Metrics for sqrt(x*x-y*y)

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze44.0ms (1%)

Memory

16.7MiB live, 16.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
23.1%	18.7%	62.4%	0.1%	0%	18.7%	0%	5
28%	21.9%	56.2%	0.1%	0%	21.9%	0%	6
48.8%	32.8%	34.3%	0.1%	0%	32.8%	0%	7
54.2%	35.1%	29.7%	0.1%	0%	35.1%	0%	8
70.2%	41.4%	17.6%	0.1%	0%	41%	0%	9
73.9%	42.5%	15%	0.1%	0%	42.3%	0%	10
83.4%	45.5%	9.1%	0.1%	0%	45.4%	0%	11
85.8%	46.1%	7.7%	0.1%	0%	46.1%	0%	12

Compiler

Compiled 24 to 16 computations (33.3% saved)

sample1.5s (34.3%)

Memory

44.5MiB live, 777.7MiB allocated

Samples

751.0ms	8 256×	0	valid
209.0ms	599×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 666.0ms

ival-mult: 241.0ms (36.2% of total)

ival-sub: 147.0ms (22.1% of total)

ival-<=: 128.0ms (19.2% of total)

ival-sqrt: 94.0ms (14.1% of total)

ival-and: 33.0ms (5% of total)

exact: 15.0ms (2.3% of total)

ival-assert: 8.0ms (1.2% of total)

Bogosity

explain244.0ms (5.5%)

Memory

-17.4MiB live, 145.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
129	-	-	`(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))`
17	-	-	`(-.f64 (.f64 x x) (.f64 y y))`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))`	oflow-rescue	118	0
↳	`(*.f64 y y)`	overflow	17
↳	`(-.f64 (.f64 x x) (.f64 y y))`	overflow	118
↳	`(*.f64 x x)`	overflow	118
`-.f64`	`(-.f64 (.f64 x x) (.f64 y y))`	nan-rescue	17	0
↳	`(*.f64 x x)`	overflow	118
↳	`(*.f64 y y)`	overflow	17
`sqrt.f64`	`(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))`	uflow-rescue	11	0
↳	`(*.f64 y y)`	underflow	103
↳	`(-.f64 (.f64 x x) (.f64 y y))`	underflow	11
↳	`(*.f64 x x)`	underflow	11

Confusion

	Predicted +	Predicted -
+	129	0
-	0	127

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	129	0	0
-	0	0	127

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	127
1	112
2	17

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

96.0ms

512×

valid

Compiler

Compiled 58 to 22 computations (62.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 80.0ms

ival-sub: 67.0ms (83.5% of total)

ival-mult: 8.0ms (10% of total)

ival-sqrt: 4.0ms (5% of total)

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

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

preprocess437.0ms (9.9%)

Memory

52.4MiB live, 52.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	54	42
2	128	42
3	330	42
4	937	42
5	1395	42
6	2075	42
7	2951	42
8	3779	42
9	4245	42
10	4349	42
11	4395	42
12	4413	42
13	6675	42
14	7376	42
0	6	8
0	10	8
1	18	8
2	29	8
3	55	8
4	115	8
5	319	8
6	591	8
7	1294	8
8	2595	8
9	4278	8
10	5106	8
11	5475	8
12	5705	8
13	5819	8
14	5819	8
15	6779	8
16	6939	8
17	7259	8
18	7259	8
19	7659	8
20	7819	8
21	7899	8
22	7899	8
23	7899	8
0	10497	8

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))

Outputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
(sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))

Symmetry

(abs y)

(abs x)

Compiler

Compiled 8 to 6 computations (25% 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
▶	52.4%	(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify408.0ms (9.3%)

Memory

-31.1MiB live, 47.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 y y)
cost-diff	0	(*.f64 x x)
cost-diff	0	(-.f64 (.f64 x x) (.f64 y y))
cost-diff	0	(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	23
0	10	23
1	18	23
2	29	23
3	55	23
4	115	23
5	319	23
6	591	23
7	1294	23
8	2595	23
9	4278	23
10	5106	23
11	5475	23
12	5705	23
13	5819	23
14	5819	23
15	6779	23
16	6939	23
17	7259	23
18	7259	23
19	7659	23
20	7819	23
21	7899	23
22	7899	23
23	7899	23
0	10497	23

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y

Outputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
(sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 (-.f64 x y) (+.f64 y x))
(*.f64 x x)
x
(*.f64 y y)
y

localize19.0ms (0.4%)

Memory

7.3MiB live, 7.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	3.3906250000000004	(-.f64 (.f64 x x) (.f64 y y))
accuracy	30.087634117593502	(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))

Samples

14.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 7.0ms

ival-mult: 4.0ms (55.8% of total)

ival-sqrt: 2.0ms (27.9% of total)

ival-sub: 1.0ms (13.9% of total)

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

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

series6.0ms (0.1%)

Memory

2.6MiB live, 2.6MiB allocated

Counts

4 → 29

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(*.f64 y y)

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

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	((sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	inf	((sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	inf	((sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* x x) (* y y))
1.0ms	y	@	0	((sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* x x) (* y y))
1.0ms	x	@	-inf	((sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* x x) (* y y))

simplify204.0ms (4.6%)

Memory

-29.6MiB live, 47.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	119	537
1	332	537
2	1153	524
3	4633	506
0	8289	471

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 28

Calls

Call 1

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

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

rewrite165.0ms (3.7%)

Memory

56.2MiB live, 56.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9388	21

Stop Event

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

Counts

4 → 326

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
(-.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
(*.f64 y y)

Outputs
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 2 binary64))))) (sqrt.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64))))) (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)) (pow.f64 (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 2 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (*.f64 y x) #s(literal 2 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (pow.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y x) #s(literal 2 binary64))) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 y y (.f64 x x))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 y y (.f64 x x))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (pow.f64 (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (pow.f64 (pow.f64 (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (hypot.f64 y x) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))
(.f64 (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(.f64 (pow.f64 (.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/4 binary64)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (-.f64 x y) (+.f64 y x))))
(.f64 (hypot.f64 y x) (sqrt.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (fma.f64 y y (*.f64 x x)))))
(.f64 (hypot.f64 y x) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)))))
(.f64 (hypot.f64 y x) (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (fma.f64 y y (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 y x) (pow.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (hypot.f64 y x) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))))
(.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 (.f64 (-.f64 x y) (+.f64 y x)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (+.f64 y x)))
(*.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (-.f64 x y)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (*.f64 (-.f64 x y) (+.f64 y x)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (neg.f64 (neg.f64 (hypot.f64 y x))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (neg.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (hypot.f64 y x))))
(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 y x))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 y x))) (sqrt.f64 (+.f64 y x)))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (-.f64 x y))) (sqrt.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)))) (hypot.f64 (.f64 y y) (.f64 x x)))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal -1 binary64)))) (sqrt.f64 (+.f64 (+.f64 (pow.f64 (*.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 18 binary64)) (pow.f64 y #s(literal 18 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))) (hypot.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (.f64 y x) #s(literal 3 binary64))))
(/.f64 (sqrt.f64 (.f64 (-.f64 x y) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y (-.f64 y x) (.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (-.f64 x y) (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (-.f64 x y)))
(/.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (fma.f64 y (+.f64 y x) (.f64 x x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 y x) (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (+.f64 y x)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (*.f64 x x))))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (*.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 y y (*.f64 x x))))))
(/.f64 (sqrt.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))))) (sqrt.f64 (neg.f64 (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (.f64 (fma.f64 y (+.f64 y x) (.f64 x x)) (fma.f64 y (-.f64 y x) (.f64 x x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))) (.f64 (-.f64 x y) (+.f64 y x)))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (.f64 (.f64 (-.f64 x y) (+.f64 y x)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (.f64 (+.f64 y x) (fma.f64 y (-.f64 y x) (.f64 x x)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (.f64 (-.f64 x y) (+.f64 y x)))) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
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(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))))))
(-.f64 (/.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))) (/.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 3 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 y y (.f64 x x)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))))
(-.f64 (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))) (/.f64 (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal 2 binary64))))
(-.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (pow.f64 y #s(literal 8 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (.f64 (fma.f64 y y (.f64 x x)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (/.f64 (pow.f64 y #s(literal 12 binary64)) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64))))) (/.f64 (pow.f64 y #s(literal 18 binary64)) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64))))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 y y (.f64 x x)))) (/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) (neg.f64 (fma.f64 y y (.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 8 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 8 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64)))) (fma.f64 y y (.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 y y (.f64 x x))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 4 binary64)) (pow.f64 y #s(literal 8 binary64))) (pow.f64 x #s(literal 8 binary64)))) (fma.f64 y y (.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))) (/.f64 (/.f64 (pow.f64 y #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (neg.f64 (pow.f64 (.f64 y x) #s(literal 2 binary64)))))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (/.f64 (pow.f64 y #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (.f64 (fma.f64 y (-.f64 y x) (.f64 x x)) (fma.f64 y (+.f64 y x) (.f64 x x)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 y #s(literal 12 binary64)) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (/.f64 (pow.f64 y #s(literal 18 binary64)) (+.f64 (+.f64 (pow.f64 (.f64 y x) #s(literal 6 binary64)) (pow.f64 y #s(literal 12 binary64))) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))))) (/.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))))))
(-.f64 (fma.f64 x x #s(literal 0 binary64)) (*.f64 y y))
(-.f64 #s(literal 0 binary64) (-.f64 (.f64 y y) (.f64 x x)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(-.f64 (.f64 x x) (.f64 y y))
(exp.f64 (.f64 (neg.f64 (log.f64 (.f64 (-.f64 x y) (+.f64 y x)))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (*.f64 (-.f64 x y) (+.f64 y x))))
(+.f64 (.f64 y (-.f64 x y)) (.f64 x (-.f64 x y)))
(+.f64 (.f64 x (-.f64 x y)) (.f64 y (-.f64 x y)))
(+.f64 (.f64 x (+.f64 y x)) (.f64 (neg.f64 y) (+.f64 y x)))
(+.f64 (.f64 (-.f64 x y) y) (.f64 (-.f64 x y) x))
(+.f64 (.f64 (-.f64 x y) x) (.f64 (-.f64 x y) y))
(+.f64 (.f64 (+.f64 y x) x) (.f64 (+.f64 y x) (neg.f64 y)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 y y (.f64 x x))) (neg.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (fma.f64 y y (.f64 x x)))))
(+.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (.f64 y y) (pow.f64 x #s(literal 4 binary64))))))
(+.f64 (.f64 (neg.f64 y) y) (.f64 x x))
(+.f64 (.f64 x x) (.f64 (neg.f64 y) y))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (neg.f64 y) (neg.f64 y))
(*.f64 y y)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(pow.f64 (neg.f64 y) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval139.0ms (3.2%)

Memory: -113.3MiB live, 28.0MiB allocated
Compiler: Compiled 10 580 to 1 299 computations (87.7% saved)

prune7.0ms (0.2%)

Memory

14.2MiB live, 14.2MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	346	5	351
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	347	5	352

Accuracy

100.0%

Counts

352 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.2%	(*.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (+.f64 y x)))
▶	53.0%	(sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))
▶	1.2%	(sqrt.f64 #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)))
▶	99.5%	#s(approx (sqrt (- (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x))
▶	1.0%	#s(approx (sqrt (- (* x x) (* y y))) (neg.f64 x))

Compiler

Compiled 116 to 82 computations (29.3% saved)

simplify134.0ms (3.1%)

Memory

31.0MiB live, 31.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	130
0	39	130
1	67	130
2	105	130
3	193	130
4	336	130
5	650	130
6	1668	130
7	3453	130
8	6488	130
0	8108	130

Stop Event

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

Calls

Call 1

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

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

localize82.0ms (1.9%)

Memory

-54.6MiB live, 30.6MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(sqrt.f64 (-.f64 x y))
accuracy	0.0078125	(sqrt.f64 (+.f64 y x))
accuracy	0.4921875	(*.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (+.f64 y x)))
accuracy	0.0	(-.f64 x y)
accuracy	0.0	(+.f64 y x)
accuracy	0.0	(*.f64 (-.f64 x y) (+.f64 y x))
accuracy	30.087634117593502	(sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))
accuracy	0.0	(*.f64 (neg.f64 y) y)
accuracy	0.0	(neg.f64 y)
accuracy	30.087634117593502	(sqrt.f64 #s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y)))
accuracy	60.17171994881486	#s(approx (- (* x x) (* y y)) (*.f64 (neg.f64 y) y))
accuracy	0.0	(neg.f64 x)
accuracy	63.344214273514865	#s(approx (sqrt (- (* x x) (* y y))) (neg.f64 x))
accuracy	0.0	(fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x)
accuracy	0.0	(/.f64 #s(literal -1/2 binary64) x)
accuracy	0.203125	(*.f64 (/.f64 #s(literal -1/2 binary64) x) y)
accuracy	0.3409668146778256	#s(approx (sqrt (- (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x))

Samples

68.0ms

256×

valid

Compiler

Compiled 111 to 23 computations (79.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-mult: 16.0ms (47.9% of total)

ival-sqrt: 7.0ms (20.9% of total)

ival-add: 3.0ms (9% of total)

ival-neg: 3.0ms (9% of total)

ival-div: 2.0ms (6% of total)

ival-sub: 2.0ms (6% of total)

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

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

exact: 0.0ms (0% of total)

series27.0ms (0.6%)

Memory

10.2MiB live, 10.2MiB allocated

Counts

17 → 119

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
6.0ms	y	@	-inf	((sqrt (- (* x x) (* y y))) (+ (* (* (/ -1/2 x) y) y) x) (* (/ -1/2 x) y) (/ -1/2 x) (sqrt (- (* x x) (* y y))) (neg x) (sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* (neg y) y) (neg y) (sqrt (* (- x y) (+ y x))) (* (- x y) (+ y x)) (- x y) (+ y x) (* (sqrt (- x y)) (sqrt (+ y x))) (sqrt (- x y)) (sqrt (+ y x)))
5.0ms	x	@	inf	((sqrt (- (* x x) (* y y))) (+ (* (* (/ -1/2 x) y) y) x) (* (/ -1/2 x) y) (/ -1/2 x) (sqrt (- (* x x) (* y y))) (neg x) (sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* (neg y) y) (neg y) (sqrt (* (- x y) (+ y x))) (* (- x y) (+ y x)) (- x y) (+ y x) (* (sqrt (- x y)) (sqrt (+ y x))) (sqrt (- x y)) (sqrt (+ y x)))
4.0ms	y	@	inf	((sqrt (- (* x x) (* y y))) (+ (* (* (/ -1/2 x) y) y) x) (* (/ -1/2 x) y) (/ -1/2 x) (sqrt (- (* x x) (* y y))) (neg x) (sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* (neg y) y) (neg y) (sqrt (* (- x y) (+ y x))) (* (- x y) (+ y x)) (- x y) (+ y x) (* (sqrt (- x y)) (sqrt (+ y x))) (sqrt (- x y)) (sqrt (+ y x)))
4.0ms	x	@	-inf	((sqrt (- (* x x) (* y y))) (+ (* (* (/ -1/2 x) y) y) x) (* (/ -1/2 x) y) (/ -1/2 x) (sqrt (- (* x x) (* y y))) (neg x) (sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* (neg y) y) (neg y) (sqrt (* (- x y) (+ y x))) (* (- x y) (+ y x)) (- x y) (+ y x) (* (sqrt (- x y)) (sqrt (+ y x))) (sqrt (- x y)) (sqrt (+ y x)))
4.0ms	x	@	0	((sqrt (- (* x x) (* y y))) (+ (* (* (/ -1/2 x) y) y) x) (* (/ -1/2 x) y) (/ -1/2 x) (sqrt (- (* x x) (* y y))) (neg x) (sqrt (- (* x x) (* y y))) (- (* x x) (* y y)) (* (neg y) y) (neg y) (sqrt (* (- x y) (+ y x))) (* (- x y) (+ y x)) (- x y) (+ y x) (* (sqrt (- x y)) (sqrt (+ y x))) (sqrt (- x y)) (sqrt (+ y x)))

simplify133.0ms (3%)

Memory

36.8MiB live, 36.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	576	2603
1	1872	2171
2	7730	2168
0	8090	2035

Stop Event

1×	iter limit
1×	node limit

Counts

119 → 117

Calls

Call 1

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

Outputs
(* y (sqrt -1))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) y)
(+ (* 1/2 (/ (pow x 2) (* y (sqrt -1)))) (* y (sqrt -1)))
(fma.f64 (.f64 (/.f64 x (.f64 (sqrt.f64 #s(literal -1 binary64)) y)) #s(literal 1/2 binary64)) x (*.f64 (sqrt.f64 #s(literal -1 binary64)) y))
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(* -1/2 (/ (pow y 2) x))
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(/ (+ (* -1/2 (pow y 2)) (pow x 2)) x)
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(*.f64 (neg.f64 y) y)
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(sqrt y)
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x
(* x (+ 1 (* -1/2 (/ (pow y 2) (pow x 2)))))
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x
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(.f64 (fma.f64 (/.f64 (.f64 (neg.f64 y) y) (*.f64 x x)) #s(literal 1/2 binary64) #s(literal 1 binary64)) x)
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(* -1 (* y (+ (sqrt -1) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt -1) 3)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt -1))))))))
(.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (*.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1 binary64)) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 y))
(* -1 (* y (+ (sqrt -1) (+ (* -1/8 (/ (pow x 4) (* (pow y 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (/ (pow x 6) (* (pow y 6) (pow (sqrt -1) 5)))) (* 1/2 (/ (pow x 2) (* (pow y 2) (sqrt -1)))))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 4 binary64))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1 binary64))) (+.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 y y)) (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal 1/16 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 y))
(* -1 (* y (+ (sqrt -1) (* -1/2 (/ (+ x (* -1 x)) (* y (sqrt -1)))))))
(neg.f64 (fma.f64 (sqrt.f64 #s(literal -1 binary64)) y (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* y (+ (sqrt -1) (* -1 (/ (+ (* -1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) (* y (sqrt -1)))) (* 1/2 (/ (+ x (* -1 x)) (sqrt -1)))) y)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (fma.f64 (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (/.f64 x y)) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) y)) (neg.f64 y))
(* -1 (* y (+ (sqrt -1) (* -1 (/ (+ (* -1 (/ (+ (* 1/4 (/ (* (+ x (* -1 x)) (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2))))) (* y (pow (sqrt -1) 3)))) (* 1/2 (/ (- (pow x 2) (* 1/4 (/ (pow (+ x (* -1 x)) 2) (pow (sqrt -1) 2)))) (sqrt -1)))) y)) (* 1/2 (/ (+ x (* -1 x)) (sqrt -1)))) y)))))
(.f64 (-.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 (-.f64 (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (fma.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64) (/.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64)))) y)) y)) (neg.f64 y))
(* (pow y 2) (- (* -1 (/ (+ x (* -1 x)) y)) 1))
(*.f64 (neg.f64 y) y)
(* (pow y 2) (- (* -1 (/ (+ x (+ (* -1 x) (* -1 (/ (pow x 2) y)))) y)) 1))
(.f64 (-.f64 #s(literal -1 binary64) (/.f64 (/.f64 (.f64 (neg.f64 x) x) y) y)) (*.f64 y y))
(* -1 (* y (+ 1 (* -1 (/ x y)))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 x y)) (neg.f64 y))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(fma.f64 (/.f64 (neg.f64 x) y) (neg.f64 y) y)
(* -1 (* (sqrt y) (sqrt -1)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 y))
(* -1 (* y (+ (* 1/2 (* (* x (sqrt -1)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt -1)))))
(.f64 (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64)))) (neg.f64 y))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (sqrt -1)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* (* x (sqrt -1)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt -1))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64))))) (neg.f64 y))
(* -1 (* y (+ (* -1/8 (* (* (pow x 2) (sqrt -1)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (* (pow x 3) (sqrt -1)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* (* x (sqrt -1)) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (sqrt -1)))))))
(.f64 (fma.f64 (.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) x) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal -1 binary64))) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) (sqrt.f64 #s(literal -1 binary64)))))) (neg.f64 y))
(* -1 (* (sqrt y) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 y) #s(literal 1 binary64))
(* -1 (* y (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))) (neg.f64 y))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(.f64 (fma.f64 (.f64 (.f64 x (/.f64 x #s(literal -1 binary64))) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64)))) (neg.f64 y))
(* -1 (* y (+ (* -1/8 (* (/ (pow x 2) (pow (sqrt -1) 2)) (sqrt (/ 1 (pow y 5))))) (+ (* 1/16 (* (/ (pow x 3) (pow (sqrt -1) 4)) (sqrt (/ 1 (pow y 7))))) (+ (* 1/2 (* x (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2)))))))
(.f64 (fma.f64 (.f64 (.f64 x (/.f64 x #s(literal -1 binary64))) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 5 binary64)))) (fma.f64 (/.f64 (.f64 (pow.f64 x #s(literal 3 binary64)) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 7 binary64)))) (fma.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) y)) #s(literal -1 binary64))))) (neg.f64 y))

rewrite186.0ms (4.2%)

Memory

-11.9MiB live, 63.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	115
0	39	114
1	123	114
2	788	114
0	8488	114

Stop Event

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

Counts

17 → 835

Calls

Call 1

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

Outputs
#s(approx (sqrt (- (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x))
(.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y))))
(.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 (neg.f64 x) x))) (/.f64 #s(literal 1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)))
(.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))))))
(.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 (neg.f64 x) x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)))
(.f64 #s(literal 1 binary64) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x))
(.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x) (pow.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))) #s(literal -1 binary64))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))) #s(literal -1 binary64)))
(.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x))))
(pow.f64 (/.f64 #s(literal 1 binary64) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 4 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x))) (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x x)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x))) (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 4 binary64)) (+.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (.f64 (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) x) #s(literal 2 binary64)))))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))) #s(literal -1 binary64))) (-.f64 (pow.f64 (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 9 binary64)) (pow.f64 x #s(literal 9 binary64))) (pow.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))) #s(literal -1 binary64))) (-.f64 (+.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 6 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) x) #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 (neg.f64 x) x)) #s(literal 1 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x)))
(/.f64 (.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x)))) (.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)))) (fma.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (/.f64 #s(literal -1 binary64) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) (fma.f64 (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (.f64 (/.f64 y x) y) x)) (.f64 (/.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) (/.f64 (.f64 (neg.f64 x) x) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)))) (neg.f64 (-.f64 x (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 (neg.f64 x) x)))) (neg.f64 (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x)))
(/.f64 (neg.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 x (-.f64 x (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))))))
(/.f64 (-.f64 (.f64 (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x)) (.f64 x x))) (.f64 (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x)) (fma.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))))
(/.f64 (-.f64 (.f64 x x) (pow.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) #s(literal 2 binary64))) (-.f64 x (.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y)))
(/.f64 (neg.f64 (fma.f64 (pow.f64 (.f64 x #s(literal -2 binary64)) #s(literal -2 binary64)) (pow.f64 y #s(literal 4 binary64)) (.f64 (neg.f64 x) x))) (fma.f64 #s(literal 1/2 binary64) (*.f64 (/.f64 y x) y) x))
(/.f64 (neg.f64 (fma.f64 #s(literal -1/8 binary64) (pow.f64 (.f64 (/.f64 y x) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (fma.f64 x x (.f64 (.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) y) y) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y (neg.f64 x))))))
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(*.f64 (sqrt.f64 (-.f64 x y)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (-.f64 x y)) #s(literal 1 binary64))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 x y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 y x))))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (.f64 (+.f64 y x) (-.f64 x y))) (pow.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (-.f64 x y))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (-.f64 x y) (-.f64 x y)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (-.f64 x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (neg.f64 y) #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (neg.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))) (neg.f64 (sqrt.f64 (+.f64 y x))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (+.f64 y x) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (neg.f64 (+.f64 y x))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (.f64 (+.f64 y x) (fma.f64 y y (.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (.f64 (+.f64 y x) (fma.f64 (.f64 y y) (fma.f64 y y (*.f64 x x)) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (neg.f64 y) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 x x (*.f64 (neg.f64 y) (-.f64 (neg.f64 y) x)))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (neg.f64 y) #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (+.f64 y x) x (*.f64 y y))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 (neg.f64 y) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 y x)) (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 x y))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (+.f64 y x)))
(sqrt.f64 (-.f64 x y))
(exp.f64 (-.f64 (.f64 (log.f64 (.f64 (+.f64 y x) (-.f64 x y))) #s(literal 1/2 binary64)) (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64))))
(exp.f64 (*.f64 (log.f64 (-.f64 x y)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y x))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 y y))) (sqrt.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (.f64 y y))) (pow.f64 (pow.f64 (-.f64 y x) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 x y) x (.f64 y y)))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 (-.f64 x y) x (.f64 y y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (+.f64 y x))) #s(literal 1/2 binary64))
(pow.f64 (*.f64 (+.f64 y x) (+.f64 y x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 y x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (+.f64 y x) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))) (neg.f64 (sqrt.f64 (-.f64 y x))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 3 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 x y) x (*.f64 y y)))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y))) (sqrt.f64 (-.f64 y x)))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y x)) (sqrt.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 x y) x (*.f64 y y))) (hypot.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 y #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (+.f64 y x) #s(literal -1 binary64))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 y x) (-.f64 x y))) (sqrt.f64 (-.f64 x y)))
(sqrt.f64 (+.f64 y x))
(hypot.f64 (pow.f64 y #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)))
(hypot.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 y #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (+.f64 y x)) #s(literal 1/2 binary64)))

eval118.0ms (2.7%)

Memory: 16.8MiB live, 91.8MiB allocated
Compiler: Compiled 28 533 to 3 675 computations (87.1% saved)

prune41.0ms (0.9%)

Memory

-47.8MiB live, 40.5MiB allocated

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	1 113	1	1 114
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 115	4	1 119

Accuracy

100.0%

Counts

1 119 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.2%	(*.f64 (sqrt.f64 (-.f64 x y)) (sqrt.f64 (+.f64 y x)))
✓	53.0%	(sqrt.f64 (*.f64 (-.f64 x y) (+.f64 y x)))
✓	99.5%	#s(approx (sqrt (- (* x x) (* y y))) (fma.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) y) y x))
	99.1%	#s(approx (sqrt (* (- x y) (+ y x))) x)

Compiler

Compiled 120 to 64 computations (46.7% saved)

regimes12.0ms (0.3%)

Memory

11.2MiB live, 11.2MiB allocated

Counts

7 → 1

Calls

Call 1

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

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

Calls

6 calls:

2.0ms	y
2.0ms	x
2.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
2.0ms	(-.f64 (.f64 x x) (.f64 y y))
2.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	1	`y`
99.5%	1	`(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))`
99.5%	1	`(-.f64 (.f64 x x) (.f64 y y))`
99.5%	1	`(*.f64 x x)`
99.5%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

regimes9.0ms (0.2%)

Memory

9.8MiB live, 9.8MiB allocated

Accuracy

Total -63.0b remaining (-10475.6%)

Threshold costs -63b (-10475.6%)

Counts

4 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (* (- x y) (+ y x))) x)

Calls

6 calls:

2.0ms	x
2.0ms	y
2.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))
1.0ms	(-.f64 (.f64 x x) (.f64 y y))
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`(sqrt.f64 (-.f64 (.f64 x x) (.f64 y y)))`
99.1%	1	`(-.f64 (.f64 x x) (.f64 y y))`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`

Compiler

Compiled 23 to 21 computations (8.7% saved)

simplify50.0ms (1.1%)

Memory

11.1MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	32	27
2	58	27
3	119	27
4	241	27
5	602	27
6	1800	27
7	3942	27

Stop Event

1×	node limit

Calls

Call 1

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

Outputs

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

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

#s(approx (sqrt (* (- x y) (+ y x))) x)

soundness404.0ms (9.2%)

Memory

8.3MiB live, 8.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	21
0	10	21
1	36	21
2	239	21
3	2135	21
0	9388	21
0	119	537
1	332	537
2	1153	524
3	4633	506
0	8289	471
0	576	2603
1	1872	2171
2	7730	2168
0	8090	2035

Stop Event

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

Compiler

Compiled 52 to 30 computations (42.3% saved)

preprocess21.0ms (0.5%)

Memory: 15.2MiB live, 15.2MiB allocated
Remove: (abs y)
Compiler: Compiled 274 to 168 computations (38.7% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

sqrt(xx-yy)

start0.0ms (0%)

analyze44.0ms (1%)

sample1.5s (34.3%)

explain244.0ms (5.5%)

preprocess437.0ms (9.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify408.0ms (9.3%)

localize19.0ms (0.4%)

series6.0ms (0.1%)

simplify204.0ms (4.6%)

rewrite165.0ms (3.7%)

eval139.0ms (3.2%)

prune7.0ms (0.2%)

simplify134.0ms (3.1%)

localize82.0ms (1.9%)

series27.0ms (0.6%)

simplify133.0ms (3%)

rewrite186.0ms (4.2%)

eval118.0ms (2.7%)

prune41.0ms (0.9%)

regimes12.0ms (0.3%)

regimes9.0ms (0.2%)

simplify50.0ms (1.1%)

soundness404.0ms (9.2%)

preprocess21.0ms (0.5%)

end0.0ms (0%)

Profiling