Metrics for Linear.Quaternion:$clog from linear-1.19.1.3

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze19.0ms (0.4%)

Memory

-3.9MiB live, 35.0MiB 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
50%	50%	50%	0.1%	0%	0%	0%	3
50%	50%	50%	0.1%	0%	0%	0%	4
62.5%	62.4%	37.5%	0.1%	0%	0%	0%	5
66.7%	62.4%	31.2%	0.1%	0%	6.2%	0%	6
75%	65.6%	21.9%	0.1%	0%	12.5%	0%	7
80%	68.7%	17.2%	0.1%	0%	14%	0%	8
85.7%	70.2%	11.7%	0.1%	0%	18%	0%	9
88.9%	71.8%	9%	0.1%	0%	19.1%	0%	10
92.3%	72.6%	6%	0.1%	0%	21.3%	0%	11
94.1%	73.4%	4.6%	0.1%	0%	22%	0%	12

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample1.2s (24.4%)

Memory

24.7MiB live, 1 054.3MiB allocated

Samples

856.0ms	8 256×	0	valid
13.0ms	311×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 694.0ms

ival-mult: 330.0ms (47.5% of total)

ival-sqrt: 308.0ms (44.4% of total)

ival-add: 46.0ms (6.6% of total)

ival-true: 7.0ms (1% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain69.0ms (1.4%)

Memory

1.4MiB live, 119.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
87	-	-	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
0	-	-	`(+.f64 (*.f64 x x) y)`
0	-	-	`y`
0	-	-	`(*.f64 x x)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (+.f64 (*.f64 x x) y))`	oflow-rescue	87	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	87
↳	`(*.f64 x x)`	overflow	87

Confusion

	Predicted +	Predicted -
+	87	0
-	0	169

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	87	0	0
-	0	0	169

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	169
1	87

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

34.0ms

512×

valid

Compiler

Compiled 58 to 24 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 14.0ms

ival-add: 5.0ms (35.9% of total)

ival-mult: 4.0ms (28.7% of total)

ival-sqrt: 4.0ms (28.7% of total)

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

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

preprocess40.0ms (0.8%)

Memory

-1.3MiB live, 37.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs x)

Compiler

Compiled 6 to 5 computations (16.7% saved)

eval0.0ms (0%)

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

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.3%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify3.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (+.f64 (*.f64 x x) y))
cost-diff	128	(+.f64 (*.f64 x x) y)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	16
0	8	16
1	9	16
0	9	14

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize26.0ms (0.5%)

Memory

-37.9MiB live, 50.1MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(+.f64 (*.f64 x x) y)
accuracy	0.0	(*.f64 x x)
accuracy	20.259541922866926	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

19.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

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

ival-sqrt: 9.0ms (66.8% of total)

ival-mult: 3.0ms (22.3% of total)

ival-add: 1.0ms (7.4% of total)

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

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

series5.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Counts

3 → 28

Calls

Call 1

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

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

Calls

6 calls:

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

simplify222.0ms (4.6%)

Memory

-12.4MiB live, 307.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	133	518
1	383	503
2	1207	495
3	4039	450
0	8278	412

Stop Event

1×	iter limit
1×	node limit

Counts

28 → 26

Calls

Call 1

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

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

rewrite224.0ms (4.6%)

Memory

12.5MiB live, 208.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12

Stop Event

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

Counts

3 → 228

Calls

Call 1

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

Outputs
(.f64 (exp.f64 (log.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (exp.f64 (neg.f64 (log.f64 (-.f64 (.f64 x x) y)))))
(.f64 (exp.f64 (log.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (exp.f64 (neg.f64 (log.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (-.f64 (.f64 x x) y) (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) #s(literal -1 binary64)) (pow.f64 (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) #s(literal -1 binary64)))
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(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (fma.f64 (-.f64 y (.f64 x x)) y (neg.f64 (pow.f64 x #s(literal 4 binary64)))) (pow.f64 x #s(literal 8 binary64)))))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x y)))
(.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (-.f64 (.f64 x x) y)))))
(.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 y (*.f64 x x)))))
(.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (-.f64 y (*.f64 x x)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (-.f64 y (*.f64 x x)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 y y))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 x) x y))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 y y))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 x x) y))))
(.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) (.f64 y y))) (pow.f64 (/.f64 #s(literal -1 binary64) (-.f64 (*.f64 x 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 6 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(.f64 (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 #s(literal 1 binary64) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (fma.f64 x x y)))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))))) (neg.f64 (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)))))
(/.f64 (neg.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))))) (neg.f64 (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 y (.f64 x x)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 y y)))) (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 x) x y))))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (-.f64 (.f64 x x) y))) (hypot.f64 y (.f64 x x)))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (-.f64 (.f64 x x) y))) (sqrt.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64)))) (sqrt.f64 (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))
(/.f64 (sqrt.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 3 binary64))))) (sqrt.f64 (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 y (.f64 x x)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y)))) (sqrt.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal 2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (-.f64 (*.f64 x x) y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 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 binary64))) (sqrt.f64 (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9 binary64))) (sqrt.f64 (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 y (.f64 x x))))
(/.f64 (sqrt.f64 (fma.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 4 binary64)) (*.f64 y y))) (sqrt.f64 (fma.f64 (neg.f64 x) x y)))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 (neg.f64 y) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 x x) y))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 y (.f64 x x))) (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3 binary64))) (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(sqrt.f64 (fma.f64 x x y))
(exp.f64 (fma.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64) (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(*.f64 x x)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 x))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval53.0ms (1.1%)

Memory: 9.0MiB live, 47.1MiB allocated
Compiler: Compiled 6 295 to 872 computations (86.1% saved)

prune4.0ms (0.1%)

Memory

13.7MiB live, 13.6MiB allocated

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	244	4	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	245	4	249

Accuracy

100.0%

Counts

249 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.3%	(sqrt.f64 (fma.f64 x x y))
▶	65.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	38.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 36 to 27 computations (25% saved)

simplify38.0ms (0.8%)

Memory

-30.7MiB live, 17.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	57
0	21	57
1	30	57
2	36	57
3	39	57
4	41	57
5	45	57
6	60	57
7	97	57
8	129	57
9	238	57
10	387	57
11	677	57
12	964	57
13	1023	57
14	1037	57
15	1049	57
0	1049	57

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize35.0ms (0.7%)

Memory

24.6MiB live, 61.4MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 x x y)
accuracy	10.692794812810433	(sqrt.f64 (fma.f64 x x y))
accuracy	0.0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.06640625	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	22.15543712070969	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
accuracy	0.0	(sqrt.f64 y)
accuracy	21.159135045558877	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0.0	(neg.f64 x)
accuracy	44.82672672507385	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Samples

19.0ms	182×	0	valid
7.0ms	74×	0	invalid

Compiler

Compiled 112 to 28 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-add: 6.0ms (35.2% of total)

ival-mult: 4.0ms (23.4% of total)

ival-sqrt: 4.0ms (23.4% of total)

ival-div: 2.0ms (11.7% of total)

ival-neg: 1.0ms (5.9% of total)

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

exact: 0.0ms (0% of total)

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

series8.0ms (0.2%)

Memory

-25.8MiB live, 12.2MiB allocated

Counts

9 → 34

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
3.0ms	y	@	inf	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	inf	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))
1.0ms	x	@	-inf	((sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (+ (* x x) y))

simplify272.0ms (5.6%)

Memory

23.1MiB live, 306.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	562
1	425	547
2	1318	539
3	4493	495
0	8684	453

Stop Event

1×	iter limit
1×	node limit

Counts

34 → 32

Calls

Call 1

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

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

rewrite139.0ms (2.8%)

Memory

-11.2MiB live, 220.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
0	21	50
1	66	50
2	396	50
3	4450	50
0	8298	50

Stop Event

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

Counts

9 → 256

Calls

Call 1

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

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

eval122.0ms (2.5%)

Memory: -12.1MiB live, 76.0MiB allocated
Compiler: Compiled 6 199 to 966 computations (84.4% saved)

prune7.0ms (0.1%)

Memory

30.6MiB live, 30.6MiB allocated

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	278	2	280
Fresh	0	0	0
Picked	0	4	4
Done	0	0	0
Total	278	6	284

Accuracy

100.0%

Counts

284 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
✓	68.3%	(sqrt.f64 (fma.f64 x x y))
▶	33.3%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	38.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 55 to 42 computations (23.6% saved)

simplify5.0ms (0.1%)

Memory

-29.6MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	51
0	19	51
1	23	51
0	23	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize28.0ms (0.6%)

Memory

21.6MiB live, 60.3MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 x x y)
accuracy	0.1640625	(/.f64 #s(literal 1 binary64) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
accuracy	0.4624736223904641	(pow.f64 (fma.f64 x x y) #s(literal -1 binary64))
accuracy	19.741878282215485	(sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
accuracy	0.0	(*.f64 x x)
accuracy	20.259541922866926	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
accuracy	22.50996036696588	#s(approx (+ (* x x) y) (*.f64 x x))

Samples

20.0ms

256×

valid

Compiler

Compiled 104 to 25 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-sqrt: 4.0ms (34.2% of total)

ival-div: 2.0ms (17.1% of total)

ival-mult: 2.0ms (17.1% of total)

ival-pow: 2.0ms (17.1% of total)

ival-add: 1.0ms (8.5% of total)

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

exact: 0.0ms (0% of total)

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

series60.0ms (1.2%)

Memory

-25.7MiB live, 59.8MiB allocated

Counts

7 → 66

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
53.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) (/ 1 (sqrt (pow (+ (* x x) y) -1))) (sqrt (pow (+ (* x x) y) -1)) (pow (+ (* x x) y) -1) (+ (* x x) y))
2.0ms	x	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) (/ 1 (sqrt (pow (+ (* x x) y) -1))) (sqrt (pow (+ (* x x) y) -1)) (pow (+ (* x x) y) -1) (+ (* x x) y))
1.0ms	x	@	0	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) (/ 1 (sqrt (pow (+ (* x x) y) -1))) (sqrt (pow (+ (* x x) y) -1)) (pow (+ (* x x) y) -1) (+ (* x x) y))
1.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) (/ 1 (sqrt (pow (+ (* x x) y) -1))) (sqrt (pow (+ (* x x) y) -1)) (pow (+ (* x x) y) -1) (+ (* x x) y))
1.0ms	y	@	0	((sqrt (+ (* x x) y)) (+ (* x x) y) (* x x) (/ 1 (sqrt (pow (+ (* x x) y) -1))) (sqrt (pow (+ (* x x) y) -1)) (pow (+ (* x x) y) -1) (+ (* x x) y))

simplify185.0ms (3.8%)

Memory

-1.7MiB live, 197.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1325
1	871	1267
2	2636	1235
3	6275	1215
0	8408	1135

Stop Event

1×	iter limit
1×	node limit

Counts

66 → 64

Calls

Call 1

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

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

rewrite230.0ms (4.7%)

Memory

40.8MiB live, 232.4MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	46
0	19	44
1	55	42
2	274	41
3	2356	41
0	8585	41

Stop Event

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

Counts

7 → 614

Calls

Call 1

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

Outputs
(.f64 (pow.f64 #s(approx (+ ( x x) y) (.f64 x x)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ ( x x) y) (*.f64 x x)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
(pow.f64 (pow.f64 #s(approx (+ (* x x) y) (*.f64 x x)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (+ (* x x) y) (*.f64 x x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (+ (* x x) y) (*.f64 x x)) #s(literal 1/2 binary64))
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(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(/.f64 (-.f64 (/.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 3 binary64))) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 3 binary64)))) (+.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64)))) (neg.f64 (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64)))) (neg.f64 (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64)))) (neg.f64 (.f64 (-.f64 (.f64 x x) y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (.f64 #s(literal 1 binary64) (-.f64 y (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 y (.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y)))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1 binary64)) (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal 2 binary64)))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1 binary64) (-.f64 y (*.f64 x x))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 x x)))
(/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))))
(/.f64 (neg.f64 (fma.f64 x x y)) #s(literal -1 binary64))
(/.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (-.f64 y (.f64 x x)) (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64))))
(/.f64 (fma.f64 x x y) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x x)) (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (fma.f64 x 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 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 x x y)
(sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal 2 binary64)))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 1 binary64)) (/.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))) #s(literal 1 binary64)))
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (*.f64 x x))))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (fma.f64 x x y)) (log.f64 (sqrt.f64 (fma.f64 x x y)))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x x y))) #s(literal -1 binary64)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))

eval233.0ms (4.8%)

Memory: -17.7MiB live, 228.0MiB allocated
Compiler: Compiled 15 790 to 2 649 computations (83.2% saved)

prune12.0ms (0.3%)

Memory

11.3MiB live, 48.2MiB allocated

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	668	1	669
Fresh	0	0	0
Picked	1	1	2
Done	0	4	4
Total	669	6	675

Accuracy

100.0%

Counts

675 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	68.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	68.3%	(sqrt.f64 (fma.f64 x x y))
✓	33.3%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	38.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 55 to 41 computations (25.5% saved)

simplify3.0ms (0.1%)

Memory

6.3MiB live, 6.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
0	12	29
1	15	29
0	15	29

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

Outputs
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
#s(literal 1 binary64)
(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))
(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
(fma.f64 x x y)
x
y

localize28.0ms (0.6%)

Memory

-35.4MiB live, 47.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(fma.f64 x x y)
accuracy	0.1640625	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
accuracy	0.4624736223904641	(/.f64 #s(literal 1 binary64) (fma.f64 x x y))
accuracy	19.741878282215485	(sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y)))

Samples

17.0ms

256×

valid

Compiler

Compiled 64 to 17 computations (73.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-div: 5.0ms (49.7% of total)

ival-mult: 2.0ms (19.9% of total)

ival-sqrt: 2.0ms (19.9% of total)

ival-add: 1.0ms (9.9% of total)

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

exact: 0.0ms (0% of total)

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

series3.0ms (0.1%)

Memory

6.4MiB live, 6.4MiB allocated

Counts

4 → 66

Calls

Call 1

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

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

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	x	@	inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	-inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	-inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	x	@	0	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))
0.0ms	y	@	inf	((/ 1 (sqrt (/ 1 (+ (* x x) y)))) (sqrt (/ 1 (+ (* x x) y))) (/ 1 (+ (* x x) y)) (+ (* x x) y))

simplify551.0ms (11.3%)

Memory

-173.2MiB live, 179.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	298	1325
1	871	1267
2	2630	1235
3	6270	1215
0	8402	1135

Stop Event

1×	iter limit
1×	node limit

Counts

66 → 64

Calls

Call 1

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

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

rewrite97.0ms (2%)

Memory

9.4MiB live, 88.2MiB allocated

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	26
0	12	26
1	49	21
2	277	21
0	2317	21

Stop Event

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

Counts

4 → 282

Calls

Call 1

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

Outputs
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal -1 binary64))) (sqrt.f64 (neg.f64 (fma.f64 x x y))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64))) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x y)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)) (sqrt.f64 (fma.f64 x x y)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)))
(*.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))) #s(literal -1 binary64))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) y))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (pow.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (pow.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 x x y)))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1/2 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1/2 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)))
(/.f64 (.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) #s(literal 1 binary64)) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(/.f64 (.f64 #s(literal 1 binary64) (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (neg.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 y (.f64 x x))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (sqrt.f64 (-.f64 (.f64 x x) y))))
(/.f64 (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (sqrt.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64))) (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (sqrt.f64 (neg.f64 (fma.f64 x x y))) (sqrt.f64 #s(literal -1 binary64)))
(/.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal 1 binary64))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x y))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (-.f64 (*.f64 x x) y)) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))) (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)))
(neg.f64 (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(sqrt.f64 (fma.f64 x x y))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (fma.f64 x x y))))
(exp.f64 (neg.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)))))
(exp.f64 (*.f64 (neg.f64 (log.f64 (fma.f64 x x y))) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (fma.f64 x x y)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(.f64 (/.f64 #s(literal 1 binary64) (hypot.f64 (pow.f64 x #s(literal 3 binary64)) (pow.f64 y #s(literal 3/2 binary64)))) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64))) (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)))
(*.f64 (pow.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (fma.f64 x x y)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (sqrt.f64 (-.f64 (.f64 x x) y)))
(.f64 (sqrt.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64))) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal 1/4 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (.f64 x x) y)))
(.f64 (pow.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(*.f64 (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) (.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)) (pow.f64 (fma.f64 x x y) #s(literal -1/4 binary64)))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (fma.f64 x x y)))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x y))))
(*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal -1 binary64) (fma.f64 x x y)) #s(literal 1/2 binary64)))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x y))) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (sqrt.f64 (fma.f64 x x y))))
(*.f64 (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
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(+.f64 (.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (.f64 x x)) (*.f64 (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (neg.f64 y)))
(+.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 y (.f64 x x)) y)) (.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))))
(+.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 y (.f64 x x)) y)))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 2 binary64)))) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (*.f64 x x)) y)))
(.f64 (/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 y (.f64 x x)) y) #s(literal 3 binary64)) (pow.f64 x #s(literal 12 binary64)))) (fma.f64 (.f64 (-.f64 y (.f64 x x)) y) (-.f64 (.f64 (-.f64 y (*.f64 x x)) y) (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(*.f64 (/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y))
(.f64 (/.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 y (*.f64 x x))))
(.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))
(.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (.f64 (pow.f64 (-.f64 (*.f64 x x) y) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)))
(.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (.f64 (fma.f64 x x y) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (/.f64 (fma.f64 x x y) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 (pow.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1 binary64)))
(.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64)))
(*.f64 (neg.f64 (fma.f64 x x y)) #s(literal -1 binary64))
(*.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 x x y)))
(.f64 (fma.f64 x x y) (.f64 (-.f64 (.f64 x x) y) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))))
(.f64 (fma.f64 x x y) (/.f64 (-.f64 (.f64 x x) y) (-.f64 (*.f64 x x) y)))
(*.f64 (fma.f64 x x y) #s(literal 1 binary64))
(*.f64 #s(literal 1 binary64) (fma.f64 x x y))
(pow.f64 (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)) #s(literal -1 binary64))
(pow.f64 (fma.f64 x x y) #s(literal 1 binary64))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (*.f64 x x) y))
(/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal -1 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64))) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (pow.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) #s(literal -1 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))))
(/.f64 (.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (-.f64 y (*.f64 x x)))
(/.f64 (.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) #s(literal 1 binary64)) (neg.f64 (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) #s(literal 1 binary64)) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) #s(literal 1 binary64)) (-.f64 (.f64 x x) y))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y))) (.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))) (+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 3 binary64)) (pow.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (fma.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 y (/.f64 y (-.f64 (.f64 x x) y))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))))
(/.f64 (neg.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 y (.f64 x x))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (neg.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))))) (-.f64 (*.f64 x x) y))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64))) (-.f64 (.f64 x x) y)))
(/.f64 (.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 (-.f64 (.f64 x x) y) (.f64 y y))) (.f64 (-.f64 (.f64 x x) y) (-.f64 (.f64 x x) y)))
(/.f64 (-.f64 (pow.f64 x #s(literal 8 binary64)) (pow.f64 y #s(literal 4 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal 1 binary64) (-.f64 y (*.f64 x x))))
(/.f64 (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64))) (-.f64 y (.f64 x x)))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (-.f64 (.f64 x x) y) (fma.f64 (*.f64 y y) (fma.f64 y y (pow.f64 x #s(literal 4 binary64))) (pow.f64 x #s(literal 8 binary64)))))
(/.f64 (-.f64 (pow.f64 x #s(literal 12 binary64)) (pow.f64 y #s(literal 6 binary64))) (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 y #s(literal 3 binary64)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 9 binary64)) (pow.f64 x #s(literal 18 binary64))) (.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))) (fma.f64 (pow.f64 y #s(literal 3 binary64)) (-.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (pow.f64 x #s(literal 12 binary64)))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(/.f64 (neg.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (neg.f64 (-.f64 (*.f64 x x) y)))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (-.f64 (.f64 x x) y))))
(/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (neg.f64 (neg.f64 (-.f64 (*.f64 x x) y))))
(/.f64 (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64))) (-.f64 (*.f64 x x) y))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 (-.f64 y (.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (neg.f64 (neg.f64 (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))))
(/.f64 (+.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (-.f64 y (*.f64 x x)) y (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (fma.f64 x x y)) #s(literal -1 binary64))
(/.f64 (sqrt.f64 (fma.f64 x x y)) (pow.f64 (fma.f64 x x y) #s(literal -1/2 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (fma.f64 x x y)))
(/.f64 (fma.f64 x x y) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 y (.f64 x x)) (-.f64 (.f64 y y) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x y) #s(literal -1 binary64)))
(neg.f64 (neg.f64 (fma.f64 x 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 3 binary64)))) (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64))) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(fma.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (fma.f64 (neg.f64 y) y (pow.f64 x #s(literal 4 binary64)))) (fma.f64 x x y) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
(fma.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)) y)
(fma.f64 (pow.f64 x #s(literal 3 binary64)) (/.f64 x (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (-.f64 (.f64 x x) y) #s(literal -1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 x (/.f64 (pow.f64 x #s(literal 3 binary64)) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(fma.f64 x x y)
(-.f64 (/.f64 (.f64 y y) (-.f64 y (.f64 x x))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 y (*.f64 x x))))
(-.f64 (/.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) #s(literal 1 binary64)) (/.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))) #s(literal 1 binary64)))
(-.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (.f64 y (/.f64 y (-.f64 (*.f64 x x) y))))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x y)))
(exp.f64 (log.f64 (fma.f64 x x y)))
(+.f64 (neg.f64 (*.f64 (neg.f64 x) x)) (neg.f64 (neg.f64 y)))
(+.f64 (neg.f64 (neg.f64 y)) (neg.f64 (*.f64 (neg.f64 x) x)))
(+.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(+.f64 (*.f64 x x) y)
(+.f64 y (*.f64 x x))

eval47.0ms (1%)

Memory: -5.6MiB live, 77.5MiB allocated
Compiler: Compiled 7 291 to 1 364 computations (81.3% saved)

prune9.0ms (0.2%)

Memory

-8.8MiB live, 26.1MiB allocated

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	337	6	343

Accuracy

100.0%

Counts

343 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	68.1%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x y))))
✓	68.3%	(sqrt.f64 (fma.f64 x x y))
✓	33.3%	(sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x)))
✓	65.4%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	38.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.3%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 125 to 69 computations (44.8% saved)

regimes35.0ms (0.7%)

Memory

-11.5MiB live, 26.5MiB allocated

Counts

8 → 2

Calls

Call 1

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

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

Calls

5 calls:

23.0ms	x
3.0ms	y
3.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
83.7%	2	`y`
100.0%	2	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
100.0%	2	`(+.f64 (*.f64 x x) y)`
100.0%	2	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes10.0ms (0.2%)

Memory

17.6MiB live, 17.6MiB allocated

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
68.3%	1	`y`
68.3%	1	`x`
68.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
68.3%	1	`(+.f64 (*.f64 x x) y)`
68.3%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes13.0ms (0.3%)

Memory

-19.7MiB live, 18.0MiB allocated

Counts

3 → 2

Calls

Call 1

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

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

Calls

5 calls:

6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	x
2.0ms	y
2.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
45.7%	4	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
45.7%	4	`(+.f64 (*.f64 x x) y)`
57.8%	2	`(*.f64 x x)`
57.8%	2	`x`
52.4%	2	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
38.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
38.0%	1	`(+.f64 (*.f64 x x) y)`
38.0%	1	`y`
38.0%	1	`(*.f64 x x)`
38.0%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes6.0ms (0.1%)

Memory

14.7MiB live, 14.7MiB allocated

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
1.3%	1	`x`
1.3%	1	`y`
1.3%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.3%	1	`(+.f64 (*.f64 x x) y)`
1.3%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.2411418076703242e+240	1.0778056611231735e+246

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch44.0ms (0.9%)

Memory

-39.2MiB live, 12.3MiB allocated

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
4.0ms	7.162159883983463e-28	1.0107386685253987e-27

Samples

2.0ms	48×	0	valid
0.0ms	9×	0	invalid

Compiler

Compiled 66 to 58 computations (12.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

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

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

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

simplify22.0ms (0.4%)

Memory

24.6MiB live, 24.6MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	70
1	28	70
2	30	70
3	31	70

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000254805147818501364069927626367655683308154800821653387104782081659209545431944533510880329053340878138807089955663726104295591257190120963678815521941214074157219047400732892880902176280753059461372069733879809562530442903552 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 348449143727041/348449143727040986586495598010130648530944 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Outputs
(if (<=.f64 (.f64 x x) #s(literal 5000000000000000254805147818501364069927626367655683308154800821653387104782081659209545431944533510880329053340878138807089955663726104295591257190120963678815521941214074157219047400732892880902176280753059461372069733879809562530442903552 binary64)) (sqrt.f64 (fma.f64 x x y)) #s(approx (sqrt (+ ( x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(sqrt.f64 (fma.f64 x x y))
(if (<=.f64 x #s(literal 348449143727041/348449143727040986586495598010130648530944 binary64)) #s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y)) (sqrt.f64 #s(approx (+ (* x x) y) (*.f64 x x))))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness725.0ms (14.9%)

Memory

5.8MiB live, 396.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	149	562
1	425	547
2	1318	539
3	4493	495
0	8684	453
0	5	14
0	8	14
1	26	14
2	169	14
3	1521	14
0	8489	12
0	133	518
1	383	503
2	1207	495
3	4039	450
0	8278	412

Stop Event

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

Compiler

Compiled 119 to 63 computations (47.1% saved)

preprocess43.0ms (0.9%)

Memory: 10.8MiB live, 92.2MiB allocated
Compiler: Compiled 258 to 120 computations (53.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5

start0.0ms (0%)

analyze19.0ms (0.4%)

sample1.2s (24.4%)

explain69.0ms (1.4%)

preprocess40.0ms (0.8%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0.1%)

localize26.0ms (0.5%)

series5.0ms (0.1%)

simplify222.0ms (4.6%)

rewrite224.0ms (4.6%)

eval53.0ms (1.1%)

prune4.0ms (0.1%)

simplify38.0ms (0.8%)

localize35.0ms (0.7%)

series8.0ms (0.2%)

simplify272.0ms (5.6%)

rewrite139.0ms (2.8%)

eval122.0ms (2.5%)

prune7.0ms (0.1%)

simplify5.0ms (0.1%)

localize28.0ms (0.6%)

series60.0ms (1.2%)

simplify185.0ms (3.8%)

rewrite230.0ms (4.7%)

eval233.0ms (4.8%)

prune12.0ms (0.3%)

simplify3.0ms (0.1%)

localize28.0ms (0.6%)

series3.0ms (0.1%)

simplify551.0ms (11.3%)

rewrite97.0ms (2%)

eval47.0ms (1%)

prune9.0ms (0.2%)

regimes35.0ms (0.7%)

regimes10.0ms (0.2%)

regimes13.0ms (0.3%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

bsearch0.0ms (0%)

bsearch44.0ms (0.9%)

simplify22.0ms (0.4%)

soundness725.0ms (14.9%)

preprocess43.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	15	32
1	34	32
2	69	32
3	124	32
4	188	32
5	250	32
6	312	32
7	324	32
8	330	32
0	5	6
0	8	6
1	9	6
0	9	5