Metrics for x - sqrt(pow(y, 2)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze25.0ms (0.9%)

Memory

9.5MiB live, 9.5MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25.4%	74.6%	0%	0%	0%	0
0%	0%	25.4%	74.6%	0%	0%	0%	1
50%	12.7%	12.7%	74.6%	0%	0%	0%	2
50%	12.7%	12.7%	74.6%	0%	0%	0%	3
50%	12.7%	12.7%	74.6%	0%	0%	0%	4
57.1%	12.7%	9.5%	74.6%	0%	3.2%	0%	5
61.5%	12.7%	7.9%	74.6%	0%	4.8%	0%	6
75%	14.3%	4.8%	74.6%	0%	6.4%	0%	7
78.3%	14.3%	4%	74.6%	0%	7.2%	0%	8
86.4%	15.1%	2.4%	74.6%	0%	7.9%	0%	9
88.4%	15.1%	2%	74.6%	0%	8.3%	0%	10
92.9%	15.5%	1.2%	74.6%	0%	8.7%	0%	11
94%	15.5%	1%	74.6%	0%	8.9%	0%	12

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.1s (40.4%)

Memory

59.8MiB live, 596.9MiB allocated

Samples

765.0ms	8 256×	0	valid
21.0ms	271×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 541.0ms

ival-sqrt: 157.0ms (29% of total)

ival-pow2: 154.0ms (28.5% of total)

ival-sub: 91.0ms (16.8% of total)

ival-<=: 87.0ms (16.1% of total)

ival-and: 33.0ms (6.1% of total)

exact: 15.0ms (2.8% of total)

ival-assert: 4.0ms (0.7% of total)

Bogosity

explain106.0ms (3.7%)

Memory

-31.8MiB live, 42.0MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))`
-	-	`(-.f64 (pow.f64 y #s(literal 2 binary64)) x)`
-	-	`y`
-	-	`#s(literal 2 binary64)`
-	-	`(sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x))`
-	-	`(pow.f64 y #s(literal 2 binary64))`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

30.0ms

512×

valid

Compiler

Compiled 62 to 25 computations (59.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-pow2: 6.0ms (38.1% of total)

ival-sub: 5.0ms (31.7% of total)

ival-sqrt: 4.0ms (25.4% of total)

ival-true: 1.0ms (6.3% of total)

exact: 0.0ms (0% of total)

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

preprocess30.0ms (1.1%)

Memory

6.2MiB live, 6.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	48
1	42	42
2	109	41
3	265	41
4	458	41
5	533	41
6	571	41
7	593	41
8	607	41
0	7	8
0	11	8
1	16	8
2	24	8
3	36	8
4	54	8
5	94	8
6	143	8
7	210	8
8	256	8
9	269	8
0	269	8

Stop Event

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

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 y y) x)))

Symmetry

(abs y)

Compiler

Compiled 8 to 7 computations (12.5% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))

Compiler

Compiled 8 to 7 computations (12.5% saved)

simplify9.0ms (0.3%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(pow.f64 y #s(literal 2 binary64))
cost-diff	0	(-.f64 (pow.f64 y #s(literal 2 binary64)) x)
cost-diff	0	(sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x))
cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	25
0	11	25
1	16	25
2	24	25
3	36	25
4	54	25
5	94	25
6	143	25
7	210	25
8	256	25
9	269	25
0	269	25

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 y y) x)))
x
(sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x))
(sqrt.f64 (-.f64 (*.f64 y y) x))
(-.f64 (pow.f64 y #s(literal 2 binary64)) x)
(-.f64 (*.f64 y y) x)
(pow.f64 y #s(literal 2 binary64))
(*.f64 y y)
y
#s(literal 2 binary64)

localize20.0ms (0.7%)

Memory

8.2MiB live, 8.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(pow.f64 y #s(literal 2 binary64))
accuracy	0.0078125	(-.f64 (pow.f64 y #s(literal 2 binary64)) x)
accuracy	0.015625	(sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x))
accuracy	0.01953125	(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))

Samples

15.0ms

256×

valid

Compiler

Compiled 27 to 9 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

ival-pow2: 3.0ms (39.4% of total)

ival-sub: 2.0ms (26.3% of total)

ival-sqrt: 2.0ms (26.3% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.3%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

4 → 50

Calls

Call 1

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

Outputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (/ 1 y)))) y)
(- (* x (+ 1 (+ (* 1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y))))) y)
(- (* x (+ 1 (+ (* 1/2 (/ 1 y)) (* x (+ (* 1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3)))))))) y)
y
(+ y (* -1/2 (/ x y)))
(+ y (* x (- (* -1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* x (- (* x (- (* -1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (* -1 x) (pow y 2))
(* x (- 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ 1 (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 x)
(* x (- (/ (pow y 2) x) 1))
(* x (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* -1 (* x (- (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ 1 (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* -1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ (pow y 2) x)))))
(- x (* (sqrt x) (sqrt -1)))
(- (+ x (* -1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* (pow y 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))))))))
(- (pow y 2) x)
(* y (- (/ x y) 1))
(* y (- (+ (* 1/2 (/ x (pow y 2))) (/ x y)) 1))
(* y (- (+ (* 1/8 (/ (pow x 2) (pow y 4))) (/ x y)) (+ 1 (* -1/2 (/ x (pow y 2))))))
(* y (+ 1 (* -1/2 (/ x (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6)))))))
(* (pow y 2) (+ 1 (* -1 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 (/ x y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 2) (pow y 2))) (* -1/2 x)) y))) y)) 1)))
(* -1 (* y (+ 1 (* -1/2 (/ x (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6))))))))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	((- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (pow y 2))
2.0ms	x	@	-inf	((- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (pow y 2))
2.0ms	y	@	0	((- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (pow y 2))
1.0ms	y	@	inf	((- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (pow y 2))
1.0ms	x	@	0	((- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (pow y 2))

simplify251.0ms (8.9%)

Memory

-77.9MiB live, 43.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	242	1172
1	738	1158
2	2570	1111
3	7098	1108
0	8129	1043

Stop Event

1×	iter limit
1×	node limit

Counts

50 → 49

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (/ 1 y)))) y)
(- (* x (+ 1 (+ (* 1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y))))) y)
(- (* x (+ 1 (+ (* 1/2 (/ 1 y)) (* x (+ (* 1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3)))))))) y)
y
(+ y (* -1/2 (/ x y)))
(+ y (* x (- (* -1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* x (- (* x (- (* -1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (* -1 x) (pow y 2))
(* x (- 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ 1 (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 x)
(* x (- (/ (pow y 2) x) 1))
(* x (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* -1 (* x (- (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ 1 (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* -1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ (pow y 2) x)))))
(- x (* (sqrt x) (sqrt -1)))
(- (+ x (* -1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* (pow y 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))))))))
(- (pow y 2) x)
(* y (- (/ x y) 1))
(* y (- (+ (* 1/2 (/ x (pow y 2))) (/ x y)) 1))
(* y (- (+ (* 1/8 (/ (pow x 2) (pow y 4))) (/ x y)) (+ 1 (* -1/2 (/ x (pow y 2))))))
(* y (+ 1 (* -1/2 (/ x (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6)))))))
(* (pow y 2) (+ 1 (* -1 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 (/ x y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 2) (pow y 2))) (* -1/2 x)) y))) y)) 1)))
(* -1 (* y (+ 1 (* -1/2 (/ x (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6))))))))

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

rewrite138.0ms (4.9%)

Memory

44.2MiB live, 44.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	11	22
1	48	22
2	325	22
3	3720	22
0	8588	22

Stop Event

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

Counts

4 → 226

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (-.f64 (.f64 y y) x)) #s(literal 2 binary64)))) (-.f64 (.f64 x x) (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (-.f64 (*.f64 y y) x))))
(.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64))) (+.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (-.f64 (.f64 y y) x)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (-.f64 (.f64 y y) x)) (-.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (-.f64 (.f64 y y) x)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (-.f64 (.f64 y y) x)) (fma.f64 (neg.f64 x) x (-.f64 (.f64 y y) x))) (-.f64 x (sqrt.f64 (-.f64 (.f64 y y) x))))
(.f64 (/.f64 (fma.f64 (neg.f64 x) x (-.f64 (.f64 y y) x)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64)))) (-.f64 (fma.f64 x x (-.f64 (.f64 y y) x)) (.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x)))
(.f64 (pow.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x) #s(literal -1 binary64)) (fma.f64 (neg.f64 x) x (-.f64 (*.f64 y y) x)))
(.f64 (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (fma.f64 x x (-.f64 (.f64 y y) x))) #s(literal -1 binary64)) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64))) (pow.f64 (neg.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (fma.f64 x x (-.f64 (.f64 y y) x)))) #s(literal -1 binary64)))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (-.f64 (.f64 y y) x) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x (fma.f64 x x (-.f64 (.f64 y y) x))) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (-.f64 (.f64 y y) x))))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x) (/.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 y y) x))) (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x)))
(.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x) (.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 y y) x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 y y) x)) x) #s(literal -1 binary64))))
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(fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (pow.f64 (.f64 (fma.f64 y y x) x) #s(literal 3 binary64)) (pow.f64 y #s(literal 12 binary64)))) (fma.f64 (.f64 (fma.f64 y y x) x) (-.f64 (*.f64 (fma.f64 y y x) x) (pow.f64 y #s(literal 4 binary64))) (pow.f64 y #s(literal 8 binary64))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 3 binary64)))) (fma.f64 x (-.f64 x (.f64 y y)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (neg.f64 x) x (pow.f64 y #s(literal 4 binary64)))) (-.f64 (.f64 y y) x) (neg.f64 (.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 (pow.f64 y #s(literal 3/2 binary64)) (sqrt.f64 y) (neg.f64 x))
(fma.f64 (sqrt.f64 y) (pow.f64 y #s(literal 3/2 binary64)) (neg.f64 x))
(fma.f64 #s(literal -1 binary64) x (*.f64 y y))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (pow.f64 y #s(literal 3 binary64)) (/.f64 y (fma.f64 y y x)) (neg.f64 (*.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (/.f64 (*.f64 y y) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (fma.f64 y y x) #s(literal -1 binary64)) (neg.f64 (*.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (*.f64 y y) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(fma.f64 (.f64 y y) (/.f64 (.f64 y y) (fma.f64 y y x)) (neg.f64 (*.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 y (/.f64 (pow.f64 y #s(literal 3 binary64)) (fma.f64 y y x)) (neg.f64 (*.f64 x (/.f64 x (fma.f64 y y x)))))
(fma.f64 y y (neg.f64 x))
(fma.f64 x #s(literal -1 binary64) (*.f64 y y))
(-.f64 (fma.f64 y y #s(literal 0 binary64)) x)
(-.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y x)) (*.f64 x (/.f64 x (fma.f64 y y x))))
(-.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))))
(-.f64 #s(literal 0 binary64) (-.f64 x (*.f64 y y)))
(-.f64 (*.f64 y y) x)
(sqrt.f64 (pow.f64 (-.f64 (*.f64 y y) x) #s(literal 2 binary64)))
(fabs.f64 (-.f64 (*.f64 y y) x))
(exp.f64 (.f64 (neg.f64 (log.f64 (-.f64 (.f64 y y) x))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 y y) x)))) #s(literal 2 binary64)))
(exp.f64 (log.f64 (-.f64 (*.f64 y y) x)))
(+.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y x)) (neg.f64 (*.f64 x (/.f64 x (fma.f64 y y x)))))
(+.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 (fma.f64 y y x) x (pow.f64 y #s(literal 4 binary64))))))
(+.f64 (neg.f64 x) (*.f64 y y))
(+.f64 (*.f64 y y) (neg.f64 x))
(*.f64 (pow.f64 y #s(literal 3/2 binary64)) (sqrt.f64 y))
(*.f64 (sqrt.f64 y) (pow.f64 y #s(literal 3/2 binary64)))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 1 binary64)) (*.f64 (log.f64 y) #s(literal 2 binary64)))
(pow.f64 (pow.f64 (exp.f64 #s(literal 2 binary64)) #s(literal 1 binary64)) (log.f64 y))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (sqrt.f64 y) #s(literal 4 binary64))
(pow.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 y)) #s(literal 4 binary64)))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal 2 binary64))) (log.f64 y)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval35.0ms (1.2%)

Memory: 26.0MiB live, 26.0MiB allocated
Compiler: Compiled 7 080 to 1 107 computations (84.4% saved)

prune27.0ms (1%)

Memory

-71.4MiB live, 12.2MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	266	7	273
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	267	7	274

Accuracy

100.0%

Counts

274 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	84.2%	(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x)) (.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 y y) x)) x) (-.f64 (.f64 y y) x))) (pow.f64 (+.f64 (sqrt.f64 (-.f64 (*.f64 y y) x)) x) #s(literal 2 binary64)))
	99.5%	(-.f64 x (/.f64 (-.f64 (.f64 y y) x) (sqrt.f64 (-.f64 (.f64 y y) x))))
▶	99.9%	(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))
▶	48.0%	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y))))
▶	55.9%	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))
▶	47.7%	(-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)))
▶	47.0%	#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Compiler

Compiled 218 to 128 computations (41.3% saved)

simplify39.0ms (1.4%)

Memory

2.9MiB live, 2.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(/.f64 x y)
cost-diff	0	(fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)
cost-diff	0	#s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y))
cost-diff	0	(-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (- (pow y 2) x) (*.f64 y y))
cost-diff	0	(sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y))))
cost-diff	0	(neg.f64 x)
cost-diff	0	#s(approx (- (pow y 2) x) (neg.f64 x))
cost-diff	0	(sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))
cost-diff	0	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))
cost-diff	0	(neg.f64 y)
cost-diff	0	#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))
cost-diff	0	(neg.f64 x)
cost-diff	0	(fma.f64 y y (neg.f64 x))
cost-diff	0	(sqrt.f64 (fma.f64 y y (neg.f64 x)))
cost-diff	0	(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	144
0	39	144
1	63	144
2	87	144
3	121	144
4	161	144
5	269	144
6	410	144
7	675	144
8	1209	144
9	1501	144
10	1537	144
11	1563	144
12	1575	144
0	1575	144

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize47.0ms (1.6%)

Memory

24.0MiB live, 24.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(/.f64 x y)
accuracy	0.00390625	(fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)
accuracy	0.01953125	(-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)))
accuracy	33.48259319771388	#s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y))
accuracy	0.0	(*.f64 y y)
accuracy	0.015625	(sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y)))
accuracy	0.01953125	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y))))
accuracy	34.031270983072424	#s(approx (- (pow y 2) x) (*.f64 y y))
accuracy	0.0	(neg.f64 x)
accuracy	0.015625	(sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))
accuracy	0.01953125	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))
accuracy	27.99870702460788	#s(approx (- (pow y 2) x) (neg.f64 x))
accuracy	0.0	(neg.f64 y)
accuracy	33.92643014472911	#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))
accuracy	0.0	(fma.f64 y y (neg.f64 x))
accuracy	0.0	(neg.f64 x)
accuracy	0.015625	(sqrt.f64 (fma.f64 y y (neg.f64 x)))
accuracy	0.01953125	(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))

Samples

34.0ms

256×

valid

Compiler

Compiled 112 to 18 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-mult: 4.0ms (19.5% of total)

ival-sub: 4.0ms (19.5% of total)

ival-sqrt: 3.0ms (14.6% of total)

ival-pow2: 3.0ms (14.6% of total)

ival-div: 2.0ms (9.8% of total)

ival-add: 2.0ms (9.8% of total)

ival-neg: 2.0ms (9.8% of total)

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

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

exact: 0.0ms (0% of total)

series10.0ms (0.3%)

Memory

4.7MiB live, 4.7MiB allocated

Counts

17 → 56

Calls

Call 1

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

Outputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (/ 1 y)))) y)
(- (* x (+ 1 (+ (* 1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y))))) y)
(- (* x (+ 1 (+ (* 1/2 (/ 1 y)) (* x (+ (* 1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3)))))))) y)
y
(+ y (* -1/2 (/ x y)))
(+ y (* x (- (* -1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* x (- (* x (- (* -1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (* -1 x) (pow y 2))
(* -1 x)
(/ x y)
(* x (- 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ 1 (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (/ (pow y 2) x) 1))
(* -1/2 (/ x y))
(* x (- (/ y x) (* 1/2 (/ 1 y))))
(* x (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* -1 (* x (- (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ 1 (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* -1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (/ 1 y)))))
(- x (* (sqrt x) (sqrt -1)))
(- (+ x (* -1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* (pow y 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))))))))
(- (pow y 2) x)
(/ (+ (* -1/2 x) (pow y 2)) y)
(* y (- (/ x y) 1))
(* y (- (+ (* 1/2 (/ x (pow y 2))) (/ x y)) 1))
(* y (- (+ (* 1/8 (/ (pow x 2) (pow y 4))) (/ x y)) (+ 1 (* -1/2 (/ x (pow y 2))))))
(* y (+ 1 (* -1/2 (/ x (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6)))))))
(* (pow y 2) (+ 1 (* -1 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 (/ x y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 2) (pow y 2))) (* -1/2 x)) y))) y)) 1)))
(* -1 (* y (+ 1 (* -1/2 (/ x (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6))))))))
(* -1 (* y (- (* 1/2 (/ x (pow y 2))) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	((- x (sqrt (+ (* y y) (neg x)))) (sqrt (+ (* y y) (neg x))) (+ (* y y) (neg x)) (neg x) (- x (sqrt (- (pow y 2) x))) (neg y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (* y y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (+ (* (/ x y) -1/2) y) (/ x y))
1.0ms	x	@	inf	((- x (sqrt (+ (* y y) (neg x)))) (sqrt (+ (* y y) (neg x))) (+ (* y y) (neg x)) (neg x) (- x (sqrt (- (pow y 2) x))) (neg y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (* y y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (+ (* (/ x y) -1/2) y) (/ x y))
1.0ms	y	@	inf	((- x (sqrt (+ (* y y) (neg x)))) (sqrt (+ (* y y) (neg x))) (+ (* y y) (neg x)) (neg x) (- x (sqrt (- (pow y 2) x))) (neg y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (* y y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (+ (* (/ x y) -1/2) y) (/ x y))
1.0ms	x	@	-inf	((- x (sqrt (+ (* y y) (neg x)))) (sqrt (+ (* y y) (neg x))) (+ (* y y) (neg x)) (neg x) (- x (sqrt (- (pow y 2) x))) (neg y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (* y y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (+ (* (/ x y) -1/2) y) (/ x y))
1.0ms	y	@	0	((- x (sqrt (+ (* y y) (neg x)))) (sqrt (+ (* y y) (neg x))) (+ (* y y) (neg x)) (neg x) (- x (sqrt (- (pow y 2) x))) (neg y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (- (pow y 2) x) (* y y) (- x (sqrt (- (pow y 2) x))) (sqrt (- (pow y 2) x)) (+ (* (/ x y) -1/2) y) (/ x y))

simplify204.0ms (7.2%)

Memory

-31.5MiB live, 45.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	254	1218
1	771	1204
2	2676	1157
3	7334	1154
0	8404	1087

Stop Event

1×	iter limit
1×	node limit

Counts

56 → 55

Calls

Call 1

Inputs
(* -1 y)
(- (* x (+ 1 (* 1/2 (/ 1 y)))) y)
(- (* x (+ 1 (+ (* 1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y))))) y)
(- (* x (+ 1 (+ (* 1/2 (/ 1 y)) (* x (+ (* 1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3)))))))) y)
y
(+ y (* -1/2 (/ x y)))
(+ y (* x (- (* -1/8 (/ x (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* x (- (* x (- (* -1/16 (/ x (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(pow y 2)
(+ (* -1 x) (pow y 2))
(* -1 x)
(/ x y)
(* x (- 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* -1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1))))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (- (+ 1 (* 1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3))))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (- (+ 1 (* -1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5))))) (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* (sqrt x) (sqrt -1))
(* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ (pow y 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* x (- (/ (pow y 2) x) 1))
(* -1/2 (/ x y))
(* x (- (/ y x) (* 1/2 (/ 1 y))))
(* x (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))
(* -1 (* x (- (* -1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (+ 1 (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ 1 (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (- (* -1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ 1 (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))))
(* -1 (* (sqrt x) (sqrt -1)))
(* -1 (* x (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (* (pow y 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (* (pow y 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (* (pow y 2) (sqrt -1)))) (* (sqrt (/ 1 x)) (sqrt -1)))))))
(* -1 (* x (+ 1 (* -1 (/ (pow y 2) x)))))
(* -1 (* x (+ (* -1 (/ y x)) (* 1/2 (/ 1 y)))))
(- x (* (sqrt x) (sqrt -1)))
(- (+ x (* -1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* 1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(- (+ x (* (pow y 2) (- (* (pow y 2) (- (* -1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1))))))) (* (sqrt x) (sqrt -1)))
(+ (* 1/2 (* (sqrt (/ 1 x)) (/ (pow y 2) (sqrt -1)))) (* (sqrt x) (sqrt -1)))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ (pow y 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt x) (sqrt -1)) (* (pow y 2) (+ (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (sqrt -1)))) (* (pow y 2) (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow x 5))) (/ (pow y 2) (pow (sqrt -1) 5)))))))))
(- (pow y 2) x)
(/ (+ (* -1/2 x) (pow y 2)) y)
(* y (- (/ x y) 1))
(* y (- (+ (* 1/2 (/ x (pow y 2))) (/ x y)) 1))
(* y (- (+ (* 1/8 (/ (pow x 2) (pow y 4))) (/ x y)) (+ 1 (* -1/2 (/ x (pow y 2))))))
(* y (+ 1 (* -1/2 (/ x (pow y 2)))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4))))))
(* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6)))))))
(* (pow y 2) (+ 1 (* -1 (/ x (pow y 2)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1/2 (/ x y))) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (/ (pow x 2) (pow y 2))) (* -1/2 x)) y))) y)) 1)))
(* -1 (* y (+ 1 (* -1/2 (/ x (pow y 2))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (* -1/8 (/ (pow x 2) (pow y 4)))))))
(* -1 (* y (+ 1 (+ (* -1/2 (/ x (pow y 2))) (+ (* -1/8 (/ (pow x 2) (pow y 4))) (* -1/16 (/ (pow x 3) (pow y 6))))))))
(* -1 (* y (- (* 1/2 (/ x (pow y 2))) 1)))

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

rewrite136.0ms (4.8%)

Memory

48.9MiB live, 48.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	133
0	39	133
1	167	133
2	1089	133
0	8586	133

Stop Event

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

Counts

17 → 456

Calls

Call 1

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

Outputs
(.f64 (neg.f64 (-.f64 (.f64 x x) (fma.f64 y y (neg.f64 x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))))
(*.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))))
(.f64 (-.f64 (.f64 x x) (fma.f64 y y (neg.f64 x))) (pow.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x) #s(literal -1 binary64)))
(*.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x)))))
(.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (-.f64 (fma.f64 y y (neg.f64 x)) (.f64 x (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x)))))))))
(*.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))) (pow.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))) #s(literal -1 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))) #s(literal -1 binary64))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))) (.f64 (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)))) (+.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))) (.f64 (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))))) (+.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))))
(/.f64 (-.f64 (fma.f64 y y (neg.f64 x)) (*.f64 x x)) (-.f64 (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x)))) x))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) #s(literal 3 binary64)) (pow.f64 (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (fma.f64 (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (.f64 (/.f64 (*.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (/.f64 (fma.f64 y y (neg.f64 x)) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (*.f64 (/.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (/.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))))))
(/.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (+.f64 (fma.f64 y y (neg.f64 x)) (-.f64 (.f64 x x) (.f64 (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x)))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 y y (neg.f64 x))))) (neg.f64 (neg.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 x x (fma.f64 y y (neg.f64 x))) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 4 binary64)) (+.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 2 binary64)) (.f64 (.f64 x x) (fma.f64 y y (neg.f64 x))))) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 9 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 9/2 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3 binary64)) (pow.f64 (*.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x) #s(literal 3 binary64)))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)) (.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x) (fma.f64 y y (neg.f64 x)))) (.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))) (.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)))) (*.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))))
(/.f64 (neg.f64 (-.f64 (*.f64 x x) (fma.f64 y y (neg.f64 x)))) (neg.f64 (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (-.f64 (fma.f64 y y (neg.f64 x)) (*.f64 x (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x)))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)))) (neg.f64 (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x))))))
(/.f64 (-.f64 (*.f64 x x) (fma.f64 y y (neg.f64 x))) (+.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x)))))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 x x (-.f64 (fma.f64 y y (neg.f64 x)) (*.f64 x (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))))))) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))) (fma.f64 x x (-.f64 (fma.f64 y y (neg.f64 x)) (*.f64 x (neg.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))))))))
(/.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (neg.f64 x)) #s(literal 3/2 binary64))) (fma.f64 x x (fma.f64 (sqrt.f64 (fma.f64 y y (neg.f64 x))) x (fma.f64 y y (neg.f64 x)))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 y y (neg.f64 x))) x)
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(*.f64 (pow.f64 y #s(literal -1 binary64)) x)
(*.f64 #s(literal 1 binary64) (/.f64 x y))
(*.f64 (/.f64 x y) #s(literal 1 binary64))
(*.f64 (neg.f64 x) (/.f64 #s(literal -1 binary64) y))
(*.f64 x (pow.f64 y #s(literal -1 binary64)))
(pow.f64 (/.f64 y x) #s(literal -1 binary64))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 y x) #s(literal -2 binary64))) (+.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) y)))
(/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 (neg.f64 x) y) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (/.f64 y x) #s(literal -2 binary64)) (*.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) y)))))
(/.f64 (neg.f64 (/.f64 x #s(literal 1 binary64))) (neg.f64 y))
(/.f64 (.f64 (.f64 (neg.f64 x) x) #s(literal 1 binary64)) (*.f64 x (neg.f64 y)))
(/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1 binary64)) (.f64 (fma.f64 x x #s(literal 0 binary64)) (neg.f64 y)))
(/.f64 (-.f64 (.f64 #s(literal 0 binary64) (neg.f64 y)) (.f64 (neg.f64 y) x)) (*.f64 (neg.f64 y) (neg.f64 y)))
(/.f64 (/.f64 x #s(literal 1 binary64)) y)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 y x)))
(/.f64 #s(literal 1 binary64) (/.f64 y (/.f64 x #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 y x))))
(/.f64 #s(literal 1 binary64) (/.f64 y x))
(/.f64 (neg.f64 x) (neg.f64 y))
(/.f64 x y)
(neg.f64 (/.f64 (neg.f64 x) y))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 x) y))
(exp.f64 (*.f64 (log.f64 (/.f64 y x)) #s(literal -1 binary64)))
(+.f64 #s(literal 0 binary64) (/.f64 x y))

eval84.0ms (3%)

Memory: -26.7MiB live, 50.7MiB allocated
Compiler: Compiled 16 649 to 2 027 computations (87.8% saved)

prune12.0ms (0.4%)

Memory

21.7MiB live, 21.7MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	523	2	525
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	524	8	532

Accuracy

100.0%

Counts

532 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
	55.5%	(/.f64 (-.f64 (*.f64 x x) #s(approx (- (pow y 2) x) (neg.f64 x))) (+.f64 (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))) x))
	99.5%	(-.f64 x (/.f64 (-.f64 (.f64 y y) x) (sqrt.f64 (-.f64 (.f64 y y) x))))
✓	99.9%	(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))
✓	48.0%	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y))))
✓	55.9%	(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))
✓	47.7%	(-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y)))
	55.6%	(.f64 (neg.f64 (-.f64 (.f64 x x) #s(approx (- (pow y 2) x) (neg.f64 x)))) (/.f64 #s(literal 1 binary64) (neg.f64 (+.f64 (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))) x))))
✓	47.0%	#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Compiler

Compiled 292 to 128 computations (56.2% saved)

regimes11.0ms (0.4%)

Memory

8.9MiB live, 8.9MiB allocated

Counts

10 → 1

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))

Calls

4 calls:

3.0ms	(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
3.0ms	x
3.0ms	y
2.0ms	(pow.f64 y #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))`
100.0%	1	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 13 to 15 computations (-15.4% saved)

regimes10.0ms (0.3%)

Memory

8.3MiB live, 8.3MiB allocated

Counts

8 → 1

Calls

Call 1

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

Outputs
(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
99.9%	1	`x`
99.9%	1	`y`
99.9%	1	`(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))`
99.9%	1	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 13 to 15 computations (-15.4% saved)

regimes7.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated

Counts

4 → 2

Calls

Call 1

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

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

Calls

4 calls:

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

Results

Accuracy	Segments	Branch
78.5%	2	`x`
87.9%	2	`y`
63.8%	2	`(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))`
87.9%	2	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 13 to 15 computations (-15.4% saved)

regimes3.0ms (0.1%)

Memory

3.2MiB live, 3.2MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

2 calls:

1.0ms	y
1.0ms	(pow.f64 y #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
87.5%	2	`y`
87.5%	2	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 4 to 6 computations (-50% saved)

regimes3.0ms (0.1%)

Memory

3.0MiB live, 3.0MiB allocated

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))
(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))

Outputs
(-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x))))
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Calls

2 calls:

1.0ms	y
1.0ms	(pow.f64 y #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
87.4%	2	`y`
87.4%	2	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 4 to 6 computations (-50% saved)

regimes9.0ms (0.3%)

Memory

-82.4MiB live, 5.8MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Outputs
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Calls

4 calls:

6.0ms	y
1.0ms	(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
1.0ms	x
1.0ms	(pow.f64 y #s(literal 2 binary64))

Results

Accuracy	Segments	Branch
47.0%	1	`(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))`
47.0%	1	`x`
47.0%	1	`y`
47.0%	1	`(pow.f64 y #s(literal 2 binary64))`

Compiler

Compiled 13 to 15 computations (-15.4% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.004264603805444e-224	2.494479077218932e-218

Compiler

Compiled 11 to 12 computations (-9.1% saved)

bsearch0.0ms (0%)

Memory

0.1MiB live, 0.1MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.004264603805444e-224	2.494479077218932e-218

Compiler

Compiled 11 to 12 computations (-9.1% saved)

bsearch0.0ms (0%)

Memory

0.2MiB live, 0.2MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.004264603805444e-224	2.494479077218932e-218

Compiler

Compiled 11 to 12 computations (-9.1% saved)

simplify61.0ms (2.1%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	116
1	57	116
2	82	116
3	111	116
4	146	116
5	201	116
6	306	116
7	751	116
8	2139	116
9	6586	116

Stop Event

1×	node limit

Calls

Call 1

Inputs
(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) (-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y)))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) #s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y)))
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

Outputs
(-.f64 x (sqrt.f64 (-.f64 (pow.f64 y #s(literal 2 binary64)) x)))
(-.f64 x (sqrt.f64 (fma.f64 y y (neg.f64 x))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) (-.f64 x #s(approx (sqrt (- (pow y 2) x)) (fma.f64 (/.f64 x y) #s(literal -1/2 binary64) y))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (*.f64 y y)))))
(if (<=.f64 (pow.f64 y #s(literal 2 binary64)) #s(literal 2604693137843693/26046931378436930758124421057504913270096712196546516251547882077203270460225125279380594534654508948214569963255598595491753131461403769845169359579417304867559209294976619368996399554343023534097519594280807038990979484521392426918608896 binary64)) (-.f64 x (sqrt.f64 #s(approx (- (pow y 2) x) (neg.f64 x)))) #s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y)))
#s(approx (- x (sqrt (- (pow y 2) x))) (neg.f64 y))

soundness368.0ms (13%)

Memory

5.5MiB live, 5.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	22
0	11	22
1	48	22
2	325	22
3	3720	22
0	8588	22
0	242	1172
1	738	1158
2	2570	1111
3	7098	1108
0	8129	1043

Stop Event

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

Compiler

Compiled 165 to 78 computations (52.7% saved)

preprocess35.0ms (1.2%)

Memory: 25.2MiB live, 25.2MiB allocated
Remove: (abs y)
Compiler: Compiled 280 to 112 computations (60% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

x - sqrt(pow(y, 2) - x)

start0.0ms (0%)

analyze25.0ms (0.9%)

sample1.1s (40.4%)

explain106.0ms (3.7%)

preprocess30.0ms (1.1%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify9.0ms (0.3%)

localize20.0ms (0.7%)

series8.0ms (0.3%)

simplify251.0ms (8.9%)

rewrite138.0ms (4.9%)

eval35.0ms (1.2%)

prune27.0ms (1%)

simplify39.0ms (1.4%)

localize47.0ms (1.6%)

series10.0ms (0.3%)

simplify204.0ms (7.2%)

rewrite136.0ms (4.8%)

eval84.0ms (3%)

prune12.0ms (0.4%)

regimes11.0ms (0.4%)

regimes10.0ms (0.3%)

regimes7.0ms (0.2%)

regimes3.0ms (0.1%)

regimes3.0ms (0.1%)

regimes9.0ms (0.3%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify61.0ms (2.1%)

soundness368.0ms (13%)

preprocess35.0ms (1.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	19	48
1	42	42
2	109	41
3	265	41
4	458	41
5	533	41
6	571	41
7	593	41
8	607	41
0	7	8
0	11	8
1	16	8
2	24	8
3	36	8
4	54	8
5	94	8
6	143	8
7	210	8
8	256	8
9	269	8
0	269	8

Iter	Nodes	Cost
0	7	25
0	11	25
1	16	25
2	24	25
3	36	25
4	54	25
5	94	25
6	143	25
7	210	25
8	256	25
9	269	25
0	269	25

Iter	Nodes	Cost
0	19	48
1	42	42
2	109	41
3	265	41
4	458	41
5	533	41
6	571	41
7	593	41
8	607	41
0	7	8
0	11	8
1	16	8
2	24	8
3	36	8
4	54	8
5	94	8
6	143	8
7	210	8
8	256	8
9	269	8
0	269	8

Iter	Nodes	Cost
0	7	25
0	11	25
1	16	25
2	24	25
3	36	25
4	54	25
5	94	25
6	143	25
7	210	25
8	256	25
9	269	25
0	269	25

Iter	Nodes	Cost
0	19	48
1	42	42
2	109	41
3	265	41
4	458	41
5	533	41
6	571	41
7	593	41
8	607	41
0	7	8
0	11	8
1	16	8
2	24	8
3	36	8
4	54	8
5	94	8
6	143	8
7	210	8
8	256	8
9	269	8
0	269	8

Iter	Nodes	Cost
0	7	25
0	11	25
1	16	25
2	24	25
3	36	25
4	54	25
5	94	25
6	143	25
7	210	25
8	256	25
9	269	25
0	269	25