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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze27.0ms (0.6%)

Memory

-25.0MiB live, 13.3MiB 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)

sample737.0ms (16.2%)

Memory

5.2MiB live, 753.7MiB allocated

Samples

453.0ms	8 256×	0	valid
37.0ms	350×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 217.0ms

ival-mult: 85.0ms (39.2% of total)

ival-sqrt: 84.0ms (38.7% of total)

ival-add: 39.0ms (18% of total)

ival-true: 6.0ms (2.8% of total)

ival-assert: 3.0ms (1.4% of total)

Bogosity

explain77.0ms (1.7%)

Memory

-6.4MiB live, 125.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
94	-	-	`(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	94	0
↳	`(+.f64 (*.f64 x x) y)`	overflow	94
↳	`(*.f64 x x)`	overflow	94

Confusion

	Predicted +	Predicted -
+	94	0
-	0	162

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	94	0	0
-	0	0	162

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	162
1	94

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

27.0ms

512×

valid

Compiler

Compiled 74 to 29 computations (60.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 4.0ms (37.9% of total)

ival-sqrt: 4.0ms (37.9% of total)

ival-add: 2.0ms (19% of total)

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

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

preprocess18.0ms (0.4%)

Memory

28.9MiB live, 28.9MiB 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.9%	(sqrt.f64 (+.f64 (*.f64 x x) y))

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Memory

-35.5MiB live, 3.2MiB 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

localize17.0ms (0.4%)

Memory

30.6MiB live, 30.6MiB allocated

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (*.f64 x x) y)
accuracy	21.83844312386691	(sqrt.f64 (+.f64 (*.f64 x x) y))

Samples

11.0ms

256×

valid

Compiler

Compiled 34 to 12 computations (64.7% saved)

Precisions

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

ival-mult: 2.0ms (39.6% of total)

ival-sqrt: 2.0ms (39.6% of total)

ival-add: 1.0ms (19.8% of total)

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

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

series7.0ms (0.2%)

Memory

-27.5MiB live, 11.2MiB 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
3.0ms	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))

simplify169.0ms (3.7%)

Memory

42.5MiB live, 234.4MiB 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)

rewrite170.0ms (3.7%)

Memory

-8.6MiB live, 270.1MiB 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 (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)))) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 y (fma.f64 x x y) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (pow.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)))) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (-.f64 y (*.f64 x x)) y))))
(.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)))

eval46.0ms (1%)

Memory: 12.6MiB live, 50.2MiB allocated
Compiler: Compiled 6 295 to 872 computations (86.1% saved)

prune58.0ms (1.3%)

Memory

-20.7MiB live, 32.6MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	243	5	248
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	244	5	249

Accuracy

100.0%

Counts

249 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	63.3%	(sqrt.f64 (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))))))
▶	65.9%	(sqrt.f64 (fma.f64 x x y))
▶	70.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
▶	33.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
▶	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 120 to 74 computations (38.3% saved)

simplify306.0ms (6.7%)

Memory

-11.1MiB live, 105.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 13 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(sqrt.f64 (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))))))
cost-diff	128	(neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
cost-diff	3392	(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)))))
cost-diff	0	(fma.f64 x x y)
cost-diff	0	(sqrt.f64 (fma.f64 x x y))
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))
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))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	23	149
0	38	111
1	66	111
2	110	111
3	166	110
4	283	110
5	679	110
6	1500	110
7	2290	110
8	2475	110
9	2640	110
10	2870	110
11	2903	110
12	2959	110
13	3107	110
14	3388	110
15	4231	110
16	6123	110
17	6972	110
18	7694	110
19	7762	110
20	7772	110
0	8378	110

Stop Event

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

Calls

Call 1

Inputs
#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
#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
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
x
y
(sqrt.f64 (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 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (neg.f64 (.f64 y (/.f64 y (-.f64 (*.f64 x x) y)))))
(*.f64 x x)
x
(/.f64 (.f64 x x) (-.f64 (.f64 x x) y))
(-.f64 (*.f64 x x) y)
y
(neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
(.f64 y (/.f64 y (-.f64 (.f64 x x) y)))
(/.f64 y (-.f64 (*.f64 x x) y))

Outputs
#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
#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
(sqrt.f64 (fma.f64 x x y))
(fma.f64 x x y)
x
y
(sqrt.f64 (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))))))
(sqrt.f64 (fma.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 x y)
(*.f64 x x)
x
(/.f64 (.f64 x x) (-.f64 (.f64 x x) y))
(.f64 (/.f64 x (-.f64 (.f64 x x) y)) x)
(-.f64 (*.f64 x x) y)
y
(neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
(/.f64 (*.f64 y y) (fma.f64 (neg.f64 x) x y))
(.f64 y (/.f64 y (-.f64 (.f64 x x) y)))
(.f64 (/.f64 y (-.f64 (.f64 x x) y)) y)
(/.f64 y (-.f64 (*.f64 x x) y))

localize124.0ms (2.7%)

Memory

-4.3MiB live, 78.4MiB allocated

Localize:

Found 13 expressions of interest:

New	Metric	Score
accuracy	0.8429580828865414	(.f64 y (/.f64 y (-.f64 (.f64 x x) y)))
accuracy	3.7366600943742396	(/.f64 y (-.f64 (*.f64 x x) y))
accuracy	11.412774895129466	(sqrt.f64 (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))))))
accuracy	13.761110134604777	(/.f64 (.f64 x x) (-.f64 (.f64 x x) y))
accuracy	0	(fma.f64 x x y)
accuracy	11.412774895129466	(sqrt.f64 (fma.f64 x x y))
accuracy	0	(sqrt.f64 y)
accuracy	22.869524820072616	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
accuracy	0	(neg.f64 x)
accuracy	43.37042788771575	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))
accuracy	0	(/.f64 #s(literal 1/2 binary64) x)
accuracy	0.05078125	(fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)
accuracy	18.922194298854926	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))

Samples

68.0ms	80×	0	invalid
24.0ms	176×	0	valid

Compiler

Compiled 298 to 44 computations (85.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-sqrt: 41.0ms (51.6% of total)

ival-mult: 27.0ms (34% of total)

ival-div: 5.0ms (6.3% of total)

ival-add: 3.0ms (3.8% of total)

ival-neg: 2.0ms (2.5% of total)

ival-sub: 1.0ms (1.3% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.4%)

Memory

19.3MiB live, 19.3MiB allocated

Counts

16 → 107

Calls

Call 1

Inputs
#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(approx (sqrt (+ (* x x) y)) (neg.f64 x))
(neg.f64 x)
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
(sqrt.f64 y)
(sqrt.f64 (fma.f64 x x y))
(fma.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)))))
(neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))
(sqrt.f64 (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))))))
(*.f64 x x)
(/.f64 (.f64 x x) (-.f64 (.f64 x x) y))
(/.f64 y (-.f64 (*.f64 x x) y))
(.f64 y (/.f64 y (-.f64 (.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))))))))))
(* 1/2 (/ y x))
(/ (+ (* 1/2 y) (pow x 2)) x)
(/ 1/2 x)
(* -1 x)
y
(+ y (pow x 2))
(- (pow x 2) (* -1 y))
(- (* (pow x 2) (+ 1 (/ (pow x 2) y))) (* -1 y))
(- (* (pow x 2) (+ 1 (* (pow x 2) (+ (/ 1 y) (/ (pow x 2) (pow y 2)))))) (* -1 y))
(pow x 2)
(* -1 (/ (pow x 2) y))
(* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y)))
(* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y)))
(* (pow x 2) (- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 4))) (/ 1 (pow y 3)))) (/ 1 (pow y 2)))) (/ 1 y)))
-1
(- (* -1 (/ (pow x 2) y)) 1)
(- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))) 1)
(- (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 3))) (/ 1 (pow y 2)))) (/ 1 y))) 1)
(* -1 y)
(+ (* -1 y) (* -1 (pow x 2)))
(+ (* -1 y) (* (pow x 2) (- (* -1 (/ (pow x 2) y)) 1)))
(+ (* -1 y) (* (pow x 2) (- (* (pow x 2) (- (* -1 (/ (pow x 2) (pow y 2))) (/ 1 y))) 1)))
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))))
(* (pow x 2) (- (+ 1 (* -1 (/ (+ (* -1 (pow y 2)) (pow y 2)) (pow x 4)))) (* -1 (/ y (pow x 2)))))
(* -1 (/ (pow y 2) (pow x 2)))
(/ (- (* -1 (/ (pow y 3) (pow x 2))) (pow y 2)) (pow x 2))
(/ (- (+ (* -1 (/ (pow y 3) (pow x 2))) (* -1 (/ (pow y 4) (pow x 4)))) (pow y 2)) (pow x 2))
(/ (- (+ (* -1 (/ (pow y 3) (pow x 2))) (+ (* -1 (/ (pow y 4) (pow x 4))) (* -1 (/ (pow y 5) (pow x 6))))) (pow y 2)) (pow x 2))
(* x (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ y (pow x 2))))))
(* x (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2))) (pow x 4))) (+ (* 1/4 (/ (* y (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2)))) (pow x 6))) (* 1/2 (/ y (pow x 2)))))))
1
(+ 1 (/ y (pow x 2)))
(- (+ 1 (/ (pow y 2) (pow x 4))) (* -1 (/ y (pow x 2))))
(- (+ 1 (/ (pow y 3) (pow x 6))) (+ (* -1 (/ y (pow x 2))) (* -1 (/ (pow y 2) (pow x 4)))))
(/ y (pow x 2))
(/ (+ y (/ (pow y 2) (pow x 2))) (pow x 2))
(/ (- (+ y (/ (pow y 3) (pow x 4))) (* -1 (/ (pow y 2) (pow x 2)))) (pow x 2))
(/ (- (+ y (/ (pow y 4) (pow x 6))) (+ (* -1 (/ (pow y 2) (pow x 2))) (* -1 (/ (pow y 3) (pow x 4))))) (pow x 2))
(/ (pow y 2) (pow x 2))
(/ (+ (/ (pow y 3) (pow x 2)) (pow y 2)) (pow x 2))
(/ (- (+ (/ (pow y 4) (pow x 4)) (pow y 2)) (* -1 (/ (pow y 3) (pow x 2)))) (pow x 2))
(/ (- (+ (/ (pow y 5) (pow x 6)) (pow y 2)) (+ (* -1 (/ (pow y 3) (pow x 2))) (* -1 (/ (pow y 4) (pow x 4))))) (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)))
(* -1 (* x (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2))) (pow x 4))) (* 1/2 (/ y (pow x 2)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2))) (pow x 4))) (+ (* 1/4 (/ (* y (+ (* -1 (pow y 2)) (+ (* 1/4 (pow y 2)) (pow y 2)))) (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)))))
(* (pow y 2) (- (* -1 (/ y (pow x 4))) (/ 1 (pow x 2))))
(* (pow y 2) (- (* y (- (* -1 (/ y (pow x 6))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))))
(* (pow y 2) (- (* y (- (* y (- (* -1 (/ y (pow x 8))) (/ 1 (pow x 6)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))))
(+ 1 (* y (+ (/ 1 (pow x 2)) (/ y (pow x 4)))))
(+ 1 (* y (+ (* y (+ (/ 1 (pow x 4)) (/ y (pow x 6)))) (/ 1 (pow x 2)))))
(* y (+ (/ 1 (pow x 2)) (/ y (pow x 4))))
(* y (+ (* y (+ (/ 1 (pow x 4)) (/ y (pow x 6)))) (/ 1 (pow x 2))))
(* y (+ (* y (+ (* y (+ (/ 1 (pow x 6)) (/ y (pow x 8)))) (/ 1 (pow x 4)))) (/ 1 (pow x 2))))
(* (pow y 2) (+ (/ 1 (pow x 2)) (/ y (pow x 4))))
(* (pow y 2) (+ (* y (+ (/ 1 (pow x 4)) (/ y (pow x 6)))) (/ 1 (pow x 2))))
(* (pow y 2) (+ (* y (+ (* y (+ (/ 1 (pow x 6)) (/ y (pow x 8)))) (/ 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 (+ (* 1/2 (/ 1 x)) (/ x y)))
(* y (+ 1 (/ (pow x 2) y)))
(* y (+ 1 (+ (* -1 (/ (pow x 4) (pow y 2))) (+ (/ (pow x 2) y) (/ (pow x 4) (pow y 2))))))
(* y (+ 1 (+ (/ (pow x 2) y) (/ (pow x 4) (pow y 2)))))
(* y (+ 1 (+ (/ (pow x 2) y) (+ (/ (pow x 4) (pow y 2)) (/ (pow x 6) (pow y 3))))))
(* y (+ (sqrt (/ 1 y)) (+ (* 1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (pow x 4)))) (* 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 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (pow x 4)))) (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3)))))))))
(/ (+ (* -1 (/ (pow x 4) y)) (* -1 (pow x 2))) y)
(/ (- (+ (* -1 (/ (pow x 6) (pow y 2))) (* -1 (pow x 2))) (/ (pow x 4) y)) y)
(/ (- (+ (* -1 (/ (pow x 8) (pow y 3))) (* -1 (pow x 2))) (+ (/ (pow x 4) y) (/ (pow x 6) (pow y 2)))) y)
(- (* -1 (/ (pow x 4) (pow y 2))) (+ 1 (/ (pow x 2) y)))
(- (* -1 (/ (pow x 6) (pow y 3))) (+ 1 (+ (/ (pow x 2) y) (/ (pow x 4) (pow y 2)))))
(* y (- (* -1 (/ (pow x 2) y)) 1))
(* y (- (* -1 (/ (pow x 4) (pow y 2))) (+ 1 (/ (pow x 2) y))))
(* y (- (* -1 (/ (pow x 6) (pow y 3))) (+ 1 (+ (/ (pow x 2) y) (/ (pow x 4) (pow y 2))))))
(* -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)))
(* -1 (* y (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (pow x 4)) (pow x 4)) y)) (pow x 2)) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ (/ (pow x 4) y) (pow x 2)) y)) 1)))
(* -1 (* y (- (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (pow x 6) y)) (* -1 (pow x 4))) y)) (pow x 2)) y)) 1)))
(* -1 (* y (+ (* -1/2 (* (sqrt (/ 1 (pow y 5))) (+ (* -1 (pow x 4)) (pow x 4)))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (* y (+ (* -1 (/ (+ (* 1/8 (* (/ (pow x 4) (pow (sqrt -1) 2)) (sqrt y))) (* 1/2 (* (sqrt y) (+ (* -1 (pow x 4)) (pow x 4))))) (pow y 3))) (+ (* 1/2 (* (pow x 2) (sqrt (/ 1 (pow y 3))))) (* (sqrt (/ 1 y)) (pow (sqrt -1) 2))))))
(* -1 (/ (+ (/ (pow x 4) y) (pow x 2)) y))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (pow x 6) y)) (pow x 4)) y)) (pow x 2)) y))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (/ (pow x 8) y) (* -1 (pow x 6))) y)) (pow x 4)) y)) (pow x 2)) y))
(- (* -1 (/ (- (/ (pow x 4) y) (* -1 (pow x 2))) y)) 1)
(- (* -1 (/ (- (* -1 (/ (- (* -1 (/ (pow x 6) y)) (pow x 4)) y)) (* -1 (pow x 2))) y)) 1)
(* -1 (* y (+ 1 (/ (pow x 2) y))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (pow x 4) y)) (pow x 2)) y)))))
(* -1 (* y (+ 1 (* -1 (/ (- (* -1 (/ (- (/ (pow x 6) y) (* -1 (pow x 4))) y)) (pow x 2)) y)))))

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	x	@	inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y))))) (neg (* y (/ y (- (* x x) y)))) (sqrt (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y)))))) (* x x) (/ (* x x) (- (* x x) y)) (/ y (- (* x x) y)) (* y (/ y (- (* x x) y))))
4.0ms	y	@	-inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y))))) (neg (* y (/ y (- (* x x) y)))) (sqrt (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y)))))) (* x x) (/ (* x x) (- (* x x) y)) (/ y (- (* x x) y)) (* y (/ y (- (* x x) y))))
3.0ms	x	@	0	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y))))) (neg (* y (/ y (- (* x x) y)))) (sqrt (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y)))))) (* x x) (/ (* x x) (- (* x x) y)) (/ y (- (* x x) y)) (* y (/ y (- (* x x) y))))
3.0ms	y	@	0	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y))))) (neg (* y (/ y (- (* x x) y)))) (sqrt (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y)))))) (* x x) (/ (* x x) (- (* x x) y)) (/ y (- (* x x) y)) (* y (/ y (- (* x x) y))))
3.0ms	y	@	inf	((sqrt (+ (* x x) y)) (+ (* (/ 1/2 x) y) x) (/ 1/2 x) (sqrt (+ (* x x) y)) (neg x) (sqrt (+ (* x x) y)) (sqrt y) (sqrt (+ (* x x) y)) (+ (* x x) y) (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y))))) (neg (* y (/ y (- (* x x) y)))) (sqrt (+ (* (* x x) (/ (* x x) (- (* x x) y))) (neg (* y (/ y (- (* x x) y)))))) (* x x) (/ (* x x) (- (* x x) y)) (/ y (- (* x x) y)) (* y (/ y (- (* x x) y))))

simplify177.0ms (3.9%)

Memory

-5.9MiB live, 148.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	418	2075
1	1324	1974
2	4393	1865
0	8494	1730

Stop Event

1×	iter limit
1×	node limit

Counts

107 → 105

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

rewrite291.0ms (6.4%)

Memory

7.6MiB live, 171.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	135
0	38	97
1	128	97
2	897	94
0	8378	94

Stop Event

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

Counts

16 → 886

Calls

Call 1

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

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

eval224.0ms (4.9%)

Memory: -8.0MiB live, 160.3MiB allocated
Compiler: Compiled 23 871 to 2 790 computations (88.3% saved)

prune87.0ms (1.9%)

Memory

-3.9MiB live, 33.8MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	731	1	732
Fresh	0	0	0
Picked	1	4	5
Done	0	0	0
Total	732	5	737

Accuracy

100.0%

Counts

737 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	65.3%	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))
✓	65.9%	(sqrt.f64 (fma.f64 x x y))
✓	70.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	33.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 62 to 41 computations (33.9% saved)

simplify85.0ms (1.9%)

Memory

-12.9MiB live, 26.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
cost-diff	0	(fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y)))))
cost-diff	0	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))
cost-diff	128	(neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	99
0	23	99
1	43	99
2	72	99
3	116	96
4	197	96
5	435	96
6	740	96
7	994	96
8	1037	96
9	1064	96
10	1100	96
11	1100	96
0	1100	96

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize83.0ms (1.8%)

Memory

10.1MiB live, 52.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	2.2375599356723708	(.f64 y (/.f64 y (-.f64 (.f64 x x) y)))
accuracy	5.406044906885141	(/.f64 y (-.f64 (*.f64 x x) y))
accuracy	19.81810182665942	#s(approx (/ (* x x) (- (* x x) y)) #s(literal 1 binary64))
accuracy	21.83844312386691	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))

Samples

25.0ms

256×

valid

Compiler

Compiled 196 to 28 computations (85.7% saved)

Precisions

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

ival-div: 6.0ms (37.2% of total)

ival-mult: 5.0ms (31% of total)

ival-sqrt: 2.0ms (12.4% of total)

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

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

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

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

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

exact: 0.0ms (0% of total)

series5.0ms (0.1%)

Memory

9.2MiB live, 9.2MiB allocated

Counts

7 → 93

Calls

Call 1

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

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

Calls

6 calls:

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

simplify279.0ms (6.1%)

Memory

3.8MiB live, 162.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	1756
1	1155	1661
2	3788	1556
0	8222	1443

Stop Event

1×	iter limit
1×	node limit

Counts

93 → 91

Calls

Call 1

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

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

rewrite166.0ms (3.7%)

Memory

-21.6MiB live, 248.5MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	91
0	23	91
1	82	91
2	572	88
3	7157	88
0	8058	87

Stop Event

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

Counts

7 → 478

Calls

Call 1

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

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

eval149.0ms (3.3%)

Memory: 2.6MiB live, 165.7MiB allocated
Compiler: Compiled 24 338 to 2 379 computations (90.2% saved)

prune12.0ms (0.3%)

Memory

-11.5MiB live, 35.6MiB allocated

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	565	1	566
Fresh	0	0	0
Picked	1	0	1
Done	0	4	4
Total	566	5	571

Accuracy

100.0%

Counts

571 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.3%	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))))
✓	65.9%	(sqrt.f64 (fma.f64 x x y))
✓	70.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	33.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 67 to 42 computations (37.3% saved)

simplify48.0ms (1.1%)

Memory

11.3MiB live, 50.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	97
0	20	97
1	40	97
2	64	97
3	90	94
4	146	94
5	327	94
6	581	94
7	836	94
8	1179	94
9	1264	94
10	1339	94
11	1357	94
12	1379	94
13	1394	94
14	1397	94
0	1397	94

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize33.0ms (0.7%)

Memory

24.9MiB live, 63.6MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y)))
accuracy	19.81810182665942	#s(approx (/ (* x x) (- (* x x) y)) #s(literal 1 binary64))
accuracy	21.83844312386691	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))))
accuracy	43.153160411523345	#s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))

Samples

25.0ms

256×

valid

Compiler

Compiled 178 to 30 computations (83.1% saved)

Precisions

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

ival-mult: 5.0ms (35.3% of total)

ival-div: 3.0ms (21.2% of total)

ival-add: 2.0ms (14.1% of total)

ival-sqrt: 2.0ms (14.1% of total)

ival-sub: 1.0ms (7.1% of total)

ival-neg: 1.0ms (7.1% of total)

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

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

exact: 0.0ms (0% of total)

series6.0ms (0.1%)

Memory

-25.8MiB live, 13.2MiB allocated

Counts

5 → 61

Calls

Call 1

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

Calls

6 calls:

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

simplify206.0ms (4.5%)

Memory

9.2MiB live, 244.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	301	1178
1	915	1100
2	2940	1036
0	8321	961

Stop Event

1×	iter limit
1×	node limit

Counts

61 → 59

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

rewrite190.0ms (4.2%)

Memory

-6.4MiB live, 232.6MiB allocated

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	90
0	20	90
1	83	90
2	565	87
3	6734	87
0	8005	87

Stop Event

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

Counts

5 → 111

Calls

Call 1

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

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

eval22.0ms (0.5%)

Memory: -0.0MiB live, 46.0MiB allocated
Compiler: Compiled 11 911 to 656 computations (94.5% saved)

prune5.0ms (0.1%)

Memory

13.7MiB live, 13.7MiB allocated

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	158	5	163

Accuracy

100.0%

Counts

163 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	40.3%	(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))))
✓	65.9%	(sqrt.f64 (fma.f64 x x y))
✓	70.2%	#s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x))
✓	33.0%	#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
✓	1.2%	#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

Compiler

Compiled 190 to 79 computations (58.4% saved)

regimes18.0ms (0.4%)

Memory

8.0MiB live, 47.3MiB 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 (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))
(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))))
(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))
(sqrt.f64 (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))))))

Outputs

(sqrt.f64 (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))))))

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

Calls

5 calls:

4.0ms	(+.f64 (*.f64 x x) y)
3.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
3.0ms	y
3.0ms	x
3.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
100.0%	2	`x`
83.0%	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)

regimes13.0ms (0.3%)

Memory

-7.7MiB live, 31.1MiB allocated

Counts

7 → 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 (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))
(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) #s(approx (neg (* y (/ y (- (* x x) y)))) (fma.f64 x x y))))
(sqrt.f64 (fma.f64 (.f64 x x) #s(approx (/ ( x x) (- (* x x) y)) #s(literal 1 binary64)) (neg.f64 (.f64 y (/.f64 y (-.f64 (.f64 x x) y))))))

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

4 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
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 15 to 14 computations (6.7% saved)

regimes11.0ms (0.2%)

Memory

-8.1MiB live, 30.4MiB allocated

Counts

3 → 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 (fma.f64 x x y))

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
65.9%	1	`y`
65.9%	1	`x`
65.9%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
65.9%	1	`(+.f64 (*.f64 x x) y)`
65.9%	1	`(*.f64 x x)`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes11.0ms (0.2%)

Memory

-18.6MiB live, 25.5MiB 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:

4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
2.0ms	y
2.0ms	x
2.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
33.0%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
33.0%	1	`(+.f64 (*.f64 x x) y)`
33.0%	1	`(*.f64 x x)`
33.0%	1	`x`
33.0%	1	`y`

Compiler

Compiled 16 to 16 computations (0% saved)

regimes7.0ms (0.1%)

Memory

21.8MiB live, 21.8MiB 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	x
1.0ms	y
1.0ms	(sqrt.f64 (+.f64 (*.f64 x x) y))
1.0ms	(+.f64 (*.f64 x x) y)
1.0ms	(*.f64 x x)

Results

Accuracy	Segments	Branch
1.2%	1	`y`
1.2%	1	`(sqrt.f64 (+.f64 (*.f64 x x) y))`
1.2%	1	`(+.f64 (*.f64 x x) y)`
1.2%	1	`(*.f64 x x)`
1.2%	1	`x`

Compiler

Compiled 16 to 16 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2562627374758869e+265	1.1036533359747551e+266

Compiler

Compiled 9 to 10 computations (-11.1% saved)

bsearch0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	1.2562627374758869e+265	1.1036533359747551e+266

Compiler

Compiled 9 to 10 computations (-11.1% saved)

simplify37.0ms (0.8%)

Memory

12.9MiB live, 90.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	90
1	39	90
2	54	90
3	66	89
4	87	89
5	118	89
6	155	89
7	202	89
8	256	89
9	271	89
10	280	89
11	292	89
12	307	89
13	320	89
14	329	89
15	338	89
16	341	89
17	343	89

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001330293251784077024404771326911320976908787298030835333694183123784100048437476144137746460631060770586711684590915444743656162943995952194793889144970883957474817615854880173231735058974284480539885410778819330483862894400308606204866790619762130944 binary64)) (sqrt.f64 (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)))))) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001330293251784077024404771326911320976908787298030835333694183123784100048437476144137746460631060770586711684590915444743656162943995952194793889144970883957474817615854880173231735058974284480539885410778819330483862894400308606204866790619762130944 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))
#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 20000000000000001330293251784077024404771326911320976908787298030835333694183123784100048437476144137746460631060770586711684590915444743656162943995952194793889144970883957474817615854880173231735058974284480539885410778819330483862894400308606204866790619762130944 binary64)) (sqrt.f64 (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)))))) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001330293251784077024404771326911320976908787298030835333694183123784100048437476144137746460631060770586711684590915444743656162943995952194793889144970883957474817615854880173231735058974284480539885410778819330483862894400308606204866790619762130944 binary64)) (sqrt.f64 (fma.f64 (.f64 x x) (/.f64 (.f64 x x) (-.f64 (.f64 x x) y)) (.f64 (/.f64 y (-.f64 y (.f64 x x))) y))) #s(approx (sqrt (+ (* x x) y)) (fma.f64 (/.f64 #s(literal 1/2 binary64) x) y x)))
(if (<=.f64 (.f64 x x) #s(literal 20000000000000001330293251784077024404771326911320976908787298030835333694183123784100048437476144137746460631060770586711684590915444743656162943995952194793889144970883957474817615854880173231735058974284480539885410778819330483862894400308606204866790619762130944 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))
#s(approx (sqrt (+ (* x x) y)) (sqrt.f64 y))
#s(approx (sqrt (+ (* x x) y)) (neg.f64 x))

soundness566.0ms (12.4%)

Memory

-30.2MiB live, 372.2MiB 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
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

Compiler

Compiled 157 to 69 computations (56.1% saved)

preprocess41.0ms (0.9%)

Memory: 31.8MiB live, 109.3MiB allocated
Compiler: Compiled 332 to 136 computations (59% 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	27	90
1	39	90
2	54	90
3	66	89
4	87	89
5	118	89
6	155	89
7	202	89
8	256	89
9	271	89
10	280	89
11	292	89
12	307	89
13	320	89
14	329	89
15	338	89
16	341	89
17	343	89

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	27	90
1	39	90
2	54	90
3	66	89
4	87	89
5	118	89
6	155	89
7	202	89
8	256	89
9	271	89
10	280	89
11	292	89
12	307	89
13	320	89
14	329	89
15	338	89
16	341	89
17	343	89

start0.0ms (0%)

analyze27.0ms (0.6%)

sample737.0ms (16.2%)

explain77.0ms (1.7%)

preprocess18.0ms (0.4%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize17.0ms (0.4%)

series7.0ms (0.2%)

simplify169.0ms (3.7%)

rewrite170.0ms (3.7%)

eval46.0ms (1%)

prune58.0ms (1.3%)

simplify306.0ms (6.7%)

localize124.0ms (2.7%)

series20.0ms (0.4%)

simplify177.0ms (3.9%)

rewrite291.0ms (6.4%)

eval224.0ms (4.9%)

prune87.0ms (1.9%)

simplify85.0ms (1.9%)

localize83.0ms (1.8%)

series5.0ms (0.1%)

simplify279.0ms (6.1%)

rewrite166.0ms (3.7%)

eval149.0ms (3.3%)

prune12.0ms (0.3%)

simplify48.0ms (1.1%)

localize33.0ms (0.7%)

series6.0ms (0.1%)

simplify206.0ms (4.5%)

rewrite190.0ms (4.2%)

eval22.0ms (0.5%)

prune5.0ms (0.1%)

regimes18.0ms (0.4%)

regimes13.0ms (0.3%)

regimes11.0ms (0.2%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

simplify37.0ms (0.8%)

soundness566.0ms (12.4%)

preprocess41.0ms (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

Iter	Nodes	Cost
0	27	90
1	39	90
2	54	90
3	66	89
4	87	89
5	118	89
6	155	89
7	202	89
8	256	89
9	271	89
10	280	89
11	292	89
12	307	89
13	320	89
14	329	89
15	338	89
16	341	89
17	343	89