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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze3.0ms (0%)

Memory

-34.8MiB live, 3.2MiB 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)

sample2.1s (24.6%)

Memory

27.9MiB live, 1 612.7MiB allocated

Samples

1.3s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 458.0ms

ival-mult: 216.0ms (47.2% of total)

ival-div: 95.0ms (20.7% of total)

ival-add: 74.0ms (16.2% of total)

ival-sqrt: 58.0ms (12.7% of total)

ival-true: 6.0ms (1.3% of total)

exact: 5.0ms (1.1% of total)

ival-assert: 3.0ms (0.7% of total)

Bogosity

explain138.0ms (1.6%)

Memory

-10.9MiB live, 273.8MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	165	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	165
↳	`(*.f64 y y)`	overflow	74
↳	`(*.f64 x x)`	overflow	67
↳	`(*.f64 z z)`	overflow	69
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	124
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	165
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	2	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	2
↳	`(*.f64 y y)`	underflow	51
↳	`(*.f64 x x)`	underflow	53
↳	`(*.f64 z z)`	underflow	61
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	7
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2

Confusion

	Predicted +	Predicted -
+	167	0
-	0	89

Precision

1.0

Recall

1.0

Confusion?

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

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	89
1	167

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 137 to 37 computations (73% saved)

Precisions

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

ival-mult: 10.0ms (45% of total)

ival-add: 4.0ms (18% of total)

ival-sqrt: 4.0ms (18% of total)

ival-div: 3.0ms (13.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess39.0ms (0.5%)

Memory

22.1MiB live, 59.8MiB allocated

Algorithm

1×	egg-herbie

Rules

112×	`div-sub`
111×	`cancel-sign-sub`
108×	`sub-neg`
66×	`associate-/l*`
66×	`*-commutative`

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 17 to 11 computations (35.3% saved)

eval0.0ms (0%)

Memory: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.4MiB live, 2.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	39.3%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify14.0ms (0.2%)

Memory

-19.8MiB live, 17.9MiB 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))

Rules

12×	`lower-+.f32`
10×	`lower-+.f64`
9×	`lower-fma.f64`
9×	`lower-fma.f32`
5×	`+-commutative`

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)

localize30.0ms (0.3%)

Memory

25.9MiB live, 65.0MiB 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	0.09375	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	38.81274489766285	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

20.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

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

ival-mult: 5.0ms (43.2% of total)

ival-div: 2.0ms (17.3% of total)

ival-add: 2.0ms (17.3% of total)

ival-sqrt: 2.0ms (17.3% 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

-10.0MiB live, 28.0MiB 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 y 2) (pow z 2)) (taylor 0 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) (+ (pow y 2) (pow z 2))) (taylor 0 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) (+ (pow y 2) (pow z 2))) (taylor 0 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) (+ (pow y 2) (pow z 2))) (taylor 0 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 (.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 (.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) (pow z 2)) (taylor 0 y) (#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 y) (#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 y) (#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 y) (#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 y 2) (taylor inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor inf y) (#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 y 2) (taylor -inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#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 y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2))))) (taylor -inf y) (#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)) (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 (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 (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 (pow y 2) (taylor 0 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) (pow y 2)) (taylor 0 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) (pow y 2)) (taylor 0 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) (pow y 2)) (taylor 0 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) (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>) () ())) ())
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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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#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>) () ())) ())
#s(alt (* 1/3 (+ (pow x 2) (pow z 2))) (taylor 0 y) (#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 z 2))) (* 1/3 (pow y 2))) (taylor 0 y) (#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 z 2))) (* 1/3 (pow y 2))) (taylor 0 y) (#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 z 2))) (* 1/3 (pow y 2))) (taylor 0 y) (#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 y 2)) (taylor inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor inf y) (#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 y 2)) (taylor -inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor -inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor -inf y) (#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 y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))) (taylor -inf y) (#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))) (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 (* 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 (* 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>) () ())) ())

Calls

33 calls:

Time	Variable		Point	Expression
3.0ms	x	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	y	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	z	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	x	@	inf	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	z	@	inf	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))

simplify230.0ms (2.6%)

Memory

-5.5MiB live, 266.9MiB allocated

Algorithm

1×	egg-herbie

Rules

6 683×	`lower-fma.f64`
6 683×	`lower-fma.f32`
2 730×	`lower-*.f64`
2 730×	`lower-*.f32`
1 902×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

rewrite271.0ms (3.1%)

Memory

17.6MiB live, 247.1MiB allocated

Rules

2 262×	`lower-fma.f64`
2 262×	`lower-fma.f32`
2 130×	`lower-*.f32`
2 127×	`lower-*.f64`
1 524×	`lower-/.f32`

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
(.f64 (/.f64 (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 x x (fma.f64 z z (.f64 y y)))) (fma.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (fma.f64 y y (.f64 x x)) (.f64 (neg.f64 (.f64 (.f64 z z) z)) (.f64 (.f64 z z) z)))) (fma.f64 (.f64 z z) (fma.f64 x x (fma.f64 z z (.f64 y y))) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))))
(.f64 (/.f64 (fma.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (fma.f64 y y (.f64 x x)) (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 z z) z))) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (.f64 (.f64 (.f64 z z) z) z)) (-.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z))))) (-.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z))))
(.f64 (/.f64 (fma.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (fma.f64 y y (.f64 x x)) (.f64 (.f64 (.f64 z z) z) (.f64 (.f64 z z) z))) (fma.f64 (.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (.f64 (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z)) (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z))) (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z))))) (fma.f64 (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z)) (-.f64 (.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) (.f64 z z)) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))))))
(.f64 (/.f64 (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 x x (fma.f64 z z (.f64 y y)))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 x x (fma.f64 z z (.f64 y y))))) (fma.f64 x x (fma.f64 z z (.f64 y y))))
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(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 x x))) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 x x))) (.f64 #s(literal 1/3 binary64) (.f64 y y)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))

eval67.0ms (0.8%)

Memory: -6.6MiB live, 107.1MiB allocated
Compiler: Compiled 18 382 to 1 573 computations (91.4% saved)

prune214.0ms (2.5%)

Memory

-131.8MiB live, 162.6MiB 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

98.5%

Counts

483 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	39.2%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 z z (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
	39.3%	(sqrt.f64 (/.f64 (+.f64 #s(approx (+ (* x x) (* y y)) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)))
▶	39.3%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
▶	38.8%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	38.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
▶	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 168 to 110 computations (34.5% saved)

simplify7.0ms (0.1%)

Memory

14.9MiB live, 14.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

19×	`lower-*.f32`
17×	`lower-fma.f32`
16×	`lower-fma.f64`
14×	`lower-+.f64`
14×	`lower-+.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	267
0	45	256
1	61	256
2	75	256
3	78	256
0	78	245

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

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

localize78.0ms (0.9%)

Memory

-0.7MiB live, 118.7MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
accuracy	0.09375	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64))
accuracy	38.81274489766285	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
accuracy	0	(*.f64 z z)
accuracy	0.09375	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.37543346644697506	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	38.81274489766285	(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	0.14453125	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	38.81274489766285	(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	0.05078125	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.33984375	(*.f64 #s(literal 1/3 binary64) z)
accuracy	0.37410565246346733	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	38.81274489766285	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.39453125	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	1.1025332036325661	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Samples

54.0ms

256×

valid

Compiler

Compiled 204 to 20 computations (90.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 35.0ms

ival-mult: 17.0ms (49.2% of total)

ival-div: 7.0ms (20.3% of total)

ival-sqrt: 4.0ms (11.6% of total)

ival-add: 3.0ms (8.7% of total)

const: 3.0ms (8.7% of total)

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

exact: 0.0ms (0% of total)

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

series34.0ms (0.4%)

Memory

11.4MiB live, 49.0MiB allocated

Counts

19 → 504

Calls

Call 1

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

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

Calls

126 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(* (sqrt 1/3) z)
0.0ms	z	@	inf	(+ (* z z) (* y y))
0.0ms	z	@	inf	(* (* 1/3 z) z)
0.0ms	z	@	inf	(* (sqrt 1/3) z)
0.0ms	z	@	-inf	(* 1/3 z)

simplify875.0ms (10.1%)

Memory

-12.2MiB live, 189.1MiB allocated

Algorithm

1×	egg-herbie

Rules

6 809×	`lower-fma.f64`
6 809×	`lower-fma.f32`
2 826×	`lower-*.f64`
2 826×	`lower-*.f32`
1 914×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	238	9978
1	702	9978
2	2352	9798
3	5925	9429
0	8166	8226

Stop Event

1×	iter limit
1×	node limit

Counts

504 → 504

Calls

Call 1

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

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

rewrite495.0ms (5.7%)

Memory

-3.8MiB live, 396.5MiB allocated

Rules

2 927×	`lower-*.f32`
2 921×	`lower-*.f64`
2 905×	`lower-fma.f32`
2 904×	`lower-fma.f64`
2 113×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	246
0	45	235
1	130	235
2	761	235
0	8387	224

Stop Event

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

Counts

19 → 288

Calls

Call 1

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

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

eval168.0ms (1.9%)

Memory: -1.8MiB live, 236.6MiB allocated
Compiler: Compiled 21 251 to 1 141 computations (94.6% saved)

prune82.0ms (0.9%)

Memory

28.5MiB live, 186.8MiB allocated

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	891	5	896
Fresh	2	0	2
Picked	2	3	5
Done	0	0	0
Total	895	8	903

Accuracy

98.7%

Counts

903 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.7%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
✓	38.8%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	38.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
▶	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
✓	38.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
▶	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
▶	97.8%	#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)))
✓	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 152 to 100 computations (34.2% saved)

simplify22.0ms (0.3%)

Memory

-33.1MiB live, 8.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 z z)
cost-diff	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
cost-diff	0	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
cost-diff	0	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	(*.f64 y y)
cost-diff	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64))))
cost-diff	0	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
cost-diff	320	(fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 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 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 1/3 binary64))
cost-diff	0	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
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))

Rules

26×	`lower-*.f32`
19×	`lower-*.f64`
17×	`lower-fma.f32`
15×	`lower-fma.f64`
14×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	294
0	50	277
1	68	269
2	85	267
3	87	267
0	87	256

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

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

localize101.0ms (1.2%)

Memory

24.3MiB live, 134.8MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.37543346644697506	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	0.390625	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	38.76861928248404	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64))))
accuracy	0.140625	(.f64 (.f64 z z) #s(literal 1/3 binary64))
accuracy	38.81274489766285	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
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	0.14453125	(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
accuracy	38.81274489766285	(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	(*.f64 z z)
accuracy	0.14453125	(.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))
accuracy	0.37543346644697506	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	38.81274489766285	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
accuracy	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
accuracy	0.0703125	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.30078125	(.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	1.1025332036325661	#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)))

Samples

67.0ms

256×

valid

Compiler

Compiled 225 to 28 computations (87.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-mult: 27.0ms (53.6% of total)

ival-sqrt: 7.0ms (13.9% of total)

ival-pow: 5.0ms (9.9% of total)

ival-add: 4.0ms (7.9% of total)

const: 4.0ms (7.9% of total)

ival-div: 3.0ms (6% of total)

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

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

exact: 0.0ms (0% of total)

series82.0ms (0.9%)

Memory

10.0MiB live, 123.7MiB allocated

Counts

20 → 492

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

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

Calls

123 calls:

Time	Variable		Point	Expression
48.0ms	z	@	0	(* (pow 1/3 1/4) z)
1.0ms	x	@	0	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3))
1.0ms	x	@	inf	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3))
1.0ms	z	@	0	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3))
0.0ms	y	@	0	(/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3))

simplify252.0ms (2.9%)

Memory

-4.9MiB live, 355.9MiB allocated

Algorithm

1×	egg-herbie

Rules

7 993×	`lower-fma.f64`
7 993×	`lower-fma.f32`
3 457×	`lower-*.f64`
3 457×	`lower-*.f32`
2 311×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	473	10488
1	1506	10446
2	5381	10299
0	8188	9012

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 489

Calls

Call 1

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

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

rewrite209.0ms (2.4%)

Memory

17.2MiB live, 248.5MiB allocated

Rules

3 722×	`lower-fma.f32`
3 720×	`lower-fma.f64`
3 096×	`lower-*.f32`
3 089×	`lower-*.f64`
1 910×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	257
0	50	240
1	152	230
2	924	230
0	8806	220

Stop Event

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

Counts

20 → 388

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

Outputs
(.f64 (.f64 (.f64 (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 z (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (*.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (*.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(.f64 (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
(.f64 (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 1/3 binary64)))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(*.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64))) (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))))
(.f64 (neg.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1 binary64))
(pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (neg.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) (sqrt.f64 #s(literal -3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))))
(/.f64 (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))))))
(neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(exp.f64 (-.f64 (.f64 (log.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z))) #s(literal 1/2 binary64)) (.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (.f64 (log.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/2 binary64)))
(.f64 (neg.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal -1/3 binary64))
(.f64 #s(literal 1 binary64) (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
(.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))
(pow.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal -1 binary64))
(/.f64 (neg.f64 (neg.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal 3 binary64))
(/.f64 (neg.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal -3 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))
(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
(neg.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal -3 binary64)))
#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
(*.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 z)))
(*.f64 z z)
(pow.f64 (exp.f64 (log.f64 z)) #s(literal 2 binary64))
(pow.f64 (*.f64 z z) #s(literal 1 binary64))
(pow.f64 z #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 z) #s(literal 2 binary64)))
(.f64 (pow.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/4 binary64)) (pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/4 binary64)))
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(pow.f64 (.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))) #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
(exp.f64 (.f64 (log.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))) #s(literal 1/2 binary64)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64))) (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64))) (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)))) #s(literal -1/2 binary64)) (pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1/2 binary64)))
(.f64 (/.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(.f64 (/.f64 (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(.f64 (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))))
(.f64 (neg.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(pow.f64 (exp.f64 (log.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/3 binary64)) (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal -1/2 binary64))
(pow.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal -1 binary64))
(pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (neg.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) (sqrt.f64 #s(literal -3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))))
(/.f64 (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))))))
(neg.f64 (.f64 #s(literal 1 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))))))
(neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))))
(exp.f64 (-.f64 (.f64 (log.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z))) #s(literal 1/2 binary64)) (.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (.f64 (log.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (.f64 z z))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (sqrt.f64 (/.f64 #s(literal 3 binary64) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)))))
(.f64 #s(literal 1 binary64) (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))))
(.f64 (sqrt.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (.f64 z z)) #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/2 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))))
(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))))
(exp.f64 (.f64 (log.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z))) #s(literal 1/2 binary64)))
(.f64 (.f64 z #s(literal 1/3 binary64)) z)
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 z (.f64 z #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(*.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 3 binary64))) #s(literal 1/2 binary64))
(pow.f64 #s(literal 9 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 3 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(literal 3 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64)))

eval175.0ms (2%)

Memory: -4.6MiB live, 241.2MiB allocated
Compiler: Compiled 23 567 to 1 318 computations (94.4% saved)

prune404.0ms (4.6%)

Memory

1.8MiB live, 158.1MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	975	5	980
Fresh	0	0	0
Picked	2	3	5
Done	1	2	3
Total	978	10	988

Accuracy

98.8%

Counts

988 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	38.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
✓	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
✓	38.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
▶	97.7%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
▶	97.1%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
▶	97.1%	#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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
▶	97.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
▶	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
✓	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 184 to 145 computations (21.2% saved)

simplify9.0ms (0.1%)

Memory

10.5MiB live, 10.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
cost-diff	0	(.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
cost-diff	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
cost-diff	0	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z))
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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
cost-diff	6464	(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
cost-diff	0	(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
cost-diff	0	(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
cost-diff	0	(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
cost-diff	0	(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
cost-diff	0	(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
cost-diff	0	(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
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))))

Rules

44×	`lower-*.f32`
36×	`lower-*.f64`
15×	`associate-r`
14×	`*-commutative`
12×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	246
0	54	246
1	75	232
2	98	232
3	112	232
0	112	222

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
#s(literal 1/27 binary64)
#s(literal 1/8 binary64)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
z
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
#s(literal 1/27 binary64)
#s(literal 1/8 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
#s(literal 2 binary64)
z
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
(.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
#s(literal 2 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)
z

Outputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
z
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
#s(literal 1/27 binary64)
#s(literal 1/8 binary64)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
z
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
#s(literal 1/27 binary64)
#s(literal 1/8 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
#s(literal 2 binary64)
z
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
#s(literal 1/9 binary64)
#s(literal 1/16 binary64)
#s(literal 2 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)
z

localize156.0ms (1.8%)

Memory

-25.7MiB live, 172.1MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0.0703125	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.30078125	(.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
accuracy	1.1025332036325661	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
accuracy	0.0703125	(*.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)
accuracy	0.30078125	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z))
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
accuracy	1.1025332036325661	#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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
accuracy	0	(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
accuracy	0.11328125	(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
accuracy	0.33431625976844204	(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
accuracy	1.1025332036325661	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
accuracy	0	(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
accuracy	0.2578125	(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
accuracy	0.265625	(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
accuracy	1.1025332036325661	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.3828125	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	1.1025332036325661	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Samples

89.0ms

256×

valid

Compiler

Compiled 199 to 36 computations (81.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 69.0ms

ival-pow: 29.0ms (41.9% of total)

ival-mult: 16.0ms (23.1% of total)

const: 9.0ms (13% of total)

ival-sqrt: 5.0ms (7.2% of total)

ival-div: 4.0ms (5.8% of total)

ival-pow2: 3.0ms (4.3% of total)

ival-add: 2.0ms (2.9% of total)

exact: 1.0ms (1.4% of total)

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

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

series78.0ms (0.9%)

Memory

38.6MiB live, 146.4MiB allocated

Counts

19 → 288

Calls

Call 1

Inputs
#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 #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)) (patch (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (patch (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z) (patch (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z) #<representation binary64>) () ())
#s(alt #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))) (patch #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)) (patch (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)) #<representation binary64>) () ())
#s(alt (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (patch (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (patch (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) #<representation binary64>) () ())
#s(alt (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (patch (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) #<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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)) (patch (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)) #<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 #s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())
#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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>) () ())

Outputs
#s(alt (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))) (taylor 0 x) (#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 (+ (* 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))))) (taylor 0 x) (#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 (+ (* (/ 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))))))))) (taylor 0 x) (#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 (+ (* (/ 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)))))))))) (taylor 0 x) (#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 (/ x (sqrt 3)) (taylor inf x) (#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 (* x (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3)))) (taylor inf x) (#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 (* 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 #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 (* 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 #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 (* -1 (/ x (sqrt 3))) (taylor -inf x) (#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>) () ())) ())
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#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) (* (pow 1/3 1/4) z)) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor 0 z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor 0 z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor 0 z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor 0 z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/9 1/8) z) (taylor -inf z) (#s(alt (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) (patch (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (* (pow 1/3 1/4) z) (taylor 0 z) (#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 (* (pow 1/3 1/4) z) (taylor 0 z) (#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 (* (pow 1/3 1/4) z) (taylor 0 z) (#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 (* (pow 1/3 1/4) z) (taylor 0 z) (#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 (* (pow 1/3 1/4) z) (taylor inf z) (#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 (* (pow 1/3 1/4) z) (taylor inf z) (#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 (* (pow 1/3 1/4) z) (taylor inf z) (#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 (* (pow 1/3 1/4) z) (taylor inf z) (#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 (* (pow 1/3 1/4) z) (taylor -inf z) (#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 (* (pow 1/3 1/4) z) (taylor -inf z) (#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 (* (pow 1/3 1/4) z) (taylor -inf z) (#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 (* (pow 1/3 1/4) z) (taylor -inf z) (#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>) () ())) ())

Calls

72 calls:

Time	Variable		Point	Expression
54.0ms	z	@	0	(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
1.0ms	z	@	inf	(/ z (sqrt 3))
1.0ms	z	@	0	(* (pow 1/3 1/4) (* (pow (pow 1/9 1/16) 2) z))
0.0ms	z	@	inf	(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
0.0ms	z	@	0	(/ z (sqrt 3))

simplify337.0ms (3.9%)

Memory

-10.5MiB live, 354.2MiB allocated

Algorithm

1×	egg-herbie

Rules

8 013×	`lower-fma.f64`
8 013×	`lower-fma.f32`
3 314×	`lower-*.f64`
3 314×	`lower-*.f32`
2 736×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	331	7128
1	1031	7086
2	3798	6939
0	8330	6102

Stop Event

1×	iter limit
1×	node limit

Counts

288 → 288

Calls

Call 1

Inputs
(* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2))))
(+ (* 1/2 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(/ 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))))))
(* -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 (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))))))))))
(/ y (sqrt 3))
(* y (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))
(* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(* -1 (/ y (sqrt 3)))
(* -1 (* y (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(* -1 (* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(* -1 (* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))))
(* (/ 1 (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 (+ (* 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))))))
(* -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))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* (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)))))))
(* -1 (* x (sqrt 1/3)))
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(+ (* 1/2 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/8 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/9 1/16) z)
(* (pow 1/9 1/16) z)
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) z)
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(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
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(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
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(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
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(* -1 (* x (sqrt 1/3)))
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(+ (* 1/2 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/8 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(* 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 (* y (sqrt 1/3)))
(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(+ (* 1/2 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* -1/8 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (pow z 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/16 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))
(* 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 (* 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 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/9 1/8) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)

Outputs
(* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2))))
(/.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) (sqrt.f64 #s(literal 3 binary64)))
(+ (* 1/2 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))))
(fma.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y))))) x) x (/.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 3 binary64))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y)))))) (.f64 x (/.f64 x (sqrt.f64 #s(literal 3 binary64)))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (/.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) (sqrt.f64 #s(literal 3 binary64))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (/ (pow x 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))))) (.f64 x x) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (/.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 3 binary64))))
(/ x (sqrt 3))
(/.f64 x (sqrt.f64 #s(literal 3 binary64)))
(* x (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3))))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)) (/.f64 x (sqrt.f64 #s(literal 3 binary64))))
(* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(.f64 (fma.f64 (.f64 (fma.f64 z z (.f64 y y)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) x)
(* x (+ (* -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))))))
(fma.f64 (fma.f64 (.f64 (fma.f64 z z (.f64 y y)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 z z (.f64 y y))) (.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)))) x (/.f64 x (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 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(* -1 (* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow y 2) (pow z 2)) (* (pow x 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(.f64 (neg.f64 x) (fma.f64 (.f64 (fma.f64 z z (.f64 y y)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))))
(* -1 (* x (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (* (pow x 4) (sqrt 3)))) (+ (* 1/16 (/ (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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 (fma.f64 z z (.f64 y y)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) x) x)) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))))
(* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2))))
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
(+ (* 1/2 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))))
(fma.f64 (.f64 (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z))))) y) y (/.f64 (sqrt.f64 (fma.f64 x x (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/8 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(fma.f64 (fma.f64 (.f64 (.f64 y y) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z))))) (.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (.f64 y y) (/.f64 (sqrt.f64 (fma.f64 x x (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64))))
(+ (* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (/ 1 (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (/ (pow y 2) (sqrt 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(fma.f64 (.f64 (fma.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))) (.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z))))) (.f64 (.f64 (.f64 y (/.f64 y (sqrt.f64 #s(literal 3 binary64)))) #s(literal 1/16 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 z z)) #s(literal 5 binary64)))))) (.f64 y y))) y) y (/.f64 (sqrt.f64 (fma.f64 x x (.f64 z z))) (sqrt.f64 #s(literal 3 binary64))))
(/ y (sqrt 3))
(/.f64 y (sqrt.f64 #s(literal 3 binary64)))
(* y (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))
(fma.f64 (/.f64 (.f64 y (fma.f64 x x (.f64 z z))) (.f64 y (.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 y (sqrt.f64 #s(literal 3 binary64))))
(* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(.f64 (fma.f64 (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y (*.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) y)
(* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(.f64 (fma.f64 (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (pow.f64 y #s(literal 6 binary64)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y (*.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))) y)
(* -1 (/ y (sqrt 3)))
(/.f64 (neg.f64 y) (sqrt.f64 #s(literal 3 binary64)))
(* -1 (* y (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))
(.f64 (neg.f64 y) (fma.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y (.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(* -1 (* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3))))))
(.f64 (neg.f64 (fma.f64 (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y (*.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))) y)
(* -1 (* y (+ (* -1/8 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (sqrt 3)))) (+ (* 1/16 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (sqrt 3)))) (+ (* 1/2 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 3)))) (/ 1 (sqrt 3)))))))
(.f64 (neg.f64 (fma.f64 (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (pow.f64 y #s(literal 6 binary64)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/16 binary64) (fma.f64 (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 3 binary64))))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y (*.f64 y (sqrt.f64 #s(literal 3 binary64))))) #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))))) y)
(* (/ 1 (sqrt 3)) (sqrt (+ (pow x 2) (pow y 2))))
(/.f64 (sqrt.f64 (fma.f64 x x (*.f64 y y))) (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)))))
(fma.f64 (.f64 (.f64 z z) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y)))) (/.f64 (sqrt.f64 (fma.f64 x x (.f64 y y))) (sqrt.f64 #s(literal 3 binary64))))
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(+ (* (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))))))))))
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(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z 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 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) z)
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 3)) (pow z 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(* -1 (* z (sqrt 1/3)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/3 binary64))) z)
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))
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(* -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 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(* -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))))))))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (pow 1/9 1/16) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
(* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y))))
(+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))))
(fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))))) (.f64 x x) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(* x (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) x)
(* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) x)
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) x)
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (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 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) x)
(* -1 (* x (sqrt 1/3)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/3 binary64))) x)
(* -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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x 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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x 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))) (+ (* 1/16 (/ (* (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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z))))
(+ (* 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 (.f64 y y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(+ (* (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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (.f64 y y) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z)))))) (sqrt.f64 #s(literal 1/3 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 z z)) #s(literal 5 binary64))))))) (.f64 y y) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (.f64 y y) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y 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 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) y)
(* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
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(* -1 (* y (sqrt 1/3)))
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(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
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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)))))))
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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))))))))
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(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y))))
(+ (* 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 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y)))))
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(* 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)))))
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(* 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))))))
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(* 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)))))))
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(* -1 (* z (sqrt 1/3)))
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(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))
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(* -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)))))))
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(* -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))))))))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
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(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) (* (pow 1/9 1/16) z))
(.f64 (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/27 1/8) z)
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y))))
(+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))))
(fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))))) (.f64 x x) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(* x (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) x)
(* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) x)
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
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(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (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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(* -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))))))
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(* -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)))))))
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(* -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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z))))
(+ (* 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 (.f64 y y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(+ (* (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)))))))))
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(+ (* (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))))))))))
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(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y 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))))))
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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)))))))
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(* -1 (* y (sqrt 1/3)))
(*.f64 (neg.f64 y) (sqrt.f64 #s(literal 1/3 binary64)))
(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
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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)))))))
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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))))))))
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(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y))))
(+ (* 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 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y)))))
(+ (* (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)))))))))
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(+ (* (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))))))))))
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(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z 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))))))
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(* 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)))))))
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(* -1 (* z (sqrt 1/3)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/3 binary64))) z)
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))
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(* -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)))))))
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(* -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))))))))
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(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
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(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
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(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y))))
(+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))))
(fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(fma.f64 (fma.f64 (.f64 (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (fma.f64 z z (.f64 y y))))))) (.f64 x x) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (.f64 x x) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 y y)))))
(* x (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) x)
(* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) x)
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
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(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (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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(* -1 (* x (sqrt 1/3)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/3 binary64))) x)
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
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(* -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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x 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))) (+ (* 1/16 (/ (* (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 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (/.f64 (fma.f64 z z (.f64 y y)) (pow.f64 x #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z))))
(+ (* 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 (.f64 y y) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(+ (* (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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (.f64 y y) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(fma.f64 (fma.f64 (fma.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (fma.f64 x x (.f64 z z)))))) (sqrt.f64 #s(literal 1/3 binary64)) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 z z)) #s(literal 5 binary64))))))) (.f64 y y) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (.f64 y y) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 z z)))))
(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y 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 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) y)
(* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
(.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 y y) (.f64 y y)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) y)
(* -1 (* y (sqrt 1/3)))
(*.f64 (neg.f64 y) (sqrt.f64 #s(literal 1/3 binary64)))
(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
(.f64 (neg.f64 y) (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
(.f64 (neg.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 y y) (.f64 y y)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) y)
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))))
(.f64 (neg.f64 (fma.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 (fma.f64 x x (.f64 z z)) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 (.f64 y y) (.f64 y y)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))))) y)
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y))))
(+ (* 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 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y)))))
(+ (* (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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 x x (.f64 y y))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y)))))) (.f64 z z) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y)))))
(+ (* (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 -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 x x (.f64 y y)))))) (sqrt.f64 #s(literal 1/3 binary64)) (.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 z z) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y)))))) (.f64 z z) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y)))))
(* 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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z 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 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))) z)
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 3)) (pow z 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))))
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(* -1 (* z (sqrt 1/3)))
(*.f64 (neg.f64 (sqrt.f64 #s(literal 1/3 binary64))) z)
(* -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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z 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 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(* -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 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (.f64 (fma.f64 x x (.f64 y y)) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 z z) (.f64 z z)))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) (* (pow 1/3 1/4) z))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)))
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/9 1/8) z)
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
(* (pow 1/3 1/4) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)

rewrite341.0ms (3.9%)

Memory

8.5MiB live, 237.7MiB allocated

Rules

2 534×	`lower-*.f32`
2 528×	`lower-*.f64`
2 374×	`lower-fma.f64`
2 374×	`lower-fma.f32`
1 652×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	202
0	54	189
1	155	189
2	773	149
3	7998	149
0	8008	139

Stop Event

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

Counts

19 → 305

Calls

Call 1

Inputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
(.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)

Outputs
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(.f64 (.f64 #s(literal 1 binary64) (neg.f64 z)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)))
(*.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) (neg.f64 z))
(*.f64 #s(literal -1 binary64) (/.f64 (neg.f64 z) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) z) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
(*.f64 #s(literal 1 binary64) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 z (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1 binary64))
(/.f64 (/.f64 (neg.f64 z) #s(literal -1 binary64)) (sqrt.f64 #s(literal 3 binary64)))
(/.f64 (*.f64 (neg.f64 z) #s(literal 1 binary64)) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (*.f64 #s(literal 1 binary64) (neg.f64 z)) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) (neg.f64 z)))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) z))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (neg.f64 z) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 (neg.f64 z) (sqrt.f64 #s(literal 3 binary64)))))
(neg.f64 (/.f64 (neg.f64 z) (sqrt.f64 #s(literal 3 binary64))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (/.f64 (neg.f64 z) (sqrt.f64 #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (/.f64 (neg.f64 z) (sqrt.f64 #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(*.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 3 binary64))) #s(literal 1/2 binary64))
(pow.f64 #s(literal 9 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 3 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(literal 3 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
(.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)))))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)))
(.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z))
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64))) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64))) (*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64))))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64))))
(*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
(*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)))
(pow.f64 (exp.f64 #s(literal 1/8 binary64)) (log.f64 #s(literal 1/27 binary64)))
(pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))
(pow.f64 #s(literal 1/81 binary64) #s(literal 3/32 binary64))
(pow.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/3 binary64) #s(literal 3/8 binary64))
(pow.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) #s(literal 3 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 3/16 binary64))
(pow.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64))
(pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (*.f64 #s(literal 1/32 binary64) (log.f64 #s(literal 1/81 binary64)))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/27 binary64)) #s(literal 1/16 binary64) (*.f64 (log.f64 #s(literal 1/27 binary64)) #s(literal 1/16 binary64))))
(exp.f64 (log.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))))
(exp.f64 (fma.f64 #s(literal 1/32 binary64) (log.f64 #s(literal 1/81 binary64)) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/27 binary64)) #s(literal 1/16 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/729 binary64)) #s(literal 1/16 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/27 binary64)) #s(literal 1/8 binary64)))
(.f64 (.f64 z (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) z))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
(*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z)
(*.f64 z (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
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(.f64 (.f64 (.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)))
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(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
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(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
(.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/64 binary64)) (.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)))))
(.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/243 binary64) #s(literal 1/16 binary64)) z))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)))
(.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) z))
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64))) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64))))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z))
(*.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z)
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z))
(*.f64 z (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64))) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z)) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64))))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (*.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/64 binary64)) (.f64 (pow.f64 #s(literal 1/729 binary64) #s(literal 1/32 binary64)) z))
(*.f64 (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)) z)
(.f64 (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z) (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)))
(.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) (.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) z))
(*.f64 z (pow.f64 #s(literal 1/6561 binary64) #s(literal 1/32 binary64)))

eval499.0ms (5.7%)

Memory: -17.5MiB live, 161.9MiB allocated
Compiler: Compiled 14 493 to 1 027 computations (92.9% saved)

prune131.0ms (1.5%)

Memory

2.9MiB live, 127.8MiB allocated

Pruning

13 alts after pruning (7 fresh and 6 done)

	Pruned	Kept	Total
New	737	7	744
Fresh	0	0	0
Picked	4	1	5
Done	0	5	5
Total	741	13	754

Accuracy

98.8%

Counts

754 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	38.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
✓	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
✓	38.8%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	39.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
	96.6%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))))
✓	97.7%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	97.1%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z))
	89.1%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))))
	96.1%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/16 binary64)) (log.f64 #s(literal 1/9 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
	96.1%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) #s(literal 2 binary64)) z)))
	96.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
	96.1%	#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 (pow.f64 (exp.f64 #s(literal 1/16 binary64)) (log.f64 #s(literal 1/9 binary64))) #s(literal 2 binary64)) z)))
✓	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 419 to 212 computations (49.4% saved)

regimes118.0ms (1.4%)

Memory

8.0MiB live, 120.6MiB allocated

Counts

25 → 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 (.f64 #s(literal 1/3 binary64) z) z)))
(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #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))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 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 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #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)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 z z (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 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)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) #s(literal 3 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 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 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64)) (.f64 (pow.f64 (pow.f64 #s(literal 1/81 binary64) #s(literal 1/32 binary64)) #s(literal 2 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 (pow.f64 (exp.f64 #s(literal 1/16 binary64)) (log.f64 #s(literal 1/9 binary64))) #s(literal 2 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 (pow.f64 (exp.f64 #s(literal 1/16 binary64)) (log.f64 #s(literal 1/9 binary64))) #s(literal 2 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 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)) z)))

Calls

10 calls:

31.0ms	z
30.0ms	(+.f64 (.f64 x x) (.f64 y y))
10.0ms	(*.f64 z z)
7.0ms	y
7.0ms	x

Results

Accuracy	Segments	Branch
97.8%	1	`x`
97.8%	1	`y`
97.8%	1	`z`
97.8%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.8%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.8%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.8%	1	`(*.f64 x x)`
97.8%	1	`(*.f64 y y)`
97.8%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes82.0ms (0.9%)

Memory

-9.8MiB live, 101.3MiB 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 (.f64 #s(literal 1/3 binary64) z) z)))
(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #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))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 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 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))))
(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #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)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))))
(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 z z (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) z)))

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

Calls

10 calls:

28.0ms	y
11.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
7.0ms	(*.f64 z z)
5.0ms	x
5.0ms	z

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`y`
97.7%	1	`z`
97.7%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.7%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.7%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.7%	1	`(*.f64 x x)`
97.7%	1	`(*.f64 y y)`
97.7%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes23.0ms (0.3%)

Memory

-0.6MiB live, 44.3MiB allocated

Accuracy

Total -37.8b remaining (-2552%)

Threshold costs -37.8b (-2552%)

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 (*.f64 #s(literal 1/3 binary64) z) z)))

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

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

Calls

10 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
2.0ms	(*.f64 y y)
2.0ms	z
2.0ms	x
2.0ms	y

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`y`
97.7%	1	`z`
97.7%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.7%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.7%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.7%	1	`(*.f64 x x)`
97.7%	1	`(*.f64 y y)`
97.7%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify7.0ms (0.1%)

Memory

13.4MiB live, 13.4MiB allocated

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	63
1	29	63

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)) z)))

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

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

Outputs
#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 (.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(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))

soundness477.0ms (5.5%)

Memory

-20.9MiB live, 414.2MiB allocated

Rules

7 993×	`lower-fma.f64`
7 993×	`lower-fma.f32`
6 683×	`lower-fma.f64`
6 683×	`lower-fma.f32`
3 457×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	246
0	45	235
1	130	235
2	761	235
0	8387	224
0	230	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992
0	473	10488
1	1506	10446
2	5381	10299
0	8188	9012

Stop Event

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

Compiler

Compiled 79 to 54 computations (31.6% saved)

preprocess284.0ms (3.3%)

Memory: 30.8MiB live, 189.1MiB allocated
Compiler: Compiled 358 to 222 computations (38% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze3.0ms (0%)

sample2.1s (24.6%)

explain138.0ms (1.6%)

preprocess39.0ms (0.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.2%)

localize30.0ms (0.3%)

series16.0ms (0.2%)

simplify230.0ms (2.6%)

rewrite271.0ms (3.1%)

eval67.0ms (0.8%)

prune214.0ms (2.5%)

simplify7.0ms (0.1%)

localize78.0ms (0.9%)

series34.0ms (0.4%)

simplify875.0ms (10.1%)

rewrite495.0ms (5.7%)

eval168.0ms (1.9%)

prune82.0ms (0.9%)

simplify22.0ms (0.3%)

localize101.0ms (1.2%)

series82.0ms (0.9%)

simplify252.0ms (2.9%)

rewrite209.0ms (2.4%)

eval175.0ms (2%)

prune404.0ms (4.6%)

simplify9.0ms (0.1%)

localize156.0ms (1.8%)

series78.0ms (0.9%)

simplify337.0ms (3.9%)

rewrite341.0ms (3.9%)

eval499.0ms (5.7%)

prune131.0ms (1.5%)

regimes118.0ms (1.4%)

regimes82.0ms (0.9%)

regimes23.0ms (0.3%)

simplify7.0ms (0.1%)

soundness477.0ms (5.5%)

preprocess284.0ms (3.3%)

end0.0ms (0%)

Profiling