Metrics for Optimisation.CirclePacking:place from circle-packing-0.1.0.4, A

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze15.0ms (0.4%)

Memory

12.9MiB live, 12.9MiB 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
25%	25%	74.9%	0.1%	0%	0%	0%	3
28.6%	25%	62.4%	0.1%	0%	12.5%	0%	4
46.2%	37.5%	43.7%	0.1%	0%	18.7%	0%	5
52.2%	37.5%	34.3%	0.1%	0%	28.1%	0%	6
65.1%	43.7%	23.4%	0.1%	0%	32.8%	0%	7
70.9%	43.7%	18%	0.1%	0%	38.2%	0%	8
79.5%	46.8%	12.1%	0.1%	0%	41%	0%	9
83.6%	46.8%	9.2%	0.1%	0%	43.9%	0%	10
88.7%	48.4%	6.1%	0.1%	0%	45.4%	0%	11
91.3%	48.4%	4.6%	0.1%	0%	46.9%	0%	12

Compiler

Compiled 6 to 6 computations (0% saved)

sample934.0ms (21.8%)

Memory

-14.9MiB live, 696.3MiB allocated

Samples

677.0ms	8 256×	0	valid
17.0ms	515×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 321.0ms

ival-sqrt: 160.0ms (49.9% of total)

ival-add: 151.0ms (47.1% of total)

ival-true: 7.0ms (2.2% of total)

ival-assert: 3.0ms (0.9% of total)

Bogosity

explain56.0ms (1.3%)

Memory

-9.5MiB live, 113.7MiB allocated

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(sqrt.f64 (+.f64 x y))`
-	-	`y`
-	-	`(+.f64 x y)`
-	-	`x`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

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

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

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

Precision?

0/0

Recall?

0/0

Samples

19.0ms

512×

valid

Compiler

Compiled 44 to 24 computations (45.5% saved)

Precisions

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

ival-sqrt: 4.0ms (56% of total)

ival-add: 3.0ms (42% of total)

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

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

preprocess15.0ms (0.3%)

Memory

31.7MiB live, 31.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Stop Event

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

Calls

Call 1

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

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

Symmetry

(sort x y)

Compiler

Compiled 4 to 4 computations (0% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 x y))

Compiler

Compiled 4 to 4 computations (0% saved)

simplify2.0ms (0.1%)

Memory

3.9MiB live, 3.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 2 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	9
0	6	9
1	7	9
0	7	9

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize17.0ms (0.4%)

Memory

-9.6MiB live, 29.1MiB allocated

Localize:

Found 2 expressions of interest:

New	Metric	Score	Program
accuracy	0	(+.f64 x y)
accuracy	0.00390625	(sqrt.f64 (+.f64 x y))

Samples

13.0ms

256×

valid

Compiler

Compiled 20 to 10 computations (50% saved)

Precisions

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

ival-sqrt: 4.0ms (53.8% of total)

ival-add: 3.0ms (40.3% of total)

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

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

series5.0ms (0.1%)

Memory

9.7MiB live, 9.7MiB allocated

Counts

2 → 29

Calls

Call 1

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

Outputs
(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))))))))))
y
(+ x y)
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	-inf	((sqrt (+ x y)) (+ x y))
1.0ms	x	@	inf	((sqrt (+ x y)) (+ x y))
1.0ms	y	@	inf	((sqrt (+ x y)) (+ x y))
0.0ms	x	@	0	((sqrt (+ x y)) (+ x y))

simplify227.0ms (5.3%)

Memory

-8.2MiB live, 309.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	583
1	454	553
2	1425	535
3	4629	523
0	8199	487

Stop Event

1×	iter limit
1×	node limit

Counts

29 → 27

Calls

Call 1

Inputs
(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))))))))))
y
(+ x y)
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))

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

rewrite179.0ms (4.2%)

Memory

11.8MiB live, 126.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	7
0	6	7
1	22	7
2	145	7
3	1366	7
0	8310	7

Stop Event

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

Counts

2 → 226

Calls

Call 1

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

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

eval37.0ms (0.9%)

Memory: 2.5MiB live, 38.4MiB allocated
Compiler: Compiled 5 667 to 883 computations (84.4% saved)

prune49.0ms (1.1%)

Memory

-25.1MiB live, 12.4MiB allocated

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	245	2	247
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	245	3	248

Accuracy

100.0%

Counts

248 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.2%	(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
▶	98.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 25 to 19 computations (24% saved)

simplify244.0ms (5.7%)

Memory

-9.0MiB live, 115.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 6 expressions of interest:

New	Metric	Score
cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
cost-diff	192	(fma.f64 #s(literal -1 binary64) x y)
cost-diff	320	(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y))
cost-diff	1408	(/.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))
cost-diff	0	(sqrt.f64 y)
cost-diff	0	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	13	58
0	22	58
1	30	52
2	36	52
3	50	52
4	96	40
5	253	36
6	670	36
7	2105	36
8	4616	36
9	5954	36
10	7057	36
11	7363	36
12	7484	36
0	8205	36

Stop Event

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

Calls

Call 1

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

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

localize71.0ms (1.7%)

Memory

3.4MiB live, 41.4MiB allocated

Localize:

Found 6 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(sqrt.f64 (/.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
accuracy	3.5898437500000004	(fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y))
accuracy	33.22183905858748	(/.f64 (fma.f64 #s(literal -1 binary64) (.f64 x x) (.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))
accuracy	0	(sqrt.f64 y)
accuracy	0.929680515546331	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Samples

24.0ms

256×

valid

Compiler

Compiled 121 to 29 computations (76% saved)

Precisions

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

ival-mult: 6.0ms (37.6% of total)

ival-sqrt: 5.0ms (31.4% of total)

ival-add: 4.0ms (25.1% of total)

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

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.2%)

Memory

13.7MiB live, 13.7MiB allocated

Counts

7 → 41

Calls

Call 1

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

Outputs
(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))))))))))
y
(+ x y)
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(+ y (* -1 x))
(pow x 2)
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* -1 x)
(* x (- (/ y x) 1))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ x y))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (/ x y) 1)))

Calls

6 calls:

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

simplify389.0ms (9.1%)

Memory

-37.5MiB live, 268.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	177	639
1	515	601
2	1619	583
3	5251	571
0	8374	535

Stop Event

1×	iter limit
1×	node limit

Counts

41 → 39

Calls

Call 1

Inputs
(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))))))))))
y
(+ x y)
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(+ y (* -1 x))
(pow x 2)
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* -1 x)
(* x (- (/ y x) 1))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ x y))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (/ x y) 1)))

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

rewrite181.0ms (4.2%)

Memory

5.2MiB live, 199.6MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	51
0	22	51
1	81	29
2	582	29
3	6826	29
0	8980	29

Stop Event

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

Counts

7 → 509

Calls

Call 1

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

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

eval64.0ms (1.5%)

Memory: 9.1MiB live, 125.1MiB allocated
Compiler: Compiled 12 336 to 1 814 computations (85.3% saved)

prune7.0ms (0.2%)

Memory

32.0MiB live, 32.0MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	534	1	535
Fresh	0	0	0
Picked	1	1	2
Done	0	1	1
Total	535	3	538

Accuracy

100.0%

Counts

538 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.5%	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 24 to 19 computations (20.8% saved)

simplify132.0ms (3.1%)

Memory

-10.5MiB live, 147.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(fma.f64 (neg.f64 x) x (*.f64 y y))
cost-diff	0	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
cost-diff	192	(fma.f64 #s(literal -1 binary64) x y)
cost-diff	1536	(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	9	44
0	17	44
1	26	41
2	36	41
3	59	41
4	132	29
5	334	25
6	929	25
7	2596	25
8	5905	25
0	8055	25

Stop Event

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

Calls

Call 1

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

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

localize31.0ms (0.7%)

Memory

-15.6MiB live, 58.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(neg.f64 x)
accuracy	0.00390625	(fma.f64 (neg.f64 x) x (*.f64 y y))
accuracy	0.00390625	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y)))
accuracy	33.22183905858748	(/.f64 (fma.f64 (neg.f64 x) x (*.f64 y y)) (fma.f64 #s(literal -1 binary64) x y))

Samples

22.0ms

256×

valid

Compiler

Compiled 96 to 22 computations (77.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 15.0ms

ival-mult: 8.0ms (53.9% of total)

ival-add: 2.0ms (13.5% of total)

ival-sqrt: 2.0ms (13.5% of total)

ival-div: 1.0ms (6.7% of total)

ival-neg: 1.0ms (6.7% of total)

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

exact: 0.0ms (0% of total)

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

series4.0ms (0.1%)

Memory

9.0MiB live, 9.0MiB allocated

Counts

5 → 40

Calls

Call 1

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

Outputs
y
(+ x y)
(+ y (* -1 x))
(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))))))))))
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(* -1 x)
x
(* x (+ 1 (/ y x)))
(* x (- (/ y x) 1))
(sqrt x)
(* 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 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(* -1 (* (sqrt 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)))))))
(+ (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 (+ 1 (/ x y)))
(* y (+ 1 (* -1 (/ x y))))
(* 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)))))))))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (/ x y) 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
1.0ms	x	@	inf	((/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y)) (+ (* -1 x) y) (sqrt (/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y))) (+ (* (neg x) x) (* y y)) (neg x))
1.0ms	x	@	-inf	((/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y)) (+ (* -1 x) y) (sqrt (/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y))) (+ (* (neg x) x) (* y y)) (neg x))
1.0ms	y	@	-inf	((/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y)) (+ (* -1 x) y) (sqrt (/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y))) (+ (* (neg x) x) (* y y)) (neg x))
1.0ms	y	@	inf	((/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y)) (+ (* -1 x) y) (sqrt (/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y))) (+ (* (neg x) x) (* y y)) (neg x))
1.0ms	x	@	0	((/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y)) (+ (* -1 x) y) (sqrt (/ (+ (* (neg x) x) (* y y)) (+ (* -1 x) y))) (+ (* (neg x) x) (* y y)) (neg x))

simplify232.0ms (5.4%)

Memory

-15.1MiB live, 227.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	177	636
1	515	598
2	1630	580
3	5269	568
0	8397	532

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 38

Calls

Call 1

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

rewrite142.0ms (3.3%)

Memory

2.6MiB live, 158.9MiB allocated

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	9	38
0	17	30
1	66	21
2	487	19
3	5540	17
0	9257	17

Stop Event

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

Counts

5 → 660

Calls

Call 1

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

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

eval55.0ms (1.3%)

Memory: 16.4MiB live, 88.3MiB allocated
Compiler: Compiled 9 115 to 1 422 computations (84.4% saved)

prune6.0ms (0.1%)

Memory

21.7MiB live, 21.7MiB allocated

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	439	1	440
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	440	3	443

Accuracy

100.0%

Counts

443 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.5%	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(approx (+ ( -1 x) y) (-.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify362.0ms (8.4%)

Memory

-12.9MiB live, 229.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	61
0	19	55
1	29	55
2	38	55
3	61	55
4	128	55
5	275	55
6	657	55
7	1443	55
8	3209	55
9	5094	55
10	5832	55
11	5971	55
12	6043	55
13	6087	55
14	6089	55
15	6301	55
16	6579	55
17	6683	55
18	6699	55
19	6703	55
20	6705	55
21	6705	55
0	8911	55

Stop Event

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

Calls

Call 1

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

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

localize32.0ms (0.7%)

Memory

-7.7MiB live, 30.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	#s(approx (+ (* -1 x) y) (-.f64 y x))
accuracy	0.00390625	(fma.f64 (neg.f64 x) x (*.f64 y y))
accuracy	0.00390625	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(approx (+ ( -1 x) y) (-.f64 y x))))
accuracy	33.22183905858748	(/.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(approx (+ ( -1 x) y) (-.f64 y x)))

Samples

24.0ms

256×

valid

Compiler

Compiled 115 to 26 computations (77.4% saved)

Precisions

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

ival-mult: 8.0ms (49.3% of total)

ival-add: 2.0ms (12.3% of total)

ival-sqrt: 2.0ms (12.3% of total)

ival-div: 1.0ms (6.2% of total)

ival-sub: 1.0ms (6.2% of total)

ival-neg: 1.0ms (6.2% of total)

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

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

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.2MiB live, 5.2MiB allocated

Counts

5 → 40

Calls

Call 1

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

Outputs
(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))))))))))
y
(+ x y)
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(* -1 x)
(+ y (* -1 x))
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* x (- (/ y x) 1))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ x y))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (/ x y) 1)))

Calls

6 calls:

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

simplify348.0ms (8.1%)

Memory

-143.7MiB live, 193.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	177	636
1	515	598
2	1622	580
3	5258	568
0	8386	532

Stop Event

1×	iter limit
1×	node limit

Counts

40 → 38

Calls

Call 1

Inputs
(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))))))))))
y
(+ x y)
(pow y 2)
(+ (* -1 (pow x 2)) (pow y 2))
(* -1 x)
(+ y (* -1 x))
(sqrt x)
(* 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))))))
x
(* x (+ 1 (/ y x)))
(* -1 (pow x 2))
(* (pow x 2) (- (/ (pow y 2) (pow x 2)) 1))
(* x (- (/ y x) 1))
(* -1 (* (sqrt 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)))))))
(* -1 (* x (- (* -1 (/ y x)) 1)))
(* -1 (* x (+ 1 (* -1 (/ y x)))))
(+ (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 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)))))))))
(* y (+ 1 (/ x y)))
(* (pow y 2) (+ 1 (* -1 (/ (pow x 2) (pow y 2)))))
(* y (+ 1 (* -1 (/ x y))))
(* -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)))))))
(* -1 (* y (- (* -1 (/ x y)) 1)))
(* -1 (* y (- (/ x y) 1)))

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

rewrite108.0ms (2.5%)

Memory

3.3MiB live, 157.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	53
0	19	47
1	79	47
2	551	43
3	6518	43
0	8029	40

Stop Event

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

Counts

5 → 311

Calls

Call 1

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

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

eval55.0ms (1.3%)

Memory: 6.3MiB live, 120.1MiB allocated
Compiler: Compiled 9 396 to 1 204 computations (87.2% saved)

prune6.0ms (0.1%)

Memory

20.6MiB live, 20.6MiB allocated

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	336	3	339

Accuracy

100.0%

Counts

339 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	46.5%	(sqrt.f64 (/.f64 (fma.f64 (neg.f64 x) x (.f64 y y)) #s(approx (+ ( -1 x) y) (-.f64 y x))))
✓	100.0%	(sqrt.f64 (+.f64 x y))
✓	98.5%	#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Compiler

Compiled 85 to 48 computations (43.5% saved)

regimes11.0ms (0.2%)

Memory

-19.6MiB live, 19.6MiB allocated

Counts

5 → 1

Calls

Call 1

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

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

Calls

4 calls:

3.0ms	y
2.0ms	(sqrt.f64 (+.f64 x y))
2.0ms	(+.f64 x y)
2.0ms	x

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`y`
100.0%	1	`(sqrt.f64 (+.f64 x y))`
100.0%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

regimes5.0ms (0.1%)

Memory

11.7MiB live, 11.7MiB allocated

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

Outputs
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

Calls

4 calls:

1.0ms	(sqrt.f64 (+.f64 x y))
1.0ms	x
1.0ms	(+.f64 x y)
1.0ms	y

Results

Accuracy	Segments	Branch
98.5%	1	`x`
98.5%	1	`y`
98.5%	1	`(sqrt.f64 (+.f64 x y))`
98.5%	1	`(+.f64 x y)`

Compiler

Compiled 9 to 11 computations (-22.2% saved)

simplify52.0ms (1.2%)

Memory

-17.0MiB live, 32.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11

Stop Event

1×

saturated

Calls

Call 1

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

Outputs
(sqrt.f64 (+.f64 x y))
(sqrt.f64 (+.f64 y x))
#s(approx (sqrt (+ x y)) (sqrt.f64 y))

soundness180.0ms (4.2%)

Memory

-3.4MiB live, 70.6MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	156	583
1	454	553
2	1425	535
3	4629	523
0	8199	487

Stop Event

1×	done
1×	iter limit
1×	node limit

Compiler

Compiled 13 to 11 computations (15.4% saved)

preprocess17.0ms (0.4%)

Memory: 33.2MiB live, 33.2MiB allocated
Remove: (sort x y)
Compiler: Compiled 46 to 40 computations (13% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4

start0.0ms (0%)

analyze15.0ms (0.4%)

sample934.0ms (21.8%)

explain56.0ms (1.3%)

preprocess15.0ms (0.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify2.0ms (0.1%)

localize17.0ms (0.4%)

series5.0ms (0.1%)

simplify227.0ms (5.3%)

rewrite179.0ms (4.2%)

eval37.0ms (0.9%)

prune49.0ms (1.1%)

simplify244.0ms (5.7%)

localize71.0ms (1.7%)

series9.0ms (0.2%)

simplify389.0ms (9.1%)

rewrite181.0ms (4.2%)

eval64.0ms (1.5%)

prune7.0ms (0.2%)

simplify132.0ms (3.1%)

localize31.0ms (0.7%)

series4.0ms (0.1%)

simplify232.0ms (5.4%)

rewrite142.0ms (3.3%)

eval55.0ms (1.3%)

prune6.0ms (0.1%)

simplify362.0ms (8.4%)

localize32.0ms (0.7%)

series4.0ms (0.1%)

simplify348.0ms (8.1%)

rewrite108.0ms (2.5%)

eval55.0ms (1.3%)

prune6.0ms (0.1%)

regimes11.0ms (0.2%)

regimes5.0ms (0.1%)

simplify52.0ms (1.2%)

soundness180.0ms (4.2%)

preprocess17.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	24
1	26	22
2	41	22
3	63	22
4	116	22
5	155	22
6	194	22
7	205	22
8	207	22
0	4	4
0	6	4
1	7	4
0	7	4