Metrics for Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.9MiB live, 1.9MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
100%	99.9%	0%	0.1%	0%	0%	0%	4

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.3s (18.9%)

Memory

12.3MiB live, 950.4MiB allocated

Samples

965.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 648.0ms

ival-mult: 272.0ms (42% of total)

ival-add: 164.0ms (25.3% of total)

ival-div: 112.0ms (17.3% of total)

ival-sqrt: 84.0ms (13% of total)

ival-true: 6.0ms (0.9% of total)

exact: 5.0ms (0.8% of total)

ival-assert: 4.0ms (0.6% of total)

Bogosity

explain189.0ms (2.7%)

Memory

-1.0MiB live, 239.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
167	-	-	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
0	-	-	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
0	-	-	`#s(literal 3 binary64)`
0	-	-	`z`
0	-	-	`(*.f64 x x)`
0	-	-	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	-	`(*.f64 z z)`
0	-	-	`y`
0	-	-	`(*.f64 y y)`
0	-	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	165	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	165
↳	`(*.f64 y y)`	overflow	66
↳	`(*.f64 x x)`	overflow	75
↳	`(*.f64 z z)`	overflow	72
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	122
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	165
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	2	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	2
↳	`(*.f64 y y)`	underflow	60
↳	`(*.f64 x x)`	underflow	55
↳	`(*.f64 z z)`	underflow	50
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	17
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2

Confusion

	Predicted +	Predicted -
+	167	0
-	0	89

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	167	0	0
-	0	0	89

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	89
1	167

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

80.0ms

512×

valid

Compiler

Compiled 134 to 37 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-mult: 48.0ms (79.9% of total)

ival-add: 4.0ms (6.7% of total)

ival-sqrt: 4.0ms (6.7% of total)

ival-div: 3.0ms (5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess83.0ms (1.2%)

Memory

-30.4MiB live, 36.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	129
1	112	129
2	288	129
3	508	129
4	800	129
5	925	129
6	926	129
0	11	14
0	18	14
1	41	14
2	135	14
3	372	14
4	641	14
5	756	14
6	775	14
0	775	12

Stop Event

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

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Outputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal 3 binary64)))

Symmetry

(abs z)

(abs y)

(abs x)

(sort x y z)

Compiler

Compiled 14 to 11 computations (21.4% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.6%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify15.0ms (0.2%)

Memory

19.7MiB live, 19.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
cost-diff	1	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	1	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
0	18	58
1	41	58
2	135	58
3	372	58
4	641	58
5	756	58
6	775	58
0	775	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(+.f64 (.f64 x x) (.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
(*.f64 z z)
z
#s(literal 3 binary64)

Outputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal 3 binary64)))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
(/.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal 3 binary64))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(fma.f64 z z (fma.f64 y y (*.f64 x x)))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 y y (*.f64 x x))
(*.f64 x x)
x
(*.f64 y y)
y
(*.f64 z z)
z
#s(literal 3 binary64)

localize55.0ms (0.8%)

Memory

-11.6MiB live, 35.8MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	0.078125	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	38.60947559625797	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

48.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-div: 27.0ms (73.8% of total)

ival-mult: 5.0ms (13.7% of total)

ival-add: 2.0ms (5.5% of total)

ival-sqrt: 2.0ms (5.5% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.2%)

Memory

16.7MiB live, 16.7MiB allocated

Counts

6 → 60

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(+.f64 (.f64 x x) (.f64 y y))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
(*.f64 x x)
(*.f64 y y)

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

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
2.0ms	y	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
2.0ms	y	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
2.0ms	x	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
1.0ms	z	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))

simplify192.0ms (2.8%)

Memory

22.7MiB live, 249.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	1522
1	750	1522
2	3175	1522
0	8225	1335

Stop Event

1×	iter limit
1×	node limit

Counts

60 → 60

Calls

Call 1

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

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

rewrite320.0ms (4.6%)

Memory

-20.1MiB live, 174.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
0	18	51
1	78	51
2	709	51
0	8840	44

Stop Event

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

Counts

6 → 310

Calls

Call 1

Inputs
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(+.f64 (.f64 x x) (.f64 y y))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
(*.f64 x x)
(*.f64 y y)

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

eval337.0ms (4.9%)

Memory: 16.3MiB live, 118.4MiB allocated
Compiler: Compiled 11 745 to 1 772 computations (84.9% saved)

prune140.0ms (2%)

Memory

-16.7MiB live, 29.7MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	361	7	368
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	362	7	369

Accuracy

99.6%

Counts

369 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.5%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
	39.6%	(sqrt.f64 (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64) (.f64 #s(literal 3 binary64) (*.f64 z z))) #s(literal 9 binary64)))
▶	39.2%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
▶	98.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 260 to 194 computations (25.4% saved)

simplify155.0ms (2.2%)

Memory

-14.5MiB live, 33.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(*.f64 z z)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
cost-diff	0	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
cost-diff	0	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
cost-diff	0	(fma.f64 z z (*.f64 y y))
cost-diff	0	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
cost-diff	0	(*.f64 z z)
cost-diff	0	(.f64 #s(literal 1/3 binary64) (.f64 z z))
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
cost-diff	0	(hypot.f64 z y)
cost-diff	0	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	231
0	44	222
1	80	222
2	210	222
3	544	222
4	914	222
5	1062	222
6	1087	222
7	1092	222
8	1096	222
9	1100	222
10	1105	222
11	1110	222
0	1110	213

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
(hypot.f64 z y)
z
y
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
#s(literal 1/3 binary64)
(*.f64 z z)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
#s(literal 1/3 binary64)
(fma.f64 z z (*.f64 y y))
z
(*.f64 y y)
y
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
#s(literal 3 binary64)

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y)))
(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
(hypot.f64 z y)
z
y
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z z) #s(literal 1/3 binary64))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z z) #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(*.f64 z z)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
(.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(fma.f64 z z (*.f64 y y))
z
(*.f64 y y)
y
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
#s(literal 3 binary64)

localize324.0ms (4.7%)

Memory

28.9MiB live, 131.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 z z)
accuracy	0.078125	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.30279602335578104	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	38.60947559625797	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
accuracy	0.0	(*.f64 y y)
accuracy	0.0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
accuracy	0.12109375	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	38.60947559625797	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
accuracy	0.0	(*.f64 z z)
accuracy	0.12109375	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	0.30213225381889774	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	38.60947559625797	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
accuracy	0.0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.39453125	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.5491648992616865	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
accuracy	0.0	(hypot.f64 z y)
accuracy	0.0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.39453125	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))

Samples

311.0ms

256×

valid

Compiler

Compiled 191 to 21 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 297.0ms

ival-mult: 279.0ms (94% of total)

ival-hypot: 4.0ms (1.3% of total)

const: 4.0ms (1.3% of total)

ival-div: 3.0ms (1% of total)

ival-add: 3.0ms (1% of total)

ival-sqrt: 3.0ms (1% of total)

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

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

exact: 0.0ms (0% of total)

series383.0ms (5.6%)

Memory

-43.8MiB live, 50.7MiB allocated

Counts

18 → 103

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
(hypot.f64 z y)
(sqrt.f64 #s(literal 1/3 binary64))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(*.f64 z z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
(fma.f64 z z (*.f64 y y))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 y y)

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

Calls

9 calls:

Time	Variable		Point	Expression
176.0ms	x	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
5.0ms	y	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
4.0ms	z	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
4.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
3.0ms	y	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))

simplify335.0ms (4.9%)

Memory

42.8MiB live, 322.5MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	2497
1	1346	2497
2	5598	2495
0	8513	2239

Stop Event

1×	iter limit
1×	node limit

Counts

103 → 101

Calls

Call 1

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

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

rewrite130.0ms (1.9%)

Memory

-13.0MiB live, 224.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	214
0	44	205
1	136	205
2	1012	205
0	10223	196

Stop Event

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

Counts

18 → 311

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
(hypot.f64 z y)
(sqrt.f64 #s(literal 1/3 binary64))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(*.f64 z z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
(fma.f64 z z (*.f64 y y))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 y y)

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

eval125.0ms (1.8%)

Memory: -1.6MiB live, 183.3MiB allocated
Compiler: Compiled 15 022 to 1 879 computations (87.5% saved)

prune9.0ms (0.1%)

Memory

29.9MiB live, 29.9MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	432	4	436
Fresh	2	0	2
Picked	0	5	5
Done	0	0	0
Total	434	9	443

Accuracy

99.6%

Counts

443 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.1%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
✓	39.2%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
▶	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
▶	99.0%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))

Compiler

Compiled 206 to 147 computations (28.6% saved)

simplify70.0ms (1%)

Memory

-8.3MiB live, 38.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 z z)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
cost-diff	0	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
cost-diff	0	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) z)
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
cost-diff	2	(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) z)
cost-diff	0	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
cost-diff	0	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
cost-diff	0	#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
cost-diff	3	(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	288
0	57	288
1	106	285
2	287	285
3	821	279
4	1765	279
5	2619	279
6	2850	279
7	2877	279
8	2887	279
9	2887	279
10	2887	279
0	2887	247

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
z
#s(literal 1/2 binary64)
y
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
(.f64 (.f64 #s(literal 1/3 binary64) z) z)
(*.f64 #s(literal 1/3 binary64) z)
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
(*.f64 #s(literal 1/3 binary64) z)
#s(literal 1/3 binary64)
z
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(*.f64 y y)
y
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (.f64 (fma.f64 (.f64 (/.f64 y z) y) #s(literal 1/2 binary64) z) (sqrt.f64 #s(literal 1/3 binary64)))))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (.f64 (fma.f64 (.f64 (/.f64 y z) y) #s(literal 1/2 binary64) z) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (fma.f64 (.f64 (/.f64 y z) y) #s(literal 1/2 binary64) z) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
(.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y)
(*.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
z
#s(literal 1/2 binary64)
y
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
(.f64 (.f64 #s(literal 1/3 binary64) z) z)
(*.f64 #s(literal 1/3 binary64) z)
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
(*.f64 #s(literal 1/3 binary64) z)
#s(literal 1/3 binary64)
z
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(*.f64 y y)
y
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

localize81.0ms (1.2%)

Memory

-1.9MiB live, 140.8MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.30279602335578104	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	0.34375	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	38.549476092483445	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0.078125	(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
accuracy	0.1953125	(.f64 (.f64 y y) #s(literal 1/3 binary64))
accuracy	0.32421875	(*.f64 #s(literal 1/3 binary64) z)
accuracy	38.60947559625797	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
accuracy	0.078125	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.30213225381889774	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	0.32421875	(*.f64 #s(literal 1/3 binary64) z)
accuracy	38.60947559625797	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0.23226340476030194	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
accuracy	0.26409381083252853	#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
accuracy	0.29296875	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.39453125	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)

Samples

65.0ms

256×

valid

Compiler

Compiled 204 to 31 computations (84.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 47.0ms

ival-mult: 18.0ms (38.3% of total)

ival-div: 7.0ms (14.9% of total)

ival-sqrt: 7.0ms (14.9% of total)

const: 6.0ms (12.8% of total)

ival-add: 4.0ms (8.5% of total)

ival-hypot: 4.0ms (8.5% of total)

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

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

exact: 0.0ms (0% of total)

series31.0ms (0.4%)

Memory

7.6MiB live, 53.6MiB allocated

Counts

19 → 158

Calls

Call 1

Inputs
(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
(.f64 (.f64 #s(literal 1/3 binary64) z) z)
(*.f64 #s(literal 1/3 binary64) z)
(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(sqrt.f64 #s(literal 3 binary64))

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	((+ (* (* (* (/ (sqrt 1/3) z) 1/2) y) y) (* (sqrt 1/3) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (* (* (/ (sqrt 1/3) z) 1/2) y) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* 1/3 z) z) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (* (sqrt 1/3) z) (/ (sqrt 1/3) z) (* (* y y) 1/3) (sqrt 3))
5.0ms	y	@	0	((+ (* (* (* (/ (sqrt 1/3) z) 1/2) y) y) (* (sqrt 1/3) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (* (* (/ (sqrt 1/3) z) 1/2) y) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* 1/3 z) z) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (* (sqrt 1/3) z) (/ (sqrt 1/3) z) (* (* y y) 1/3) (sqrt 3))
4.0ms	z	@	0	((+ (* (* (* (/ (sqrt 1/3) z) 1/2) y) y) (* (sqrt 1/3) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (* (* (/ (sqrt 1/3) z) 1/2) y) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* 1/3 z) z) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (* (sqrt 1/3) z) (/ (sqrt 1/3) z) (* (* y y) 1/3) (sqrt 3))
3.0ms	z	@	inf	((+ (* (* (* (/ (sqrt 1/3) z) 1/2) y) y) (* (sqrt 1/3) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (* (* (/ (sqrt 1/3) z) 1/2) y) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* 1/3 z) z) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (* (sqrt 1/3) z) (/ (sqrt 1/3) z) (* (* y y) 1/3) (sqrt 3))
3.0ms	z	@	-inf	((+ (* (* (* (/ (sqrt 1/3) z) 1/2) y) y) (* (sqrt 1/3) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (* (* (/ (sqrt 1/3) z) 1/2) y) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* 1/3 z) z) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (* (sqrt 1/3) z) (/ (sqrt 1/3) z) (* (* y y) 1/3) (sqrt 3))

simplify164.0ms (2.4%)

Memory

1.9MiB live, 230.4MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	563	4525
1	2016	4480
0	8550	3921

Stop Event

1×	iter limit
1×	node limit

Counts

158 → 155

Calls

Call 1

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

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

rewrite190.0ms (2.8%)

Memory

-19.3MiB live, 268.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	263
0	57	260
1	187	257
2	1439	257
0	9204	230

Stop Event

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

Counts

19 → 269

Calls

Call 1

Inputs
(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
(.f64 (.f64 #s(literal 1/3 binary64) z) z)
(*.f64 #s(literal 1/3 binary64) z)
(fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 z z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(sqrt.f64 #s(literal 3 binary64))

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

eval53.0ms (0.8%)

Memory: 25.6MiB live, 117.2MiB allocated
Compiler: Compiled 17 810 to 1 787 computations (90% saved)

prune13.0ms (0.2%)

Memory

-19.0MiB live, 32.3MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	422	2	424
Fresh	0	0	0
Picked	1	3	4
Done	1	4	5
Total	424	9	433

Accuracy

100.0%

Counts

433 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
✓	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
✓	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	98.6%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
✓	99.0%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))

Compiler

Compiled 208 to 150 computations (27.9% saved)

simplify12.0ms (0.2%)

Memory

22.1MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(hypot.f64 y z)
cost-diff	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
cost-diff	0	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	23	71
1	44	71
2	124	71
3	281	71
4	399	71
5	409	71
6	413	71
7	417	71
8	421	71
9	427	71
10	435	71
11	443	71
0	443	65

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
(hypot.f64 y z)
y
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

Outputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
(hypot.f64 y z)
y
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

localize43.0ms (0.6%)

Memory

-19.3MiB live, 72.0MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0.0	(hypot.f64 y z)
accuracy	0.0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
accuracy	0.34375	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.34765625	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.5491648992616865	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Samples

31.0ms

256×

valid

Compiler

Compiled 65 to 16 computations (75.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-add: 6.0ms (28.5% of total)

ival-mult: 5.0ms (23.8% of total)

ival-hypot: 4.0ms (19% of total)

ival-div: 3.0ms (14.3% of total)

ival-sqrt: 3.0ms (14.3% of total)

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

exact: 0.0ms (0% of total)

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

series6.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB allocated

Counts

6 → 90

Calls

Call 1

Inputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
(hypot.f64 y z)

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

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	inf	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* y y) (* z z))))
1.0ms	z	@	-inf	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* y y) (* z z))))
1.0ms	z	@	0	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* y y) (* z z))))
0.0ms	x	@	0	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* y y) (* z z))))
0.0ms	y	@	0	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* y y) (* z z))))

simplify175.0ms (2.5%)

Memory

26.6MiB live, 259.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	370	2772
1	1253	2730
2	5620	2622
0	8267	2259

Stop Event

1×	iter limit
1×	node limit

Counts

90 → 87

Calls

Call 1

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

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

rewrite225.0ms (3.3%)

Memory

-40.6MiB live, 229.1MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	64
0	23	63
1	92	63
2	846	63
0	9344	57

Stop Event

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

Counts

6 → 93

Calls

Call 1

Inputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
(hypot.f64 y z)

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

eval89.0ms (1.3%)

Memory: 3.4MiB live, 52.2MiB allocated
Compiler: Compiled 6 305 to 769 computations (87.8% saved)

prune140.0ms (2%)

Memory

-17.6MiB live, 22.6MiB allocated

Pruning

9 alts after pruning (0 fresh and 9 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	2	2
Done	0	7	7
Total	189	9	198

Accuracy

100.0%

Counts

198 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
✓	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
✓	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	39.6%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	39.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
✓	98.6%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
✓	99.0%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))

Compiler

Compiled 496 to 226 computations (54.4% saved)

regimes195.0ms (2.8%)

Memory

11.2MiB live, 96.7MiB allocated

Counts

14 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64) (.f64 #s(literal 3 binary64) (*.f64 z z))) #s(literal 9 binary64)))
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))

Outputs
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))

Calls

10 calls:

155.0ms	(*.f64 z z)
8.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
4.0ms	y
4.0ms	z
4.0ms	x

Results

Accuracy	Segments	Branch
99.5%	1	`(*.f64 z z)`
99.5%	1	`(*.f64 y y)`
99.5%	1	`(*.f64 x x)`
99.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.5%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.5%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.5%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.5%	1	`x`
99.5%	1	`y`
99.5%	1	`z`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes56.0ms (0.8%)

Memory

44.8MiB live, 77.5MiB allocated

Counts

13 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64) (.f64 #s(literal 3 binary64) (*.f64 z z))) #s(literal 9 binary64)))
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))

Calls

10 calls:

22.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	y
4.0ms	x
4.0ms	z
4.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
99.4%	1	`(*.f64 z z)`
99.4%	1	`(*.f64 y y)`
99.4%	1	`(*.f64 x x)`
99.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.4%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.4%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.4%	1	`x`
99.4%	1	`y`
99.4%	1	`z`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes134.0ms (1.9%)

Memory

-45.8MiB live, 109.5MiB allocated

Counts

12 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64) (.f64 #s(literal 3 binary64) (*.f64 z z))) #s(literal 9 binary64)))
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))

Outputs

#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (*.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))

Calls

10 calls:

30.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
14.0ms	z
6.0ms	y
4.0ms	x
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
99.0%	1	`(*.f64 z z)`
99.0%	1	`(*.f64 y y)`
99.0%	1	`(*.f64 x x)`
99.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.0%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.0%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.0%	1	`x`
99.0%	1	`y`
99.0%	1	`z`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes76.0ms (1.1%)

Memory

12.1MiB live, 98.0MiB allocated

Counts

11 → 1

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 #s(literal 1/3 binary64) z) z (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64) (.f64 #s(literal 3 binary64) (*.f64 z z))) #s(literal 9 binary64)))
(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))

Outputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Calls

10 calls:

32.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
18.0ms	(*.f64 z z)
3.0ms	z
3.0ms	x
3.0ms	y

Results

Accuracy	Segments	Branch
98.6%	1	`(*.f64 z z)`
98.6%	1	`(*.f64 y y)`
98.6%	1	`(*.f64 x x)`
98.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.6%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.6%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.6%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.6%	1	`x`
98.6%	1	`y`
98.6%	1	`z`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes16.0ms (0.2%)

Memory

23.8MiB live, 69.6MiB allocated

Accuracy

Total -38.1b remaining (-4069.8%)

Threshold costs -38.1b (-4069.8%)

Counts

3 → 1

Calls

Call 1

Inputs

#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (*.f64 #s(literal 1/3 binary64) (*.f64 z z))))

(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (*.f64 (*.f64 #s(literal 1/3 binary64) z) z)))

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Calls

10 calls:

3.0ms	(+.f64 (.f64 x x) (.f64 y y))
1.0ms	y
1.0ms	z
1.0ms	x
1.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
98.5%	1	`(*.f64 z z)`
98.5%	1	`(*.f64 y y)`
98.5%	1	`(*.f64 x x)`
98.5%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.5%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.5%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.5%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.5%	1	`x`
98.5%	1	`y`
98.5%	1	`z`

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify46.0ms (0.7%)

Memory

18.1MiB live, 68.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	120
1	64	120
2	162	120
3	410	120
4	679	120
5	803	120
6	846	120

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Outputs
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

soundness855.0ms (12.4%)

Memory

-30.9MiB live, 736.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	563	4525
1	2016	4480
0	8550	3921
0	30	214
0	44	205
1	136	205
2	1012	205
0	10223	196
0	230	1522
1	750	1522
2	3175	1522
0	8225	1335
0	394	2497
1	1346	2497
2	5598	2495
0	8513	2239

Stop Event

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

Compiler

Compiled 232 to 122 computations (47.4% saved)

preprocess113.0ms (1.6%)

Memory: 14.5MiB live, 147.0MiB allocated
Compiler: Compiled 484 to 260 computations (46.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	40	129
1	112	129
2	288	129
3	508	129
4	800	129
5	925	129
6	926	129
0	11	14
0	18	14
1	41	14
2	135	14
3	372	14
4	641	14
5	756	14
6	775	14
0	775	12

Iter	Nodes	Cost
0	18	71
0	23	71
1	44	71
2	124	71
3	281	71
4	399	71
5	409	71
6	413	71
7	417	71
8	421	71
9	427	71
10	435	71
11	443	71
0	443	65

Iter	Nodes	Cost
0	40	129
1	112	129
2	288	129
3	508	129
4	800	129
5	925	129
6	926	129
0	11	14
0	18	14
1	41	14
2	135	14
3	372	14
4	641	14
5	756	14
6	775	14
0	775	12

Iter	Nodes	Cost
0	18	71
0	23	71
1	44	71
2	124	71
3	281	71
4	399	71
5	409	71
6	413	71
7	417	71
8	421	71
9	427	71
10	435	71
11	443	71
0	443	65

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (18.9%)

explain189.0ms (2.7%)

preprocess83.0ms (1.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize55.0ms (0.8%)

series14.0ms (0.2%)

simplify192.0ms (2.8%)

rewrite320.0ms (4.6%)

eval337.0ms (4.9%)

prune140.0ms (2%)

simplify155.0ms (2.2%)

localize324.0ms (4.7%)

series383.0ms (5.6%)

simplify335.0ms (4.9%)

rewrite130.0ms (1.9%)

eval125.0ms (1.8%)

prune9.0ms (0.1%)

simplify70.0ms (1%)

localize81.0ms (1.2%)

series31.0ms (0.4%)

simplify164.0ms (2.4%)

rewrite190.0ms (2.8%)

eval53.0ms (0.8%)

prune13.0ms (0.2%)

simplify12.0ms (0.2%)

localize43.0ms (0.6%)

series6.0ms (0.1%)

simplify175.0ms (2.5%)

rewrite225.0ms (3.3%)

eval89.0ms (1.3%)

prune140.0ms (2%)

regimes195.0ms (2.8%)

regimes56.0ms (0.8%)

regimes134.0ms (1.9%)

regimes76.0ms (1.1%)

regimes16.0ms (0.2%)

simplify46.0ms (0.7%)

soundness855.0ms (12.4%)

preprocess113.0ms (1.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	40	129
1	112	129
2	288	129
3	508	129
4	800	129
5	925	129
6	926	129
0	11	14
0	18	14
1	41	14
2	135	14
3	372	14
4	641	14
5	756	14
6	775	14
0	775	12

Iter	Nodes	Cost
0	18	71
0	23	71
1	44	71
2	124	71
3	281	71
4	399	71
5	409	71
6	413	71
7	417	71
8	421	71
9	427	71
10	435	71
11	443	71
0	443	65