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

1.7MiB live, 1.7MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.3s (20%)

Memory

-12.8MiB live, 1 185.7MiB allocated

Samples

970.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 540.0ms

ival-mult: 215.0ms (39.8% of total)

ival-add: 152.0ms (28.2% of total)

ival-div: 95.0ms (17.6% of total)

ival-sqrt: 63.0ms (11.7% of total)

ival-true: 6.0ms (1.1% of total)

exact: 5.0ms (0.9% of total)

ival-assert: 3.0ms (0.6% of total)

Bogosity

explain198.0ms (2.9%)

Memory

2.1MiB live, 239.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
157	-	-	`(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	155	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	155
↳	`(*.f64 y y)`	overflow	69
↳	`(*.f64 x x)`	overflow	73
↳	`(*.f64 z z)`	overflow	67
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	124
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	155
`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	54
↳	`(*.f64 x x)`	underflow	61
↳	`(*.f64 z z)`	underflow	70
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	12
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2

Confusion

	Predicted +	Predicted -
+	157	0
-	0	99

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	157	0	0
-	0	0	99

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	99
1	157

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

72.0ms

512×

valid

Compiler

Compiled 192 to 48 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-mult: 41.0ms (76.8% of total)

ival-add: 4.0ms (7.5% of total)

ival-sqrt: 4.0ms (7.5% of total)

ival-div: 3.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

preprocess45.0ms (0.7%)

Memory

12.3MiB live, 50.6MiB 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: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	43.0%	(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)

simplify24.0ms (0.4%)

Memory

-22.1MiB live, 19.6MiB 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)

localize33.0ms (0.5%)

Memory

7.8MiB live, 45.0MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 y y)
accuracy	0.0	(*.f64 x x)
accuracy	0.07421875	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	36.46032819098802	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

19.0ms

256×

valid

Compiler

Compiled 118 to 24 computations (79.7% saved)

Precisions

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

ival-mult: 4.0ms (38.2% of total)

ival-div: 2.0ms (19.1% of total)

ival-add: 2.0ms (19.1% of total)

ival-sqrt: 2.0ms (19.1% of total)

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

exact: 0.0ms (0% of total)

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

series16.0ms (0.2%)

Memory

-0.9MiB live, 36.6MiB 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
4.0ms	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))
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))

simplify387.0ms (5.7%)

Memory

10.3MiB live, 207.0MiB 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)))))

rewrite665.0ms (9.9%)

Memory

15.4MiB live, 224.7MiB 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))))

eval54.0ms (0.8%)

Memory: 2.9MiB live, 117.2MiB allocated
Compiler: Compiled 11 745 to 1 772 computations (84.9% saved)

prune11.0ms (0.2%)

Memory

-13.4MiB live, 29.5MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	362	6	368
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	363	6	369

Accuracy

99.6%

Counts

369 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.9%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
▶	42.8%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	43.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	42.8%	(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 228 to 170 computations (25.4% saved)

simplify33.0ms (0.5%)

Memory

-8.8MiB live, 30.6MiB 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)

localize92.0ms (1.4%)

Memory

8.3MiB live, 128.9MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f64 z z)
accuracy	0.07421875	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.11166246394762544	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	36.46032819098802	(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	0.1484375	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	36.46032819098802	(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	0.11328370417568595	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	0.1484375	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	36.46032819098802	(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	0.4140625	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.5491728398669992	#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	0.4140625	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))

Samples

76.0ms

256×

valid

Compiler

Compiled 422 to 52 computations (87.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 12.0ms (42.6% of total)

ival-hypot: 4.0ms (14.2% of total)

ival-add: 3.0ms (10.7% of total)

ival-sqrt: 3.0ms (10.7% of total)

const: 3.0ms (10.7% of total)

ival-div: 2.0ms (7.1% of total)

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

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

exact: 0.0ms (0% of total)

series30.0ms (0.4%)

Memory

0.8MiB live, 40.1MiB 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
14.0ms	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))
3.0ms	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))
2.0ms	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))
2.0ms	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))
2.0ms	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))

simplify239.0ms (3.6%)

Memory

15.4MiB live, 211.4MiB 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))))
(+ (* (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)))))))))
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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))

rewrite138.0ms (2%)

Memory

12.5MiB live, 203.5MiB 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))))

eval69.0ms (1%)

Memory: -13.0MiB live, 150.2MiB allocated
Compiler: Compiled 15 022 to 1 879 computations (87.5% saved)

prune12.0ms (0.2%)

Memory

-1.9MiB live, 42.6MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	432	4	436
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	433	9	442

Accuracy

99.6%

Counts

442 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	42.7%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
✓	42.8%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	42.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	43.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	42.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	90.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 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))
▶	98.9%	#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 204 to 148 computations (27.5% saved)

simplify208.0ms (3.1%)

Memory

-21.3MiB live, 182.4MiB 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	(.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	(hypot.f64 (exp.f64 (log.f64 z)) y)
cost-diff	0	(*.f64 (hypot.f64 (exp.f64 (log.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 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64))))
cost-diff	2	(exp.f64 (log.f64 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	261
0	59	243
1	114	243
2	320	243
3	1194	237
4	4034	237
0	8511	220

Stop Event

1×	iter limit
1×	node limit
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)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64)))
(hypot.f64 (exp.f64 (log.f64 z)) y)
(exp.f64 (log.f64 z))
(log.f64 z)
z
y
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(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
(/.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 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) 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)))
#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) 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 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) z))
(.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)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64))))
#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 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64)))
(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))
(hypot.f64 (exp.f64 (log.f64 z)) y)
(hypot.f64 z y)
(exp.f64 (log.f64 z))
z
(log.f64 z)
z
y
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(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
(/.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)

localize625.0ms (9.3%)

Memory

9.5MiB live, 128.4MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0.0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.11166246394762544	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	0.3359375	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	36.38084984125903	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0.0859375	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.11328370417568595	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	0.31640625	(*.f64 #s(literal 1/3 binary64) z)
accuracy	36.46032819098802	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0.0	(log.f64 z)
accuracy	0.0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.4140625	(*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	6.140542914929031	(exp.f64 (log.f64 z))
accuracy	0.24609375	(.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) #s(literal 1/2 binary64)) y)
accuracy	0.31928801476920815	#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	0.37890625	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.4140625	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)

Samples

606.0ms

256×

valid

Compiler

Compiled 464 to 74 computations (84.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 589.0ms

ival-hypot: 358.0ms (60.8% of total)

ival-sqrt: 198.0ms (33.6% of total)

ival-mult: 15.0ms (2.5% of total)

ival-div: 5.0ms (0.8% of total)

const: 4.0ms (0.7% of total)

ival-exp: 3.0ms (0.5% of total)

ival-add: 3.0ms (0.5% of total)

ival-log: 3.0ms (0.5% of total)

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

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

exact: 0.0ms (0% of total)

series83.0ms (1.2%)

Memory

3.8MiB live, 159.1MiB allocated

Counts

20 → 176

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

Calls

9 calls:

Time	Variable		Point	Expression
35.0ms	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) (exp (log z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt 1/3)) (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (/ (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) (log z) (sqrt 3))
19.0ms	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) (exp (log z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt 1/3)) (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (/ (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) (log z) (sqrt 3))
10.0ms	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) (exp (log z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt 1/3)) (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (/ (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) (log z) (sqrt 3))
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) (exp (log z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt 1/3)) (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (/ (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) (log z) (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) (exp (log z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt 1/3)) (sqrt (+ (* (exp (log z)) (exp (log z))) (* y y))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (/ (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) (log z) (sqrt 3))

simplify178.0ms (2.6%)

Memory

3.7MiB live, 272.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	637	4894
1	2251	4848
0	8792	4258

Stop Event

1×	iter limit
1×	node limit

Counts

176 → 173

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))
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)))))
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y
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(* -1 y)
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(* -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)))))))
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(/ (+ (* 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))))
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(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
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(+ (log -1) (* -1 (log (/ -1 z))))

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

rewrite185.0ms (2.8%)

Memory

-17.5MiB live, 267.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	240
0	59	221
1	198	221
2	1326	221
0	8742	207

Stop Event

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

Counts

20 → 291

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

eval63.0ms (0.9%)

Memory: 9.2MiB live, 127.8MiB allocated
Compiler: Compiled 18 773 to 2 051 computations (89.1% saved)

prune10.0ms (0.2%)

Memory

-2.1MiB live, 37.3MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	457	3	460
Fresh	0	0	0
Picked	3	1	4
Done	1	4	5
Total	461	8	469

Accuracy

100.0%

Counts

469 → 8

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)))
✓	42.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	43.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	42.8%	(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))
▶	98.9%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (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))))

Compiler

Compiled 183 to 133 computations (27.3% saved)

simplify67.0ms (1%)

Memory

30.7MiB live, 69.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	186
0	46	176
1	85	176
2	224	176
3	631	176
4	1296	170
5	2114	170
6	2548	170
7	2619	170
8	2640	170
9	2656	170
10	2664	170
11	2672	170
0	2672	159

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

localize76.0ms (1.1%)

Memory

-22.0MiB live, 138.1MiB allocated

Localize:

Found 11 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	0.3359375	(/.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	0.33203125	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.5491728398669992	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
accuracy	0.24609375	(.f64 y (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
accuracy	0.31928801476920815	#s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (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)))
accuracy	0.37890625	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.41015625	(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))

Samples

59.0ms

256×

valid

Compiler

Compiled 325 to 65 computations (80% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 12.0ms (26.2% of total)

ival-hypot: 12.0ms (26.2% of total)

ival-div: 6.0ms (13.1% of total)

ival-sqrt: 6.0ms (13.1% of total)

const: 6.0ms (13.1% of total)

ival-add: 3.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

series20.0ms (0.3%)

Memory

-16.1MiB live, 28.3MiB allocated

Counts

12 → 150

Calls

Call 1

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

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 (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))))))))
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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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(/ 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)))))
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x
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
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(* -1 (* x (sqrt 1/3)))
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(* -1 x)
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
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(* 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)))))
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(* (/ 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)))))
(* 1/2 (/ (* y (sqrt 1/3)) z))
(* 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)))))))
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(/ y (sqrt 3))
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(* 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))))))
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(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
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(* -1 (* y (sqrt 1/3)))
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(* -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))))))
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(* -1 y)
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(/ (+ (* 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)))))
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(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
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(* (/ 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)))))
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(/ z (sqrt 3))
(sqrt (+ (pow x 2) (pow y 2)))
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(/ (sqrt 1/3) z)
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(* -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
2.0ms	z	@	-inf	((+ (* (sqrt 1/3) z) (* (* y (* 1/2 (/ (sqrt 1/3) z))) y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt 1/3) (/ (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))) (/ (sqrt 1/3) z) (* y (* 1/2 (/ (sqrt 1/3) z))))
2.0ms	z	@	0	((+ (* (sqrt 1/3) z) (* (* y (* 1/2 (/ (sqrt 1/3) z))) y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt 1/3) (/ (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))) (/ (sqrt 1/3) z) (* y (* 1/2 (/ (sqrt 1/3) z))))
2.0ms	z	@	inf	((+ (* (sqrt 1/3) z) (* (* y (* 1/2 (/ (sqrt 1/3) z))) y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt 1/3) (/ (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))) (/ (sqrt 1/3) z) (* y (* 1/2 (/ (sqrt 1/3) z))))
2.0ms	y	@	inf	((+ (* (sqrt 1/3) z) (* (* y (* 1/2 (/ (sqrt 1/3) z))) y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt 1/3) (/ (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))) (/ (sqrt 1/3) z) (* y (* 1/2 (/ (sqrt 1/3) z))))
1.0ms	y	@	0	((+ (* (sqrt 1/3) z) (* (* y (* 1/2 (/ (sqrt 1/3) z))) y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt 1/3) (/ (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))) (/ (sqrt 1/3) z) (* y (* 1/2 (/ (sqrt 1/3) z))))

simplify180.0ms (2.7%)

Memory

27.3MiB live, 255.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	596	4649
1	2106	4604
0	8485	4035

Stop Event

1×	iter limit
1×	node limit

Counts

150 → 147

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

rewrite130.0ms (1.9%)

Memory

-5.1MiB live, 191.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	159
0	46	148
1	163	148
2	1329	148
0	9519	140

Stop Event

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

Counts

12 → 171

Calls

Call 1

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

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

eval62.0ms (0.9%)

Memory: 21.0MiB live, 63.1MiB allocated
Compiler: Compiled 14 581 to 1 541 computations (89.4% saved)

prune23.0ms (0.3%)

Memory

-15.0MiB live, 22.4MiB allocated

Pruning

8 alts after pruning (0 fresh and 8 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	337	8	345

Accuracy

100.0%

Counts

345 → 8

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)))
✓	42.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	43.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	42.8%	(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))
✓	98.9%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (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))))

Compiler

Compiled 494 to 211 computations (57.3% saved)

regimes43.0ms (0.6%)

Memory

25.6MiB live, 62.6MiB 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)))
(/.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)))
(/.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 (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))))
#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)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 (exp.f64 (log.f64 z)) y) (sqrt.f64 #s(literal 1/3 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:

7.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
4.0ms	x
4.0ms	z
4.0ms	y
4.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes83.0ms (1.2%)

Memory

-21.7MiB live, 68.3MiB 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)))
(/.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)))
(/.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 (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))))
#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:

48.0ms	y
6.0ms	(*.f64 z z)
4.0ms	x
4.0ms	z
3.0ms	(*.f64 y y)

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes41.0ms (0.6%)

Memory

-12.5MiB live, 59.9MiB 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)))
(/.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)))
(/.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 (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))))
#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 (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))))

Calls

10 calls:

8.0ms	(+.f64 (.f64 x x) (.f64 y y))
6.0ms	x
4.0ms	z
3.0ms	y
3.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
98.9%	1	`x`
98.9%	1	`y`
98.9%	1	`z`
98.9%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.9%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.9%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.9%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.9%	1	`(*.f64 x x)`
98.9%	1	`(*.f64 y y)`
98.9%	1	`(*.f64 z z)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes31.0ms (0.5%)

Memory

15.7MiB live, 53.3MiB allocated

Counts

9 → 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)))
(/.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)))
(/.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:

5.0ms	z
3.0ms	y
3.0ms	x
3.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes20.0ms (0.3%)

Memory

-15.6MiB live, 29.7MiB allocated

Accuracy

Total -35.8b remaining (-3742.3%)

Threshold costs -35.8b (-3742.3%)

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:

2.0ms	y
2.0ms	z
1.0ms	x
1.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
1.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify18.0ms (0.3%)

Memory

17.3MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	120
1	65	120
2	163	120
3	412	120
4	677	120
5	801	120
6	844	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 (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))))
#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 (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))))
#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))

soundness1.0s (15.3%)

Memory

24.5MiB live, 577.2MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	240
0	59	221
1	198	221
2	1326	221
0	8742	207
0	394	2497
1	1346	2497
2	5598	2495
0	8513	2239
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	637	4894
1	2251	4848
0	8792	4258

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

Compiler

Compiled 273 to 149 computations (45.4% saved)

preprocess162.0ms (2.4%)

Memory: -17.1MiB live, 179.8MiB allocated
Compiler: Compiled 484 to 262 computations (45.9% 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	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

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (20%)

explain198.0ms (2.9%)

preprocess45.0ms (0.7%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify24.0ms (0.4%)

localize33.0ms (0.5%)

series16.0ms (0.2%)

simplify387.0ms (5.7%)

rewrite665.0ms (9.9%)

eval54.0ms (0.8%)

prune11.0ms (0.2%)

simplify33.0ms (0.5%)

localize92.0ms (1.4%)

series30.0ms (0.4%)

simplify239.0ms (3.6%)

rewrite138.0ms (2%)

eval69.0ms (1%)

prune12.0ms (0.2%)

simplify208.0ms (3.1%)

localize625.0ms (9.3%)

series83.0ms (1.2%)

simplify178.0ms (2.6%)

rewrite185.0ms (2.8%)

eval63.0ms (0.9%)

prune10.0ms (0.2%)

simplify67.0ms (1%)

localize76.0ms (1.1%)

series20.0ms (0.3%)

simplify180.0ms (2.7%)

rewrite130.0ms (1.9%)

eval62.0ms (0.9%)

prune23.0ms (0.3%)

regimes43.0ms (0.6%)

regimes83.0ms (1.2%)

regimes41.0ms (0.6%)

regimes31.0ms (0.5%)

regimes20.0ms (0.3%)

simplify18.0ms (0.3%)

soundness1.0s (15.3%)

preprocess162.0ms (2.4%)

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