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) y)
(* y (- (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))) (/ x y)))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (/.f64 x y))) y)
(* y (- (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))) (/ x y)))
(.f64 (-.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) (/.f64 x y)) y)
(* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2)))))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2))))))
(.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64))) y)
(* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64)))) y y)
(* -1 (* (sqrt y) (* (sqrt -1) (sqrt 1/2))))
(.f64 (.f64 (neg.f64 (sqrt.f64 y)) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 #s(literal 1/2 binary64)))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))))
(* -1 (* y (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (+ (* -1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 5))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 #s(literal -1/4 binary64) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/2 binary64)))) (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y))) (* 1/4 (* (* (pow x 2) (* (sqrt -1) (sqrt 1/2))) (sqrt y)))) (pow y 3))) (+ (* -1/2 (* (* x (* (sqrt -1) (sqrt 1/2))) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (* (sqrt -1) (sqrt 1/2)))))))
(.f64 (neg.f64 y) (-.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) y))) (sqrt.f64 #s(literal 1/2 binary64)) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (sqrt.f64 #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))))) (.f64 (.f64 (.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) x)) (*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 y))) (/.f64 #s(literal 3/8 binary64) (pow.f64 y #s(literal 3 binary64))))))
(* -1/2 y)
(*.f64 #s(literal -1/2 binary64) y)
(* -1 (* y (+ 1/2 (* 1/2 (/ x y)))))
(*.f64 (neg.f64 y) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal 1/2 binary64)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1/2 x) (* -1/4 (/ (pow x 2) y))) y)))))
(.f64 (neg.f64 y) (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/4 binary64) (.f64 x (/.f64 x y)) (*.f64 #s(literal -1/2 binary64) x)) y)))
(* -1 (* y (+ 1/2 (* -1 (/ (+ (* -1 (/ (+ (* -1/16 (/ (pow x 4) (pow y 2))) (* 1/4 (pow x 2))) y)) (* -1/2 x)) y)))))
(.f64 (neg.f64 y) (-.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 #s(literal -1/2 binary64) x (/.f64 (fma.f64 (/.f64 #s(literal -1/16 binary64) y) (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (.f64 (*.f64 x x) #s(literal 1/4 binary64))) (neg.f64 y))) y)))
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (/ x y))))
(neg.f64 (fma.f64 (/.f64 x y) y y))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1/2 (/ (pow x 2) y)) x) y)))))
(fma.f64 (/.f64 (-.f64 (.f64 (.f64 x (/.f64 x y)) #s(literal -1/2 binary64)) x) y) y (neg.f64 y))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (+ (* -1/8 (/ (pow x 4) (pow y 2))) (* 1/2 (pow x 2))) y)) x) y)))))
(neg.f64 (fma.f64 (/.f64 (+.f64 (/.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) y) (/.f64 #s(literal -1/8 binary64) y) (.f64 (.f64 x x) #s(literal 1/2 binary64))) y) x) y) y y))
(* -1 (* y (+ 1 (* 1/2 (/ (pow x 2) (pow y 2))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (* 1/2 (/ (pow x 2) (pow y 2)))))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64))))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow x 4) (pow y 4))) (+ (* 1/16 (/ (pow x 6) (pow y 6))) (* 1/2 (/ (pow x 2) (pow y 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64)))) y y))
(* -1 (* y (- (* 1/2 (/ x y)) 1/2)))
(*.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) y) x #s(literal -1/2 binary64)) (neg.f64 y))
(* -1 (* y (- (* -1 (/ (+ (* -1/2 x) (* 1/4 (/ (pow x 2) y))) y)) 1/2)))
(.f64 (-.f64 #s(literal -1/2 binary64) (/.f64 (.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x) y)) (neg.f64 y))
(* -1 (* y (- (* -1/2 (/ (pow x 2) (pow y 2))) 1)))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal -1/2 binary64) #s(literal -1 binary64)) (neg.f64 y))

rewrite155.0ms (3.2%)

Memory

61.1MiB live, 61.1MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	269
0	66	224
1	253	219
2	1542	209
0	8149	209

Stop Event

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

Counts

21 → 604

Calls

Call 1

Inputs
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
(*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))
(-.f64 (hypot.f64 y x) x)
(hypot.f64 y x)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))
(neg.f64 x)
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) x)
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y)))
(fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))
(fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64))
(.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)
(/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64))
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
(*.f64 #s(literal 1/2 binary64) y)
#s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))

Outputs
(*.f64 (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 x y) x)) #s(literal -1/4 binary64)) (pow.f64 (/.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 x y) x)) #s(literal -1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (-.f64 (hypot.f64 x y) x))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(literal 2 binary64)))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (hypot.f64 x y) x))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -2 binary64))))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (hypot.f64 x y) x))) (sqrt.f64 #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (-.f64 (hypot.f64 x y) x))) (pow.f64 #s(literal -1/2 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (hypot.f64 x y) x)))
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 x y) x)) (pow.f64 #s(literal 2 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (hypot.f64 x y) x)) (sqrt.f64 #s(literal 1/2 binary64)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (-.f64 (hypot.f64 x y) x) #s(literal 1/2 binary64))))
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(fma.f64 x #s(literal -1 binary64) #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 2 binary64)) (-.f64 #s(approx (sqrt (+ ( x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) (neg.f64 x))) (/.f64 (.f64 x x) (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) (neg.f64 x))))
(-.f64 (+.f64 #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 0 binary64)) x)
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 2 binary64)) (+.f64 #s(approx (sqrt (+ ( x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)) (/.f64 (.f64 x x) (+.f64 #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)))
(-.f64 (/.f64 (pow.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 3 binary64)) (fma.f64 x (+.f64 #s(approx (sqrt (+ ( x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) (pow.f64 #s(approx (sqrt (+ ( x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 2 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x (+.f64 #s(approx (sqrt (+ ( x x) (* y y))) (.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) (pow.f64 #s(approx (sqrt (+ ( x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) #s(literal 2 binary64)))))
(-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x)
(+.f64 #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) (neg.f64 x))
(+.f64 (neg.f64 x) #s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)))
(*.f64 #s(literal 1/2 binary64) y)
(*.f64 y #s(literal 1/2 binary64))
#s(approx (sqrt (+ (* x x) (* y y))) (*.f64 (fma.f64 (pow.f64 (/.f64 x y) #s(literal 2 binary64)) #s(literal 1/2 binary64) #s(literal 1 binary64)) y))

eval97.0ms (2%)

Memory: -15.3MiB live, 63.2MiB allocated
Compiler: Compiled 24 654 to 3 123 computations (87.3% saved)

prune23.0ms (0.5%)

Memory

-47.9MiB live, 31.8MiB allocated

Pruning

17 alts after pruning (13 fresh and 4 done)

	Pruned	Kept	Total
New	704	7	711
Fresh	3	6	9
Picked	1	4	5
Done	0	0	0
Total	708	17	725

Accuracy

100.0%

Counts

725 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	80.2%	(/.f64 (sqrt.f64 (-.f64 (hypot.f64 y x) x)) (sqrt.f64 #s(literal 2 binary64)))
	80.3%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 x y) x))))
	63.9%	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (*.f64 x x))) x) #s(literal 2 binary64)))
✓	80.7%	(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
	54.8%	(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
✓	53.0%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
	54.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
	8.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
	31.1%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
	51.1%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
✓	31.0%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
	40.8%	(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) #s(approx (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y)) y)) y))))
	22.4%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
	22.4%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) y))))
	22.3%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) y)))
	22.4%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
✓	22.4%	#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))

Compiler

Compiled 767 to 381 computations (50.3% saved)

regimes29.0ms (0.6%)

Memory

19.6MiB live, 19.6MiB allocated

Counts

22 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (*.f64 x x))) x) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) #s(approx (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y)) y)) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 (hypot.f64 y x) x)) (sqrt.f64 #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal -2 binary64) (-.f64 x (hypot.f64 y x)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 2 binary64) (-.f64 (hypot.f64 x y) x))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (.f64 (fma.f64 (*.f64 y (/.f64 y (pow.f64 x #s(literal 3 binary64)))) #s(literal -1/16 binary64) (/.f64 #s(literal 1/4 binary64) x)) y) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) (.f64 #s(literal 1/2 binary64) y)))

Outputs
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
(sqrt.f64 (*.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64)))

Calls

6 calls:

5.0ms	y
5.0ms	x
5.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
5.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
5.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))

Results

Accuracy	Segments	Branch
91.1%	2	`x`
80.7%	1	`y`
95.1%	2	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`
95.1%	2	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
95.1%	2	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`
80.7%	1	`(*.f64 y y)`

Compiler

Compiled 40 to 33 computations (17.5% saved)

regimes16.0ms (0.3%)

Memory

11.4MiB live, 11.4MiB allocated

Counts

16 → 3

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (*.f64 x x))) x) #s(literal 2 binary64)))
(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) #s(approx (+ (* (+ (* (/ 1/4 y) x) -1/2) x) (* 1/2 y)) (/.f64 (fma.f64 (.f64 x x) #s(literal 1/4 binary64) (.f64 (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y)) y)) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (neg.f64 x) (fma.f64 (/.f64 (/.f64 (.f64 y y) x) x) #s(literal 1/4 binary64) #s(literal 1 binary64)))))
(sqrt.f64 (/.f64 (-.f64 #s(approx (sqrt (+ (* x x) (* y y))) (.f64 (fma.f64 (/.f64 (.f64 x (/.f64 x y)) y) #s(literal 1/2 binary64) #s(literal 1 binary64)) y)) x) #s(literal 2 binary64)))

Outputs

#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))

(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (*.f64 x x))) x) #s(literal 2 binary64)))

Calls

4 calls:

4.0ms	x
4.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
4.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
4.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)

Results

Accuracy	Segments	Branch
85.9%	3	`x`
90.4%	3	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
90.4%	3	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`
90.4%	4	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes18.0ms (0.4%)

Memory

13.9MiB live, 13.9MiB allocated

Counts

11 → 3

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))

Outputs

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (*.f64 #s(literal 1/2 binary64) y))))

#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))

Calls

6 calls:

3.0ms	y
3.0ms	x
3.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
3.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
3.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)

Results

Accuracy	Segments	Branch
62.4%	2	`(*.f64 y y)`
64.7%	2	`y`
80.0%	3	`x`
69.9%	2	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`
72.6%	3	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
72.6%	3	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`

Compiler

Compiled 40 to 33 computations (17.5% saved)

regimes3.0ms (0.1%)

Memory

2.8MiB live, 2.8MiB allocated

Counts

10 → 3

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 x) (*.f64 #s(literal 1/2 binary64) y))))

Outputs

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y)))

#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
79.7%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes3.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

8 → 3

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (/.f64 (.f64 y y) x) #s(literal 1/4 binary64))))

Outputs

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

(sqrt.f64 (*.f64 #s(approx (- (sqrt (+ (* y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))

#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
79.7%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes2.0ms (0%)

Memory

2.2MiB live, 2.2MiB allocated

Counts

5 → 3

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))
#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))

Outputs

(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

(sqrt.f64 (*.f64 #s(approx (- (sqrt (+ (* y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))

#s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
79.7%	3	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes7.0ms (0.2%)

Memory

7.0MiB live, 7.0MiB allocated

Counts

4 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 #s(literal -1/2 binary64) x (*.f64 #s(literal 1/2 binary64) y))))

Outputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64)))

Calls

4 calls:

2.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
2.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
2.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
2.0ms	x

Results

Accuracy	Segments	Branch
54.8%	1	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`
56.5%	2	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
56.5%	2	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`
68.6%	2	`x`

Compiler

Compiled 36 to 28 computations (22.2% saved)

regimes2.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))

Outputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y)))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
68.2%	2	`x`

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes7.0ms (0.1%)

Memory

8.3MiB live, 8.3MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

Outputs
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

Calls

6 calls:

1.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))
1.0ms	x
1.0ms	(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))
1.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)
1.0ms	y

Results

Accuracy	Segments	Branch
31.0%	1	`(sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64)))`
31.0%	1	`(/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))`
31.0%	1	`(-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x)`
31.0%	1	`(*.f64 y y)`
31.0%	1	`y`
31.0%	1	`x`

Compiler

Compiled 40 to 33 computations (17.5% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.9678568161920736e-147

Compiler

Compiled 16 to 15 computations (6.3% saved)

bsearch1.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Algorithm

2×	left-value

Steps

Time	Left	Right
0.0ms	2.3598186646394957e-158	2.6549906224807384e-155
0.0ms	0.0	7.74492089806721e-294

Compiler

Compiled 16 to 15 computations (6.3% saved)

bsearch34.0ms (0.7%)

Memory

-78.2MiB live, 8.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
14.0ms	4.324606393131315e-101	9.712909097652635e-101
17.0ms	-2.144520684316691e-150	-2.3784740908390017e-153

Samples

10.0ms	150×	0	valid
6.0ms	34×	2	valid
3.0ms	24×	1	valid

Compiler

Compiled 569 to 443 computations (22.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-hypot: 6.0ms (47.3% of total)

ival-div: 2.0ms (15.8% of total)

ival-sqrt: 2.0ms (15.8% of total)

adjust: 1.0ms (7.9% of total)

ival-sub: 1.0ms (7.9% of total)

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

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

exact: 0.0ms (0% of total)

bsearch16.0ms (0.3%)

Memory

4.6MiB live, 4.6MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	4.324606393131315e-101	9.712909097652635e-101
13.0ms	-2.553178110689904e-138	-1.490593211980168e-141

Samples

8.0ms

128×

valid

Compiler

Compiled 530 to 417 computations (21.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-hypot: 2.0ms (40.6% of total)

ival-sub: 1.0ms (20.3% of total)

ival-div: 1.0ms (20.3% of total)

ival-sqrt: 1.0ms (20.3% of total)

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

exact: 0.0ms (0% of total)

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

bsearch2.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	4.324606393131315e-101	9.712909097652635e-101
1.0ms	-2.553178110689904e-138	-1.490593211980168e-141

Compiler

Compiled 465 to 365 computations (21.5% saved)

bsearch2.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Algorithm

2×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
1.0ms	4.324606393131315e-101	9.712909097652635e-101
1.0ms	-2.553178110689904e-138	-1.490593211980168e-141

Compiler

Compiled 465 to 365 computations (21.5% saved)

bsearch1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
1.0ms	-2.553178110689904e-138	-1.490593211980168e-141

Compiler

Compiled 280 to 220 computations (21.4% saved)

bsearch6.0ms (0.1%)

Memory

2.0MiB live, 2.0MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
6.0ms	-2.144520684316691e-150	-2.3784740908390017e-153

Samples

3.0ms

48×

valid

Compiler

Compiled 280 to 228 computations (18.6% saved)

Precisions

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

ival-hypot: 1.0ms (52.7% of total)

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

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

ival-true: 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)

simplify91.0ms (1.9%)

Memory

11.2MiB live, 11.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	84	471
1	98	471
2	104	471
3	116	471
4	143	471
5	177	471
6	246	471
7	463	471
8	749	471
9	1608	471
10	1888	471
11	2011	471
12	2243	471
13	2636	471
14	3587	471
15	6047	471

Stop Event

1×	node limit

Calls

Call 1

Inputs
(if (<=.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x))) (sqrt.f64 (.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 0 binary64)) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x))) (if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 4946608029462091/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ ( x x) (* y y))) x) 2) (.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (.f64 x x))) x) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -1916465293854689/3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742230126362624 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (.f64 #s(literal 1/2 binary64) y)))) #s(approx (sqrt (/ (- (sqrt (+ ( x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))) #s(approx (sqrt (/ (- (sqrt (+ ( x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -6781338732101207/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

Outputs
(if (<=.f64 (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 2 binary64))) #s(literal 0 binary64)) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x))) (sqrt.f64 (.f64 (-.f64 (hypot.f64 y x) x) #s(literal 1/2 binary64))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 0 binary64)) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x))) (if (<=.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))) x) #s(literal 4946608029462091/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ ( x x) (* y y))) x) 2) (.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))) (sqrt.f64 (/.f64 (-.f64 (sqrt.f64 (fma.f64 y y (.f64 x x))) x) #s(literal 2 binary64)))))
(if (<=.f64 x #s(literal -1916465293854689/3685510180489786476798393145496356338786055879312930105836138965083617346086082863365358130056307390177215209990980317284932211552660930305235775636164742230126362624 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (fma.f64 (fma.f64 (/.f64 #s(literal 1/4 binary64) y) x #s(literal -1/2 binary64)) x (.f64 #s(literal 1/2 binary64) y)))) #s(approx (sqrt (/ (- (sqrt (+ ( x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (.f64 (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) #s(literal 1/2 binary64)) y))) #s(approx (sqrt (/ (- (sqrt (+ ( x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (/.f64 (*.f64 #s(literal 1/2 binary64) y) (sqrt.f64 x)))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (if (<=.f64 x #s(literal 1733688272641357/39402006196394479212279040100143613805079739270465446667948293404245721771497210611414266254884915640806627990306816 binary64)) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))) #s(approx (sqrt (/ (- (sqrt (+ (* x x) (* y y))) x) 2)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) y))))
(if (<=.f64 x #s(literal -3620108141084501/6703903964971298549787012499102923063739682910296196688861780721860882015036773488400937149083451713845015929093243025426876941405973284973216824503042048 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (sqrt.f64 (.f64 #s(approx (- (sqrt (+ ( y y) (* x x))) x) (-.f64 y x)) #s(literal 1/2 binary64))))
(if (<=.f64 x #s(literal -6781338732101207/14742040721959145907193572581985425355144223517251720423344555860334469384344331453461432520225229560708860839963921269139728846210643721220943102544658968920505450496 binary64)) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x))) (sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (*.f64 #s(literal 1/2 binary64) y))))
(sqrt.f64 #s(approx (/ (- (sqrt (+ (* x x) (* y y))) x) 2) (neg.f64 x)))

soundness674.0ms (14.1%)

Memory

18.1MiB live, 18.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	497	2274
1	1538	2196
2	5312	2191
0	8649	2051
0	10	50
0	17	50
1	64	50
2	447	50
3	5120	50
0	8164	28
0	40	269
0	66	224
1	253	219
2	1542	209
0	8149	209
0	449	2079
1	1416	2009
2	4934	2006
0	8272	1874

Stop Event

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

Compiler

Compiled 885 to 395 computations (55.4% saved)

preprocess46.0ms (1%)

Memory: 31.0MiB live, 31.0MiB allocated
Compiler: Compiled 1 056 to 250 computations (76.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	26	69
1	64	67
2	129	67
3	241	67
4	385	67
5	502	67
6	594	67
7	713	67
8	829	67
9	854	67
0	10	13
0	17	13
1	23	13
2	30	13
3	43	13
4	66	13
5	90	13
6	144	13
7	215	13
8	316	13
9	397	13
10	463	13
11	477	13
12	496	13
13	518	13
14	548	13
15	590	13
16	604	13
17	606	13
0	606	8

Iter	Nodes	Cost
0	10	59
0	17	59
1	23	59
2	30	59
3	43	59
4	66	59
5	90	59
6	144	59
7	215	59
8	316	59
9	397	59
10	463	59
11	477	59
12	496	59
13	518	59
14	548	59
15	590	59
16	604	59
17	606	59
0	606	38

Iter	Nodes	Cost
0	26	69
1	64	67
2	129	67
3	241	67
4	385	67
5	502	67
6	594	67
7	713	67
8	829	67
9	854	67
0	10	13
0	17	13
1	23	13
2	30	13
3	43	13
4	66	13
5	90	13
6	144	13
7	215	13
8	316	13
9	397	13
10	463	13
11	477	13
12	496	13
13	518	13
14	548	13
15	590	13
16	604	13
17	606	13
0	606	8

Iter	Nodes	Cost
0	10	59
0	17	59
1	23	59
2	30	59
3	43	59
4	66	59
5	90	59
6	144	59
7	215	59
8	316	59
9	397	59
10	463	59
11	477	59
12	496	59
13	518	59
14	548	59
15	590	59
16	604	59
17	606	59
0	606	38

start0.0ms (0%)

analyze164.0ms (3.4%)

sample1.8s (36.7%)

explain428.0ms (9%)

preprocess55.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify70.0ms (1.5%)

localize38.0ms (0.8%)

series15.0ms (0.3%)

simplify168.0ms (3.5%)

rewrite184.0ms (3.9%)

eval68.0ms (1.4%)

prune17.0ms (0.4%)

simplify128.0ms (2.7%)

localize210.0ms (4.4%)

series22.0ms (0.5%)

simplify216.0ms (4.5%)

rewrite155.0ms (3.2%)

eval97.0ms (2%)

prune23.0ms (0.5%)

regimes29.0ms (0.6%)

regimes16.0ms (0.3%)

regimes18.0ms (0.4%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes2.0ms (0%)

regimes7.0ms (0.2%)

regimes2.0ms (0%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

bsearch1.0ms (0%)

bsearch34.0ms (0.7%)

bsearch16.0ms (0.3%)

bsearch2.0ms (0%)

bsearch2.0ms (0%)

bsearch1.0ms (0%)

bsearch6.0ms (0.1%)

simplify91.0ms (1.9%)

soundness674.0ms (14.1%)

preprocess46.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	26	69
1	64	67
2	129	67
3	241	67
4	385	67
5	502	67
6	594	67
7	713	67
8	829	67
9	854	67
0	10	13
0	17	13
1	23	13
2	30	13
3	43	13
4	66	13
5	90	13
6	144	13
7	215	13
8	316	13
9	397	13
10	463	13
11	477	13
12	496	13
13	518	13
14	548	13
15	590	13
16	604	13
17	606	13
0	606	8

Iter	Nodes	Cost
0	10	59
0	17	59
1	23	59
2	30	59
3	43	59
4	66	59
5	90	59
6	144	59
7	215	59
8	316	59
9	397	59
10	463	59
11	477	59
12	496	59
13	518	59
14	548	59
15	590	59
16	604	59
17	606	59
0	606	38