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

1.5MiB live, 1.5MiB 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 (17%)

Memory

51.5MiB live, 1 307.1MiB allocated

Samples

772.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 538.0ms

ival-mult: 193.0ms (35.8% of total)

ival-div: 187.0ms (34.7% of total)

ival-add: 77.0ms (14.3% of total)

ival-sqrt: 66.0ms (12.3% of total)

ival-true: 7.0ms (1.3% of total)

exact: 5.0ms (0.9% of total)

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

Bogosity

explain154.0ms (2%)

Memory

-15.2MiB live, 263.2MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
143	-	-	`(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	143	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	143
↳	`(*.f64 y y)`	overflow	64
↳	`(*.f64 x x)`	overflow	62
↳	`(*.f64 z z)`	overflow	51
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	111
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	143

Confusion

	Predicted +	Predicted -
+	143	0
-	0	113

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	143	0	0
-	0	0	113

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	113
1	143

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 134 to 37 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 25.0ms

ival-mult: 13.0ms (51.1% of total)

ival-add: 4.0ms (15.7% of total)

ival-sqrt: 4.0ms (15.7% of total)

ival-div: 3.0ms (11.8% of total)

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

exact: 0.0ms (0% of total)

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

preprocess42.0ms (0.6%)

Memory

7.2MiB live, 83.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	129
1	76	129
2	155	129
3	321	129
4	583	129
5	941	129
6	1271	129
7	1286	129
0	11	14
0	18	14
1	22	14
2	29	14
3	31	14
0	31	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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.3MiB live, 1.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.9%	(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)

simplify3.0ms (0%)

Memory

6.3MiB live, 6.3MiB 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	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	128	(+.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	22	58
2	29	58
3	31	58
0	31	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)

localize47.0ms (0.6%)

Memory

-44.4MiB live, 64.3MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	0.00390625	(+.f64 (.f64 x x) (.f64 y y))
accuracy	0.11328125	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	33.31902687691456	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

36.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-mult: 16.0ms (72.5% of total)

ival-div: 2.0ms (9.1% of total)

ival-add: 2.0ms (9.1% of total)

ival-sqrt: 2.0ms (9.1% 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

27.6MiB live, 27.6MiB allocated

Counts

4 → 132

Calls

Call 1

Inputs
#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())
#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())
#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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)))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (+ (pow x 2) (pow y 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow z 2) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* z (sqrt 1/3)) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 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)))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 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))))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow z 2)) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow z 2) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (sqrt 1/3))) (taylor -inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))) (taylor -inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
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#s(alt (* x (sqrt 1/3)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 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)))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 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))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
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#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
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))
2.0ms	z	@	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))
2.0ms	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))
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))
1.0ms	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))

simplify399.0ms (5.3%)

Memory

-15.5MiB live, 176.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2442
1	673	2442
2	2273	2406
3	5705	2289
0	8205	1992

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

Inputs
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 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)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 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)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 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)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 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)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* -1 (* z (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))))))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(+ (pow x 2) (pow z 2))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(pow x 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 2))
(+ (pow x 2) (pow y 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)))
(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(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)) (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 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)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (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)))))
(* (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)) (/ (pow z 2) (pow y 2)))))
(pow y 2)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow x 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))))))))
(* 1/3 (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 x 2) (pow z 2)) (pow y 2)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(+ (pow y 2) (pow z 2))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(pow y 2)
(+ (pow x 2) (pow y 2))
(+ (pow x 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)))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 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)) (/ (pow z 2) (pow x 2)))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 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)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (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)))))
(* (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)) (/ (pow z 2) (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow y 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))))))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))

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

rewrite172.0ms (2.3%)

Memory

-0.4MiB live, 282.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
0	18	45
1	65	45
2	486	45
3	6616	45
0	8497	38

Stop Event

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

Counts

4 → 350

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))

Outputs
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eval570.0ms (7.5%)

Memory: -8.8MiB live, 188.0MiB allocated
Compiler: Compiled 12 817 to 1 605 computations (87.5% saved)

prune207.0ms (2.7%)

Memory

14.6MiB live, 52.2MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	475	7	482
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	476	7	483

Accuracy

99.7%

Counts

483 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.8%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
	47.9%	(sqrt.f64 (/.f64 (+.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)))
▶	47.3%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	47.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	47.2%	(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))))
▶	98.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 120 to 120 computations (0% saved)

simplify6.0ms (0.1%)

Memory

14.1MiB live, 14.1MiB 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	60	222
2	75	222
3	78	222
0	78	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)

localize343.0ms (4.5%)

Memory

-6.0MiB live, 118.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 z z)
accuracy	0.11328125	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.39031894019383795	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	33.31902687691456	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
accuracy	0.19140625	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	33.31902687691456	(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	(*.f64 z z)
accuracy	0.19140625	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	0.39286923577846905	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	33.31902687691456	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.375	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	0.6598943849641551	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
accuracy	0	(hypot.f64 z y)
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.390625	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))

Samples

236.0ms

256×

valid

Compiler

Compiled 191 to 21 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 10.0ms (36.7% of total)

ival-hypot: 5.0ms (18.3% of total)

ival-sqrt: 4.0ms (14.7% of total)

ival-add: 3.0ms (11% of total)

const: 3.0ms (11% of total)

ival-div: 2.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

series236.0ms (3.1%)

Memory

-1.5MiB live, 79.4MiB allocated

Counts

18 → 468

Calls

Call 1

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

Outputs
#s(alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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)))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt 1/3)) (taylor 0 z) (#s(alt (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) (patch (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3))) (taylor 0 z) (#s(alt (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) (patch (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/8 (/ (* (pow z 2) (sqrt 1/3)) (pow y 3))) (* 1/2 (/ (sqrt 1/3) y))))) (taylor 0 z) (#s(alt (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) (patch (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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)))))))) (taylor 0 z) (#s(alt (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) (patch (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))) #<representation binary64>) () ())) ())
#s(alt y (taylor 0 z) (#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt (+ y (* 1/2 (/ (pow z 2) y))) (taylor 0 z) (#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y))))) (taylor 0 z) (#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
#s(alt (+ 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))))) (taylor 0 z) (#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())) ())
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#s(alt (* 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))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -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))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
202.0ms	z	@	-inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
4.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
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	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))
2.0ms	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))

simplify346.0ms (4.6%)

Memory

11.8MiB live, 280.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	10018
1	1212	10018
2	4140	9836
0	8344	8662

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 464

Calls

Call 1

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

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

rewrite177.0ms (2.3%)

Memory

-17.3MiB live, 351.9MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	214
0	44	205
1	124	205
2	726	205
0	8336	196

Stop Event

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

Counts

18 → 284

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
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eval93.0ms (1.2%)

Memory: 22.8MiB live, 251.3MiB allocated
Compiler: Compiled 15 233 to 1 622 computations (89.4% saved)

prune47.0ms (0.6%)

Memory

-38.9MiB live, 92.9MiB allocated

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	768	5	773
Fresh	2	0	2
Picked	1	4	5
Done	0	0	0
Total	771	9	780

Accuracy

99.9%

Counts

780 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	47.2%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
✓	47.3%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	47.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
▶	47.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
✓	47.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
▶	98.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) 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))))
✓	98.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 120 to 121 computations (-0.8% saved)

simplify7.0ms (0.1%)

Memory

14.2MiB live, 14.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
cost-diff	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
cost-diff	12608	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
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	(fma.f64 y y (*.f64 z z))
cost-diff	0	(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
cost-diff	0	(*.f64 #s(literal 1/3 binary64) z)
cost-diff	0	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
cost-diff	0	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))
cost-diff	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
cost-diff	12608	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	269
0	51	260
1	72	244
2	92	240
3	96	240
0	96	231

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 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(literal 1/3 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))
(hypot.f64 z y)
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)
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
#s(literal 1/3 binary64)
(fma.f64 y y (*.f64 z z))
y
(*.f64 z z)
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)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(literal 1/3 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
z

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
#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 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(literal 1/3 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))
(*.f64 (hypot.f64 z y) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(hypot.f64 z y)
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)
#s(literal 1/3 binary64)
z
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
(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 y y (.f64 z z))))
#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 y y (.f64 z z)))
(.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
(fma.f64 y y (*.f64 z z))
(fma.f64 z z (*.f64 y y))
y
(*.f64 z z)
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)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(literal 1/3 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
z

localize83.0ms (1.1%)

Memory

13.5MiB live, 170.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
accuracy	0.046875	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.28515625	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
accuracy	0.6598943849641551	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.36328125	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.39031894019383795	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	33.24709140706664	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))
accuracy	0.00390625	(fma.f64 y y (*.f64 z z))
accuracy	0.19140625	(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
accuracy	33.31902687691456	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
accuracy	0.10546875	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.3359375	(*.f64 #s(literal 1/3 binary64) z)
accuracy	0.39286923577846905	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	33.31902687691456	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0	(hypot.f64 z y)
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
accuracy	0.05859375	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))
accuracy	0.27734375	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))

Samples

62.0ms

256×

valid

Compiler

Compiled 224 to 28 computations (87.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-mult: 18.0ms (39.7% of total)

ival-pow: 7.0ms (15.4% of total)

ival-sqrt: 5.0ms (11% of total)

ival-hypot: 4.0ms (8.8% of total)

const: 4.0ms (8.8% of total)

ival-div: 3.0ms (6.6% of total)

ival-add: 3.0ms (6.6% of total)

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

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

exact: 0.0ms (0% of total)

series811.0ms (10.7%)

Memory

-0.5MiB live, 196.2MiB allocated

Counts

21 → 504

Calls

Call 1

Inputs
#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (patch (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) #<representation binary64>) () ())
#s(alt (.f64 (.f64 #s(literal 1/3 binary64) z) z) (patch (.f64 (.f64 #s(literal 1/3 binary64) z) z) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/3 binary64) z) (patch (.f64 #s(literal 1/3 binary64) z) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #<representation binary64>) () ())
#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #<representation binary64>) () ())
#s(alt (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) (patch (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) #<representation binary64>) () ())
#s(alt (fma.f64 y y (.f64 z z)) (patch (fma.f64 y y (.f64 z z)) #<representation binary64>) () ())
#s(alt (/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (patch (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())
#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())
#s(alt (.f64 z z) (patch (.f64 z z) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) #<representation binary64>) () ())
#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 3 binary64)) (patch (sqrt.f64 #s(literal 3 binary64)) #<representation binary64>) () ())

Outputs
#s(alt (* y (sqrt 1/3)) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3))) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3))))))) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3))))))) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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)))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/3 1/4) y) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) y))) (* (pow 1/3 1/4) y)) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 3)))) (* 1/2 (* (pow 1/3 1/4) (/ 1 y)))))) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) #<representation binary64>) () ())) ())
#s(alt (+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* 1/2 (* (pow 1/3 1/4) (/ 1 y))) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ 1 (pow y 3)))) (* 1/16 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 5))))))))) (taylor 0 z) (#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)) #<representation binary64>) () ())) ())
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#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) (patch (sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (patch #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #<representation binary64>) () ())) ())
#s(alt (* -1 (/ x (sqrt 3))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 x) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (patch (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (patch (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (patch (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) (patch (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) (patch #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())) ())
#s(alt (* -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))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())) ())
#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
457.0ms	z	@	0	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z 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)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* y y) (* z z))) (+ (* y y) (* z 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) (* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) z) (sqrt (+ (* z z) (* y y))) (sqrt 3))
274.0ms	z	@	-inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z 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)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* y y) (* z z))) (+ (* y y) (* z 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) (* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) z) (sqrt (+ (* z z) (* y y))) (sqrt 3))
17.0ms	y	@	-inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z 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)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* y y) (* z z))) (+ (* y y) (* z 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) (* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) z) (sqrt (+ (* z z) (* y y))) (sqrt 3))
11.0ms	z	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z 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)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* y y) (* z z))) (+ (* y y) (* z 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) (* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) z) (sqrt (+ (* z z) (* y y))) (sqrt 3))
3.0ms	y	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z 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)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* y y) (* z z))) (+ (* y y) (* z 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) (* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) z) (sqrt (+ (* z z) (* y y))) (sqrt 3))

simplify219.0ms (2.9%)

Memory

-4.3MiB live, 349.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	712	11340
1	2299	11286
0	8250	9991

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 497

Calls

Call 1

Inputs
(* y (sqrt 1/3))
(+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3)))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(* (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))))))))))
(* (pow 1/3 1/4) y)
(+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) y))) (* (pow 1/3 1/4) y))
(+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 3)))) (* 1/2 (* (pow 1/3 1/4) (/ 1 y))))))
(+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* 1/2 (* (pow 1/3 1/4) (/ 1 y))) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ 1 (pow y 3)))) (* 1/16 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 5)))))))))
(* (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)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 z)
(* 1/3 z)
(* 1/3 z)
(* 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))))))))))
(* 1/3 (+ (pow x 2) (pow y 2)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(* 1/3 (pow y 2))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(pow y 2)
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2))))
(+ (* 1/2 (* (/ (pow z 2) (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2)))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* -1/8 (* (/ (pow z 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (pow z 2) (+ (* -1/8 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/16 (* (/ (pow z 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))
(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 x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* (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))))))))))
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
y
(+ y (* 1/2 (/ (pow z 2) y)))
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))
(* 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)))))))
(* (pow 1/3 1/4) z)
(* z (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4)))
(* z (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow y 4) (pow z 4)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4))))
(* z (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow y 4) (pow z 4)))) (+ (* 1/16 (* (pow 1/3 1/4) (/ (pow y 6) (pow z 6)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4)))))
(* 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)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 z)
(* 1/3 z)
(* 1/3 z)
(* 1/3 z)
(* 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)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(/ z (sqrt 3))
(* z (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3))))
(* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (* (pow z 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(pow z 2)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* 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)))))))
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(* -1 (* z (sqrt 1/3)))
(* -1 (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))))
(* -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 (* (pow 1/3 1/4) z))
(* -1 (* z (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4))))
(* -1 (* z (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow y 4) (pow z 4)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4)))))
(* -1 (* z (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow y 4) (pow z 4)))) (+ (* 1/16 (* (pow 1/3 1/4) (/ (pow y 6) (pow z 6)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 2)))) (pow 1/3 1/4))))))
(* -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))))))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 (pow z 2))
(* 1/3 z)
(* 1/3 z)
(* 1/3 z)
(* 1/3 z)
(* -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))))))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
(* -1 (/ z (sqrt 3)))
(* -1 (* z (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(* -1 (* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(* -1 (* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (* (pow z 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3)))))))
(* -1 z)
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))))
(pow z 2)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* -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))))))))
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* -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))))))))
(* z (sqrt 1/3))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/72 (/ (pow y 2) (* (pow z 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* z (sqrt 1/3)))))))
(+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/432 (/ (pow y 2) (* (pow z 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow z 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* 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))))))))))
(* (pow 1/3 1/4) z)
(+ (* 1/2 (* (pow 1/3 1/4) (/ (pow y 2) z))) (* (pow 1/3 1/4) z))
(+ (* (pow 1/3 1/4) z) (* (pow y 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 3)))) (* 1/2 (* (pow 1/3 1/4) (/ 1 z))))))
(+ (* (pow 1/3 1/4) z) (* (pow y 2) (+ (* 1/2 (* (pow 1/3 1/4) (/ 1 z))) (* (pow y 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ 1 (pow z 3)))) (* 1/16 (* (pow 1/3 1/4) (/ (pow y 2) (pow z 5)))))))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
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(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(* 1/3 (pow z 2))
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(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(pow z 2)
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
(+ (pow y 2) (pow z 2))
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z
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(* (pow 1/3 1/4) y)
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(* y (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 4) (pow y 4)))) (+ (* 1/16 (* (pow 1/3 1/4) (/ (pow z 6) (pow y 6)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 2)))) (pow 1/3 1/4)))))
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(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
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(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
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(* 1/3 (pow y 2))
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(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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(pow y 2)
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(* 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
(* 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)))))))
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(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))
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(* -1 (* (pow 1/3 1/4) y))
(* -1 (* y (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 2)))) (pow 1/3 1/4))))
(* -1 (* y (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 4) (pow y 4)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 2)))) (pow 1/3 1/4)))))
(* -1 (* y (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 4) (pow y 4)))) (+ (* 1/16 (* (pow 1/3 1/4) (/ (pow z 6) (pow y 6)))) (+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 2)))) (pow 1/3 1/4))))))
(* -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))) (+ (* 1/16 (/ (* (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))
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(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* -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))))))))
(* 1/3 (pow y 2))
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(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* 1/3 (pow y 2))
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(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(pow y 2)
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(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
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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)))))))
(* -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)))))))
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(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)
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(* -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 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))))))))))
(* (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)))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 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)))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 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)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(+ (pow x 2) (+ (pow y 2) (pow z 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))))))))))
(* 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 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) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 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)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (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)))))
(* (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)) (/ (pow z 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 (* 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 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))))))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (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))))))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* (pow x 2) (+ 1/3 (* 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))))))))
(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)) (/ (pow z 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))))))))

Outputs
(* y (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)
(+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3)))
(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)) z) z (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(fma.f64 (fma.f64 (.f64 (/.f64 z (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/3 binary64))) (/.f64 z (pow.f64 y #s(literal 3 binary64)))) #s(literal -1/72 binary64) (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (.f64 z z) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 #s(literal 1/432 binary64) (pow.f64 y #s(literal 5 binary64))) (/.f64 (.f64 z z) (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64))) (/.f64 #s(literal -1/72 binary64) (.f64 (.f64 (pow.f64 y #s(literal 3 binary64)) #s(literal 1/3 binary64)) (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 z z) (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (.f64 z z) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(*.f64 (hypot.f64 x y) (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)))))
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(+ (* (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 x x (.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 x x (.f64 y y)))))) (.f64 z z) (*.f64 (hypot.f64 x y) (sqrt.f64 #s(literal 1/3 binary64))))
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(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 y y)) #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 x x (.f64 y y)) #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 x x (.f64 y y)))))) (.f64 z z) (*.f64 (hypot.f64 x y) (sqrt.f64 #s(literal 1/3 binary64))))
(* (pow 1/3 1/4) y)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y)
(+ (* 1/2 (* (pow 1/3 1/4) (/ (pow z 2) y))) (* (pow 1/3 1/4) y))
(fma.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))) (/.f64 (.f64 z z) y) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y))
(+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 3)))) (* 1/2 (* (pow 1/3 1/4) (/ 1 y))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y) #s(literal 1/2 binary64) (.f64 (.f64 #s(literal -1/8 binary64) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))) (.f64 z (/.f64 z (pow.f64 y #s(literal 3 binary64)))))) (.f64 z z) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y))
(+ (* (pow 1/3 1/4) y) (* (pow z 2) (+ (* 1/2 (* (pow 1/3 1/4) (/ 1 y))) (* (pow z 2) (+ (* -1/8 (* (pow 1/3 1/4) (/ 1 (pow y 3)))) (* 1/16 (* (pow 1/3 1/4) (/ (pow z 2) (pow y 5)))))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y) #s(literal 1/2 binary64) (.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))) (.f64 z (/.f64 z (pow.f64 y #s(literal 5 binary64)))) (.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))) (.f64 z z))) (.f64 z z) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) y))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(*.f64 (hypot.f64 x y) (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 x x (.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 x y) (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 x x (.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 x x (.f64 y y)))))) (.f64 z z) (*.f64 (hypot.f64 x y) (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 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 y y)) #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 x x (.f64 y y)) #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 x x (.f64 y y)))))) (.f64 z z) (*.f64 (hypot.f64 x y) (sqrt.f64 #s(literal 1/3 binary64))))
(* 1/3 (+ (pow x 2) (pow y 2)))
(.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 x x (fma.f64 z z (.f64 y y))))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 x x (fma.f64 z z (.f64 y y))))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 x x (fma.f64 z z (.f64 y y))))
(* 1/3 (pow z 2))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(* 1/3 (pow z 2))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(* 1/3 (pow z 2))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(* 1/3 (pow z 2))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(* 1/3 z)
(*.f64 z #s(literal 1/3 binary64))
(* 1/3 z)
(*.f64 z #s(literal 1/3 binary64))
(* 1/3 z)
(*.f64 z #s(literal 1/3 binary64))
(* 1/3 z)
(*.f64 z #s(literal 1/3 binary64))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(*.f64 (hypot.f64 x y) (sqrt.f64 #s(literal 1/3 binary64)))
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(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
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(* -1 (* x (sqrt 1/3)))
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(.f64 (neg.f64 x) (+.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 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 #s(literal 1/2 binary64) x) (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) x)))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (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))
(* (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))
(* (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 (sqrt.f64 #s(literal 1/3 binary64)) x) (/.f64 (fma.f64 z z (*.f64 y y)) 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) x) (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #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 -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 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 #s(literal 1/2 binary64) x) (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) x)))))
(* 1/3 (pow x 2))
(.f64 (.f64 x x) #s(literal 1/3 binary64))
(* (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))
(* (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))
(* (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 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 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 (/.f64 (fma.f64 z z (.f64 y y)) x) x) (/.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 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 (/.f64 (fma.f64 z z (*.f64 y y)) x) 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 z z (.f64 y y)) #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 z z (.f64 y y)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 3 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 (/.f64 (fma.f64 z z (.f64 y y)) x) x) (/.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 z z (.f64 y y)) 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)))))))
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(* -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))))))))
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(pow x 2)
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(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 y x) (/.f64 y x) (fma.f64 (/.f64 z x) (/.f64 z x) #s(literal 1 binary64))) (.f64 x x))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 (fma.f64 (/.f64 y x) (/.f64 y x) (fma.f64 (/.f64 z x) (/.f64 z x) #s(literal 1 binary64))) (.f64 x x))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
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(* -1 (* x (sqrt 1/3)))
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(* -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 (sqrt.f64 #s(literal 1/3 binary64)) x) (/.f64 (fma.f64 z z (*.f64 y y)) 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) x) (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #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))))))))
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rewrite148.0ms (2%)

Memory

17.4MiB live, 295.3MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	249
0	51	239
1	151	223
2	909	219
0	8581	210

Stop Event

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

Counts

21 → 311

Calls

Call 1

Inputs
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.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)
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(fma.f64 y y (*.f64 z 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 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(hypot.f64 z y)
(sqrt.f64 #s(literal 3 binary64))

Outputs
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eval145.0ms (1.9%)

Memory: -21.5MiB live, 334.2MiB allocated
Compiler: Compiled 18 273 to 2 297 computations (87.4% saved)

prune25.0ms (0.3%)

Memory

-5.1MiB live, 78.2MiB allocated

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	859	3	862
Fresh	0	0	0
Picked	3	2	5
Done	1	3	4
Total	863	8	871

Accuracy

100.0%

Counts

871 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
✓	47.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	47.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
✓	47.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	98.4%	#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))))
✓	98.4%	#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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))

Compiler

Compiled 64 to 67 computations (-4.7% saved)

simplify11.0ms (0.1%)

Memory

25.3MiB live, 25.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(hypot.f64 z y)
cost-diff	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
cost-diff	0	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (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	(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y)
cost-diff	0	(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
cost-diff	0	#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	176
0	45	176
1	63	168
2	101	166
3	157	166
4	228	166
5	389	166
6	459	166
0	459	158

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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))
#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))
(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y)
(/.f64 #s(literal 1/6 binary64) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
#s(literal 1/6 binary64)
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
z
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
y
#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 z y)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
z
y
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))
#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y)
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y)
(/.f64 #s(literal 1/6 binary64) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(/.f64 #s(literal 1/6 binary64) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
#s(literal 1/6 binary64)
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
z
(sqrt.f64 #s(literal 1/3 binary64))
#s(literal 1/3 binary64)
y
#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 z y)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
z
y
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

localize83.0ms (1.1%)

Memory

12.0MiB live, 127.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(hypot.f64 z y)
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
accuracy	0.36328125	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.359375	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.6598943849641551	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
accuracy	0.23563253162065376	(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y)
accuracy	0.365281129328455	#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))
accuracy	0.375	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	0.3828125	(/.f64 #s(literal 1/6 binary64) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Samples

69.0ms

256×

valid

Compiler

Compiled 134 to 30 computations (77.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 55.0ms

const: 13.0ms (23.8% of total)

ival-mult: 12.0ms (22% of total)

ival-sqrt: 10.0ms (18.3% of total)

ival-div: 6.0ms (11% of total)

ival-pow: 5.0ms (9.2% of total)

ival-hypot: 4.0ms (7.3% of total)

ival-add: 3.0ms (5.5% of total)

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

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

exact: 0.0ms (0% of total)

series35.0ms (0.5%)

Memory

-25.0MiB live, 50.9MiB allocated

Counts

12 → 276

Calls

Call 1

Inputs
#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) #<representation binary64>) () ())
#s(alt #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) (patch #s(approx ( (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) #<representation binary64>) () ())
#s(alt (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (patch (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) (patch (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) #<representation binary64>) () ())
#s(alt #s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) (patch #s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #<representation binary64>) () ())
#s(alt (/.f64 z (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 z (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt (sqrt.f64 #s(literal 3 binary64)) (patch (sqrt.f64 #s(literal 3 binary64)) #<representation binary64>) () ())
#s(alt (/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64))) (patch (/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64))) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())
#s(alt (hypot.f64 z y) (patch (hypot.f64 z y) #<representation binary64>) () ())
#s(alt (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (patch (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) #<representation binary64>) () ())
#s(alt (.f64 z (sqrt.f64 #s(literal 1/3 binary64))) (patch (.f64 z (sqrt.f64 #s(literal 1/3 binary64))) #<representation binary64>) () ())

Outputs
#s(alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 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))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (+ (* (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)))))))))) (taylor 0 z) (#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) (patch #s(approx (sqrt (/ (+ (+ ( x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))) #<representation binary64>) () ())) ())
#s(alt (* y (sqrt 1/3)) (taylor 0 z) (#s(alt #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) (patch #s(approx ( (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3))) (taylor 0 z) (#s(alt #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) (patch #s(approx ( (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3))))))) (taylor 0 z) (#s(alt #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) (patch #s(approx ( (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
#s(alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3))))))) (taylor 0 z) (#s(alt #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) (patch #s(approx ( (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (* -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)))))))) (taylor -inf x) (#s(alt #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (patch #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) #<representation binary64>) () ())) ())

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	z	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (+ (* (* (/ 1/6 (* z (sqrt 1/3))) y) y) (* z (sqrt 1/3))) (* (/ 1/6 (* z (sqrt 1/3))) y) (/ (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 (+ (* z z) (* y y))) (/ 1/6 (* z (sqrt 1/3))) (* z (sqrt 1/3)))
3.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (+ (* (* (/ 1/6 (* z (sqrt 1/3))) y) y) (* z (sqrt 1/3))) (* (/ 1/6 (* z (sqrt 1/3))) y) (/ (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 (+ (* z z) (* y y))) (/ 1/6 (* z (sqrt 1/3))) (* z (sqrt 1/3)))
3.0ms	z	@	-inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (+ (* (* (/ 1/6 (* z (sqrt 1/3))) y) y) (* z (sqrt 1/3))) (* (/ 1/6 (* z (sqrt 1/3))) y) (/ (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 (+ (* z z) (* y y))) (/ 1/6 (* z (sqrt 1/3))) (* z (sqrt 1/3)))
2.0ms	y	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (+ (* (* (/ 1/6 (* z (sqrt 1/3))) y) y) (* z (sqrt 1/3))) (* (/ 1/6 (* z (sqrt 1/3))) y) (/ (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 (+ (* z z) (* y y))) (/ 1/6 (* z (sqrt 1/3))) (* z (sqrt 1/3)))
2.0ms	y	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (+ (* (* (/ 1/6 (* z (sqrt 1/3))) y) y) (* z (sqrt 1/3))) (* (/ 1/6 (* z (sqrt 1/3))) y) (/ (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 (+ (* z z) (* y y))) (/ 1/6 (* z (sqrt 1/3))) (* z (sqrt 1/3)))

simplify215.0ms (2.8%)

Memory

0.8MiB live, 322.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	608	6706
1	1911	6619
2	6868	6599
0	8028	5850

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 269

Calls

Call 1

Inputs
(* (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))))))))))
(* y (sqrt 1/3))
(+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3)))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* (/ 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))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* (/ 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))))))))))
y
(+ 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)))))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* 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)))))))
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(/ 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 (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* z (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3))))
(* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(* z (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (* (pow z 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (* (pow z 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow y 2)) (* (pow z 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(* z (+ 1 (+ (* -1/8 (/ (pow (+ (pow x 2) (pow y 2)) 2) (pow z 4))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow y 2)) 3) (pow z 6))) (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))))
z
(* 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)))))))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* -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 (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))))
(* z (sqrt 1/3))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* -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)))))))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* -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 (* 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))))))))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(/ 1/6 (* z (sqrt 1/3)))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* 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))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/72 (/ (pow y 2) (* (pow z 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* z (sqrt 1/3)))))))
(+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/432 (/ (pow y 2) (* (pow z 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow z 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* z (sqrt 1/3)))))))
(* z (sqrt 1/3))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* (/ 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))))))))))
(* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2))))
(+ (* 1/2 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/8 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(sqrt (+ (pow x 2) (pow z 2)))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* 1/2 (* (pow y 2) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* -1/8 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))))))
(+ (sqrt (+ (pow x 2) (pow z 2))) (* (pow y 2) (+ (* 1/2 (sqrt (/ 1 (+ (pow x 2) (pow z 2))))) (* (pow y 2) (+ (* -1/8 (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3)))) (* 1/16 (* (pow y 2) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))
(* y (sqrt 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))
(* y (+ (sqrt 1/3) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow z 6) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
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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))))))
(* 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
(* 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))))))
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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 (* y (+ (sqrt 1/3) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow z 6) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
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(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
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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)))))))
(* -1 (/ y (sqrt 3)))
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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)))))))
(* -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 (* 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 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)))))
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(* (/ 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)))))
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(+ (* (/ 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 (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)))
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(* -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 (sqrt 3)))
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(* -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))))))))

Outputs
(* (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)))))
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(+ (* (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))))
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(* y (sqrt 1/3))
(*.f64 y (sqrt.f64 #s(literal 1/3 binary64)))
(+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3)))
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(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))
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(fma.f64 (fma.f64 (fma.f64 #s(literal -1/24 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal 3 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (.f64 (.f64 z z) #s(literal 1/432 binary64)) (.f64 (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64)) (pow.f64 y #s(literal 5 binary64))))) (.f64 z z) (/.f64 #s(literal 1/6 binary64) (.f64 y (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 z z) (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
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(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
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(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/.f64 (fma.f64 (.f64 z (sqrt.f64 #s(literal 1/3 binary64))) z (/.f64 (.f64 (*.f64 y y) #s(literal 1/6 binary64)) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/.f64 (fma.f64 (.f64 z (sqrt.f64 #s(literal 1/3 binary64))) z (/.f64 (.f64 (*.f64 y y) #s(literal 1/6 binary64)) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(* 1/6 (/ y (* z (sqrt 1/3))))
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(* 1/6 (/ y (* z (sqrt 1/3))))
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(* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2))))
(/.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 3 binary64)))
(+ (* 1/2 (* (/ (pow z 2) (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2)))))
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(fma.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (.f64 y y)) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal 3 binary64))))) x (/.f64 x (sqrt.f64 #s(literal 3 binary64))))
(* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (* (pow x 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.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 x) (.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) 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 (fma.f64 z z (.f64 y y)) x) (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) x x)
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(fma.f64 (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (fma.f64 z z (.f64 y y)) x) (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x)
(* -1 (* x (sqrt 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) (sqrt.f64 #s(literal 1/3 binary64))) x) (/.f64 (fma.f64 z z (*.f64 y y)) 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) (sqrt.f64 #s(literal 1/3 binary64))) x) (/.f64 (fma.f64 z z (.f64 y y)) x) (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #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 -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 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) (sqrt.f64 #s(literal 1/3 binary64))) x) (/.f64 (fma.f64 z z (.f64 y y)) x)))))
(* -1 (/ x (sqrt 3)))
(/.f64 (neg.f64 x) (sqrt.f64 #s(literal 3 binary64)))
(* -1 (* x (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (.f64 y y)) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal 3 binary64))))) x (/.f64 x (sqrt.f64 #s(literal 3 binary64)))))
(* -1 (* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (* (pow x 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 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 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.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 (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (.f64 y y)) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (*.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal 3 binary64))))) x (/.f64 x (sqrt.f64 #s(literal 3 binary64)))))
(* -1 (* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (* (pow x 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (sqrt.f64 #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (/.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 3 binary64)) x)) (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.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 (fma.f64 z z (.f64 y y)) x) (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64)))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(.f64 (neg.f64 x) (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 z z (*.f64 y y)) x) (/.f64 #s(literal 1/2 binary64) x) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))
(neg.f64 (fma.f64 (fma.f64 (/.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (fma.f64 z z (.f64 y y)) x) (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) x x))

rewrite163.0ms (2.2%)

Memory

26.5MiB live, 214.4MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	163
0	45	162
1	159	152
2	1030	152
0	8730	144

Stop Event

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

Counts

12 → 295

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))
#s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))))
(fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y)
#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 z y)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
(/.f64 #s(literal 1/6 binary64) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Outputs
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eval79.0ms (1%)

Memory: 2.1MiB live, 167.0MiB allocated
Compiler: Compiled 13 534 to 2 073 computations (84.7% saved)

prune20.0ms (0.3%)

Memory

-28.5MiB live, 53.6MiB allocated

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	610	1	611
Fresh	0	0	0
Picked	0	3	3
Done	0	5	5
Total	610	9	619

Accuracy

100.0%

Counts

619 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
✓	47.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	47.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
✓	47.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
✓	98.4%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	97.7%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (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))))
✓	98.4%	#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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))

Compiler

Compiled 229 to 148 computations (35.4% saved)

regimes54.0ms (0.7%)

Memory

29.9MiB live, 108.1MiB allocated

Counts

17 → 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 y y (.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)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(sqrt.f64 (/.f64 (+.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y)) (.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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (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 #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)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))

Outputs

#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))

Calls

10 calls:

6.0ms	z
6.0ms	(+.f64 (.f64 x x) (.f64 y y))
5.0ms	y
5.0ms	x
5.0ms	(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)

regimes79.0ms (1%)

Memory

-4.8MiB live, 81.9MiB allocated

Counts

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

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

Calls

10 calls:

27.0ms	(*.f64 z z)
11.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
5.0ms	y
5.0ms	z
5.0ms	x

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)

regimes55.0ms (0.7%)

Memory

-11.9MiB live, 62.1MiB 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 y y (.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)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(sqrt.f64 (/.f64 (+.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y)) (.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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (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))))

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:

10.0ms	(*.f64 y y)
9.0ms	y
5.0ms	z
5.0ms	x
4.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))

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)

regimes77.0ms (1%)

Memory

-8.5MiB live, 70.3MiB allocated

Counts

13 → 1

Calls

Call 1

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

Outputs

#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (*.f64 (/.f64 #s(literal 1/6 binary64) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))

Calls

10 calls:

33.0ms	x
9.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	z
4.0ms	y
4.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

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)

regimes44.0ms (0.6%)

Memory

22.7MiB live, 59.5MiB allocated

Counts

12 → 1

Calls

Call 1

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

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

Results

Accuracy	Segments	Branch
98.4%	1	`x`
98.4%	1	`y`
98.4%	1	`z`
98.4%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.4%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.4%	1	`(*.f64 x x)`
98.4%	1	`(*.f64 y y)`
98.4%	1	`(*.f64 z z)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes22.0ms (0.3%)

Memory

0.8MiB live, 37.8MiB allocated

Accuracy

Total -32.8b remaining (-3196.6%)

Threshold costs -32.8b (-3196.6%)

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:

5.0ms	x
2.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
2.0ms	y
2.0ms	(*.f64 z z)
2.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
98.4%	1	`z`
98.4%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.4%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.4%	1	`(*.f64 z z)`
98.4%	1	`x`
98.4%	1	`y`
98.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.4%	1	`(*.f64 x x)`
98.4%	1	`(*.f64 y y)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify27.0ms (0.4%)

Memory

-5.1MiB live, 40.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	151
1	48	151

Stop Event

1×

saturated

Calls

Call 1

Inputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
(/.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)) 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 (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (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))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Outputs
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (.f64 (hypot.f64 z y) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 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)) 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)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) y) y (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) #s(approx (* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (fma.f64 (.f64 (/.f64 #s(literal 1/6 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) y) y (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

soundness882.0ms (11.6%)

Memory

-15.7MiB live, 474.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	712	11340
1	2299	11286
0	8250	9991
0	230	2442
1	673	2442
2	2273	2406
3	5705	2289
0	8205	1992
0	30	214
0	44	205
1	124	205
2	726	205
0	8336	196

Stop Event

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

Compiler

Compiled 140 to 122 computations (12.9% saved)

preprocess144.0ms (1.9%)

Memory: -5.0MiB live, 192.3MiB allocated
Compiler: Compiled 580 to 442 computations (23.8% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	35	176
0	45	176
1	63	168
2	101	166
3	157	166
4	228	166
5	389	166
6	459	166
0	459	158

Iter	Nodes	Cost
0	35	176
0	45	176
1	63	168
2	101	166
3	157	166
4	228	166
5	389	166
6	459	166
0	459	158

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (17%)

explain154.0ms (2%)

preprocess42.0ms (0.6%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify3.0ms (0%)

localize47.0ms (0.6%)

series16.0ms (0.2%)

simplify399.0ms (5.3%)

rewrite172.0ms (2.3%)

eval570.0ms (7.5%)

prune207.0ms (2.7%)

simplify6.0ms (0.1%)

localize343.0ms (4.5%)

series236.0ms (3.1%)

simplify346.0ms (4.6%)

rewrite177.0ms (2.3%)

eval93.0ms (1.2%)

prune47.0ms (0.6%)

simplify7.0ms (0.1%)

localize83.0ms (1.1%)

series811.0ms (10.7%)

simplify219.0ms (2.9%)

rewrite148.0ms (2%)

eval145.0ms (1.9%)

prune25.0ms (0.3%)

simplify11.0ms (0.1%)

localize83.0ms (1.1%)

series35.0ms (0.5%)

simplify215.0ms (2.8%)

rewrite163.0ms (2.2%)

eval79.0ms (1%)

prune20.0ms (0.3%)

regimes54.0ms (0.7%)

regimes79.0ms (1%)

regimes55.0ms (0.7%)

regimes77.0ms (1%)

regimes44.0ms (0.6%)

regimes22.0ms (0.3%)

simplify27.0ms (0.4%)

soundness882.0ms (11.6%)

preprocess144.0ms (1.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	35	176
0	45	176
1	63	168
2	101	166
3	157	166
4	228	166
5	389	166
6	459	166
0	459	158