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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.3s (15.4%)

Memory

9.6MiB live, 1 497.9MiB allocated

Samples

956.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 718.0ms

ival-mult: 320.0ms (44.5% of total)

ival-div: 182.0ms (25.3% of total)

ival-add: 137.0ms (19.1% of total)

ival-sqrt: 64.0ms (8.9% of total)

ival-true: 6.0ms (0.8% of total)

exact: 5.0ms (0.7% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain135.0ms (1.6%)

Memory

33.0MiB live, 310.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
153	-	-	`(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	151	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	151
↳	`(*.f64 y y)`	overflow	71
↳	`(*.f64 x x)`	overflow	67
↳	`(*.f64 z z)`	overflow	59
↳	`(+.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	151
`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	81
↳	`(*.f64 x x)`	underflow	60
↳	`(*.f64 z z)`	underflow	50
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	17
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2

Confusion

	Predicted +	Predicted -
+	153	0
-	0	103

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	153	0	0
-	0	0	103

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	103
1	153

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 (45.8% of total)

ival-add: 4.0ms (18.3% of total)

ival-sqrt: 4.0ms (18.3% of total)

ival-div: 3.0ms (13.7% of total)

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

exact: 0.0ms (0% of total)

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

preprocess342.0ms (4.1%)

Memory

-18.1MiB live, 61.1MiB allocated

Algorithm

1×	egg-herbie

Rules

224×	`div-sub`
222×	`cancel-sign-sub`
216×	`sub-neg`
132×	`associate-/l*`
132×	`*-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 y y (fma.f64 x x (*.f64 z z))) #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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.5MiB live, 1.5MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.4%	(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)

simplify5.0ms (0.1%)

Memory

8.1MiB live, 8.1MiB 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

24×	`lower-+.f32`
20×	`lower-+.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
10×	`+-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 y y (fma.f64 x x (*.f64 z z))) #s(literal 3 binary64)))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
(/.f64 (fma.f64 y y (fma.f64 x x (*.f64 z z))) #s(literal 3 binary64))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(fma.f64 y y (fma.f64 x x (*.f64 z z)))
(+.f64 (.f64 x x) (.f64 y y))
(fma.f64 x x (*.f64 y y))
(*.f64 x x)
x
(*.f64 y y)
y
(*.f64 z z)
z
#s(literal 3 binary64)

localize132.0ms (1.6%)

Memory

-57.5MiB live, 52.8MiB 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	35.576348746996025	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

113.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 105.0ms

ival-add: 96.0ms (91.8% of total)

ival-mult: 4.0ms (3.8% of total)

ival-div: 2.0ms (1.9% of total)

ival-sqrt: 2.0ms (1.9% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.2%)

Memory

26.9MiB live, 26.9MiB 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
1.0ms	y	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	x	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	z	@	0	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	z	@	inf	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
1.0ms	y	@	inf	(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))

simplify1.0s (12.2%)

Memory

6.3MiB live, 512.0MiB allocated

Algorithm

1×	egg-herbie

Rules

13 366×	`lower-fma.f64`
13 366×	`lower-fma.f32`
5 460×	`lower-*.f64`
5 460×	`lower-*.f32`
3 804×	`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 y y (*.f64 z z))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.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)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.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 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.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 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.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 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.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 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 x x (.f64 y y)) #s(literal 1 binary64)))
(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 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
(+ (* 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 x x) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z)))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(+ (* (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 x x) (fma.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z))))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(+ (* (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 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 z z)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z))))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(* 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 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) (.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 x (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x 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))) (+ (* 1/16 (/ (* (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 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 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (*.f64 z z)))) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* x (sqrt 1/3)))
(neg.f64 (*.f64 x (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) (neg.f64 (.f64 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)))))))
(neg.f64 (.f64 x (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.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 (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 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (*.f64 z z)))) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 x))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x))))
(+ (* 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 y y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(+ (* (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 y y) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 y y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(+ (* (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 y y) (fma.f64 (.f64 y y) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 x x)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(* 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 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) y)) (.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 y (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (.f64 y 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))) (+ (* 1/16 (/ (* (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 y (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (fma.f64 (.f64 (fma.f64 z z (.f64 x x)) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (*.f64 y y))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (sqrt 1/3)))
(neg.f64 (*.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))))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) y)) (neg.f64 (.f64 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 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 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 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (fma.f64 (.f64 (fma.f64 z z (.f64 x x)) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (*.f64 y y))))) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 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 z z) (.f64 #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 (.f64 z z) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (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 -1/8 binary64)) (.f64 z z)) (.f64 #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) (+ (* 1/2 (* (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 z z) (fma.f64 (.f64 z z) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))))) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 #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)))))
(* 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 z (sqrt.f64 #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) 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 z (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 (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))) (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))) (+ (* 1/16 (/ (* (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 z (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) (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 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (*.f64 y y)))) #s(literal 1/16 binary64)) (pow.f64 z #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* z (sqrt 1/3)))
(*.f64 z (neg.f64 (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))))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (/.f64 (fma.f64 x x (.f64 y y)) z)) (.f64 z (neg.f64 (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 z (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 (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))) (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 (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) (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 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (*.f64 y y)))) #s(literal 1/16 binary64)) (pow.f64 z #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 z))
(* 1/3 (+ (pow y 2) (pow z 2)))
(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* 1/3 (pow x 2))
(.f64 x (.f64 x #s(literal 1/3 binary64)))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)) (.f64 x (.f64 x #s(literal 1/3 binary64))))
(* 1/3 (+ (pow x 2) (pow z 2)))
(.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))
(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(* 1/3 (pow y 2))
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* 1/3 (pow y 2))
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(fma.f64 y (.f64 y #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64))))
(* 1/3 (+ (pow x 2) (pow y 2)))
(.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (fma.f64 z z (.f64 x x))))
(* 1/3 (pow z 2))
(.f64 z (.f64 z #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))
(* 1/3 (pow z 2))
(.f64 z (.f64 z #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(fma.f64 z (.f64 z #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) #s(literal 1/3 binary64))))

rewrite300.0ms (3.6%)

Memory

-12.4MiB live, 587.3MiB allocated

Rules

4 524×	`lower-fma.f64`
4 524×	`lower-fma.f32`
4 260×	`lower-*.f32`
4 254×	`lower-*.f64`
3 048×	`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 x x) (fma.f64 y y (.f64 z z)))
(+.f64 (.f64 y y) (fma.f64 x x (.f64 z z)))
(+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z))
(+.f64 (fma.f64 x x (.f64 y y)) (neg.f64 (neg.f64 (.f64 z z))))
(+.f64 (.f64 z z) (fma.f64 x x (.f64 y y)))
(+.f64 (fma.f64 y y (.f64 z z)) (.f64 x x))
(+.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 (+.f64 x z) (-.f64 x z) (.f64 y y))) (neg.f64 (/.f64 (.f64 z (.f64 z (.f64 z z))) (fma.f64 (+.f64 x z) (-.f64 x z) (.f64 y y)))))
(+.f64 (fma.f64 x x (.f64 z z)) (.f64 y y))
(+.f64 (neg.f64 (neg.f64 (.f64 z z))) (fma.f64 x x (.f64 y y)))
(+.f64 (neg.f64 (neg.f64 (.f64 x x))) (neg.f64 (neg.f64 (fma.f64 y y (.f64 z z)))))
(-.f64 #s(literal 0 binary64) (neg.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))))
(-.f64 (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (fma.f64 (+.f64 x z) (-.f64 x z) (.f64 y y))) (/.f64 (.f64 z (.f64 z (.f64 z z))) (fma.f64 (+.f64 x z) (-.f64 x z) (.f64 y y))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x y) (-.f64 x y))) (-.f64 (/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (+.f64 x y) (-.f64 x y))) (*.f64 z z)))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 x x) (fma.f64 y y (.f64 z z)))) (/.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) (-.f64 (.f64 x x) (fma.f64 y y (.f64 z z)))))
(-.f64 (/.f64 (.f64 z (.f64 z (.f64 z z))) (-.f64 (.f64 z z) (fma.f64 x x (.f64 y y)))) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (-.f64 (.f64 z z) (fma.f64 x x (.f64 y y)))))
(-.f64 (fma.f64 z z (/.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 x y) (-.f64 x y)))) (/.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 (+.f64 x y) (-.f64 x y))))
(fma.f64 x x (fma.f64 y y (*.f64 z z)))
(fma.f64 y y (fma.f64 x x (*.f64 z z)))
(fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y)))) (*.f64 z z))
(fma.f64 (fma.f64 x x (.f64 y y)) (.f64 (.f64 (+.f64 x y) (-.f64 x y)) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x y) (-.f64 x y)))) (neg.f64 (neg.f64 (*.f64 z z))))
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eval83.0ms (1%)

Memory: 28.4MiB live, 188.9MiB allocated
Compiler: Compiled 18 366 to 1 562 computations (91.5% saved)

prune75.0ms (0.9%)

Memory

1.2MiB live, 200.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	477	5	482
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	478	5	483

Accuracy

98.7%

Counts

483 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.3%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
▶	43.8%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	44.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
▶	43.7%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64)))))
▶	97.8%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 114 to 76 computations (33.3% saved)

simplify10.0ms (0.1%)

Memory

-24.6MiB live, 14.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

38×	`lower-*.f32`
34×	`lower-fma.f32`
30×	`lower-fma.f64`
28×	`lower-*.f64`
28×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	243
0	46	227
1	57	227
2	72	227
3	76	227
4	78	227
0	78	227

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

localize79.0ms (0.9%)

Memory

17.8MiB live, 175.5MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.00390625	(fma.f64 y y (*.f64 z z))
accuracy	0.30859375	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	35.51934390543802	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))
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	0.39961600435544226	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	35.576348746996025	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
accuracy	0.00390625	(fma.f64 y y (*.f64 z z))
accuracy	0.16015625	(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
accuracy	35.576348746996025	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
accuracy	0.09765625	(.f64 z (.f64 z #s(literal 1/3 binary64)))
accuracy	0.33203125	(*.f64 z #s(literal 1/3 binary64))
accuracy	0.40057347458137327	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64))))
accuracy	35.576348746996025	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64)))))
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.45703125	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	0.9595001323915289	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Samples

49.0ms

256×

valid

Compiler

Compiled 207 to 24 computations (88.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-mult: 13.0ms (38.8% of total)

ival-sqrt: 9.0ms (26.8% of total)

ival-add: 4.0ms (11.9% of total)

const: 4.0ms (11.9% of total)

ival-div: 3.0ms (8.9% of total)

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

exact: 0.0ms (0% of total)

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

series70.0ms (0.8%)

Memory

-12.3MiB live, 70.0MiB allocated

Counts

19 → 492

Calls

Call 1

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

Calls

123 calls:

Time	Variable		Expression
31.0ms	y	@	(* (+ (* y y) (* z z)) 1/3)
1.0ms	z	@	(* z (sqrt 1/3))
1.0ms	x	@	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3))
0.0ms	y	@	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3))
0.0ms	z	@	(/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3))

simplify343.0ms (4.1%)

Memory

26.7MiB live, 539.0MiB allocated

Algorithm

1×	egg-herbie

Rules

15 994×	`lower-fma.f64`
15 994×	`lower-fma.f32`
6 910×	`lower-*.f64`
6 910×	`lower-*.f32`
4 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	471	10680
1	1504	10638
2	5373	10491
0	8180	9165

Stop Event

1×	iter limit
1×	node limit

Counts

492 → 489

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))))
(+ (* 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))
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(* (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 z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 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))))))))
(+ (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)))))

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

rewrite1.2s (14.5%)

Memory

-31.8MiB live, 530.4MiB allocated

Rules

7 724×	`lower-fma.f32`
7 720×	`lower-fma.f64`
5 338×	`lower-*.f32`
5 328×	`lower-*.f64`
3 850×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	218
0	46	201
1	138	201
2	892	201
0	8509	201

Stop Event

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

Counts

19 → 461

Calls

Call 1

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

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

eval169.0ms (2%)

Memory: 15.4MiB live, 279.4MiB allocated
Compiler: Compiled 28 390 to 2 084 computations (92.7% saved)

prune141.0ms (1.7%)

Memory

18.9MiB live, 347.6MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 052	3	1 055
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 054	6	1 060

Accuracy

99.1%

Counts

1 060 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	43.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
✓	44.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
✓	43.7%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64)))))
▶	98.0%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
▶	98.0%	#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)))
✓	97.8%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 62 to 42 computations (32.3% saved)

simplify10.0ms (0.1%)

Memory

-20.2MiB live, 21.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 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	(.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	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
cost-diff	0	(*.f64 (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

24×	`lower-+.f64`
24×	`lower-*.f32`
24×	`lower-+.f32`
18×	`lower-fma.f64`
18×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	127
0	37	127
1	47	119
2	58	117
3	59	117
0	59	107

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
#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)
(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)

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

localize75.0ms (0.9%)

Memory

3.3MiB live, 201.7MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 z z)
accuracy	0.16015625	(.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64))
accuracy	0.39961600435544226	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	35.576348746996025	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.30078125	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.9595001323915289	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
accuracy	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
accuracy	0.06640625	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.2890625	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
accuracy	0.9595001323915289	#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

52.0ms

256×

valid

Compiler

Compiled 102 to 26 computations (74.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 41.0ms

ival-mult: 11.0ms (26.8% of total)

ival-sqrt: 9.0ms (22% of total)

ival-div: 7.0ms (17.1% of total)

ival-pow: 5.0ms (12.2% of total)

ival-add: 4.0ms (9.8% of total)

const: 3.0ms (7.3% of total)

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

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

exact: 0.0ms (0% of total)

series61.0ms (0.7%)

Memory

-10.5MiB live, 157.1MiB allocated

Counts

11 → 228

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 #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 (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>) () ())

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

Calls

57 calls:

Time	Variable		Point	Expression
46.0ms	z	@	0	(* (pow 1/3 1/4) z)
1.0ms	z	@	inf	(/ z (sqrt 3))
0.0ms	z	@	0	(/ z (sqrt 3))
0.0ms	z	@	-inf	(/ z (sqrt 3))
0.0ms	z	@	inf	(* (pow 1/3 1/4) (* (pow 1/3 1/4) z))

simplify320.0ms (3.8%)

Memory

37.0MiB live, 420.1MiB allocated

Algorithm

1×	egg-herbie

Rules

12 576×	`lower-fma.f64`
12 576×	`lower-fma.f32`
6 356×	`lower-*.f64`
6 356×	`lower-*.f32`
3 390×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	357	5100
1	1126	5058
2	4125	4983
0	8131	4368

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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))))
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(* (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)
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(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
(* (pow 1/3 1/4) z)
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(* 1/3 (+ (pow y 2) (pow z 2)))
(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
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(+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))
(* 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)))))
(* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(* 1/3 (pow x 2))
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(* 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)))
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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)))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(* 1/3 (pow y 2))
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(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
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(+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))
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(* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
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(* (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 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 z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)
(pow z 2)

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

rewrite415.0ms (5%)

Memory

-172.9MiB live, 416.6MiB allocated

Rules

7 646×	`lower-fma.f64`
7 646×	`lower-fma.f32`
5 370×	`lower-*.f32`
5 362×	`lower-*.f64`
3 752×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	120
0	37	119
1	134	109
2	885	109
0	8437	99

Stop Event

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

Counts

11 → 93

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)
#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))
(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)

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

eval43.0ms (0.5%)

Memory: 25.5MiB live, 63.7MiB allocated
Compiler: Compiled 6 880 to 573 computations (91.7% saved)

prune71.0ms (0.8%)

Memory

-33.5MiB live, 88.6MiB allocated

Pruning

9 alts after pruning (3 fresh and 6 done)

	Pruned	Kept	Total
New	331	3	334
Fresh	0	0	0
Picked	0	3	3
Done	0	3	3
Total	331	9	340

Accuracy

99.1%

Counts

340 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	43.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
✓	44.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
✓	43.7%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64)))))
▶	96.9%	#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))))))
✓	98.0%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
▶	97.2%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z))
▶	89.6%	#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))))
✓	98.0%	#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)))
✓	97.8%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 96 to 69 computations (28.1% saved)

simplify11.0ms (0.1%)

Memory

16.8MiB live, 16.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
cost-diff	0	#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))))))
cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z))
cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
cost-diff	0	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
cost-diff	0	#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))))
cost-diff	320	(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
cost-diff	12800	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Rules

76×	`lower-*.f32`
72×	`lower-*.f64`
50×	`lower-/.f32`
46×	`lower-fma.f64`
46×	`lower-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	137
0	35	125
1	54	124
2	79	112
3	109	111
4	134	111
5	154	111
6	169	111
7	174	111
8	178	111
9	179	111
0	179	105

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)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
z
#s(literal -1 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))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
#s(literal 1 binary64)
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
z
#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 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
z
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)

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

localize74.0ms (0.9%)

Memory

0.9MiB live, 113.9MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score
accuracy	0.30078125	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
accuracy	0.9595001323915289	#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))))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.45703125	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
accuracy	0.9595001323915289	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z))
accuracy	1.0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
accuracy	0.3828125	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
accuracy	0.9595001323915289	#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))))
accuracy	5.916035447194129	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Samples

48.0ms

256×

valid

Compiler

Compiled 114 to 24 computations (78.9% saved)

Precisions

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

ival-mult: 13.0ms (36.8% of total)

ival-div: 10.0ms (28.3% of total)

ival-exp: 3.0ms (8.5% of total)

ival-log: 3.0ms (8.5% of total)

ival-sqrt: 3.0ms (8.5% of total)

ival-add: 2.0ms (5.7% of total)

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

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

exact: 0.0ms (0% of total)

series68.0ms (0.8%)

Memory

17.0MiB live, 86.7MiB allocated

Counts

12 → 180

Calls

Call 1

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

Outputs
#s(alt (/ z (sqrt 3)) (taylor 0 z) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
#s(alt (/ z (sqrt 3)) (taylor 0 z) (#s(alt (exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))) (patch (exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))) #<representation binary64>) () ())) ())
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#s(alt (/ z (sqrt 3)) (taylor 0 z) (#s(alt (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) (patch (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ z (sqrt 3)) (taylor inf z) (#s(alt (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) (patch (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ z (sqrt 3)) (taylor -inf z) (#s(alt (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) (patch (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))) #<representation binary64>) () ())) ())
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#s(alt (/ (sqrt 3) z) (taylor 0 z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor 0 z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor 0 z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor -inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor -inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor -inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())
#s(alt (/ (sqrt 3) z) (taylor -inf z) (#s(alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (patch (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #<representation binary64>) () ())) ())

Calls

45 calls:

Time	Variable		Point	Expression
33.0ms	z	@	-inf	(* (log (/ (sqrt 3) z)) -1)
13.0ms	z	@	0	(* (log (/ (sqrt 3) z)) -1)
12.0ms	z	@	inf	(* (log (/ (sqrt 3) z)) -1)
0.0ms	z	@	0	(exp (* (log (/ (sqrt 3) z)) -1))
0.0ms	z	@	-inf	(exp (* (log (/ (sqrt 3) z)) -1))

simplify362.0ms (4.3%)

Memory

-1.2MiB live, 431.0MiB allocated

Algorithm

1×	egg-herbie

Rules

18 022×	`lower-fma.f64`
18 022×	`lower-fma.f32`
6 132×	`lower-*.f64`
6 132×	`lower-*.f32`
3 112×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	199	4420
1	587	4278
2	2192	4261
3	5632	4207
0	8286	3712

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

Outputs
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
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(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)

rewrite296.0ms (3.5%)

Memory

-1.5MiB live, 320.6MiB allocated

Rules

4 896×	`lower-fma.f64`
4 896×	`lower-fma.f32`
4 618×	`lower-*.f32`
4 614×	`lower-*.f64`
3 302×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	120
0	35	105
1	122	91
2	706	90
3	7562	90
0	8268	84

Stop Event

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

Counts

12 → 384

Calls

Call 1

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

Outputs
(exp.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(exp.f64 (*.f64 (log.f64 (exp.f64 #s(literal -1 binary64))) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))))
(-.f64 #s(literal 0 binary64) (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(neg.f64 (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) z))
(/.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))) #s(literal 1 binary64))
(/.f64 (neg.f64 z) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) z))
(/.f64 (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #s(literal -1 binary64))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 z)))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 z))))
(/.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)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1 binary64))
(pow.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal -1 binary64)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1/2 binary64))
(*.f64 z (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 #s(literal -1 binary64) (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(*.f64 #s(literal 1 binary64) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
(*.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))) #s(literal 1 binary64))
(*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) (neg.f64 z))
(*.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 (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 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) (/.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) #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)) (/.f64 #s(literal 1 binary64) z)))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) (.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) z))
(*.f64 (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #s(literal -1 binary64))
(.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 z))))
(*.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(*.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/4 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 (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)) (/.f64 #s(literal 1 binary64) z)))
(*.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 2 binary64))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 2 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 (.f64 #s(literal 1 binary64) (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)))
(log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(+.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #s(literal 0 binary64))
(+.f64 (log.f64 z) (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))
(+.f64 (log.f64 (neg.f64 z)) (neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))))
(+.f64 (neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (neg.f64 z)))
(+.f64 (neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))))
(+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (log.f64 z))
(+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(+.f64 (log.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (log.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) z))))
(+.f64 (log.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (log.f64 (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) z)))
(+.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64))) (log.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64))))
(+.f64 (log.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64))) (log.f64 (/.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(+.f64 (log.f64 (neg.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))) (log.f64 #s(literal -1 binary64)))
(+.f64 (log.f64 (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal -1 binary64))) (neg.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))))
(+.f64 (log.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))))) (log.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 z)))))
(+.f64 (log.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))) (log.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(+.f64 (log.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))) (log.f64 (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(+.f64 (log.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) #s(literal 1 binary64))) (log.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) (/.f64 #s(literal 1 binary64) z))))
(+.f64 (log.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 2 binary64)))) (log.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 2 binary64)))))
(+.f64 (log.f64 (*.f64 z (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))) (log.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))
(+.f64 (log.f64 (*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)))) (log.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64))))
(-.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #s(literal 0 binary64))
(-.f64 (log.f64 z) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))))
(-.f64 #s(literal 0 binary64) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(-.f64 (log.f64 (neg.f64 z)) (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
(-.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))))
(-.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (neg.f64 (log.f64 z)))
(fma.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64) #s(literal 0 binary64))
(fma.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (exp.f64 #s(literal -1 binary64))) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 0 binary64))
(fma.f64 #s(literal -1 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) (log.f64 z))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(fma.f64 #s(literal 1 binary64) (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (log.f64 z))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64))) (.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(fma.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal -1 binary64) (log.f64 z))
(fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal -1 binary64) (.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(fma.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal -1 binary64) (.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(fma.f64 #s(literal 1/2 binary64) (*.f64 (log.f64 #s(literal 3 binary64)) #s(literal -1 binary64)) (log.f64 z))
(fma.f64 #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(fma.f64 #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 3 binary64)) #s(literal -1 binary64)) (.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(fma.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64)) (log.f64 z))
(fma.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64)) (*.f64 (neg.f64 (log.f64 z)) #s(literal -1 binary64)))
(fma.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 3 binary64)) (*.f64 #s(literal -1 binary64) (neg.f64 (log.f64 z))))
(neg.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(neg.f64 (*.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))) #s(literal -1 binary64)))
(/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) (neg.f64 (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64)))))
(/.f64 (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))) (neg.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) z))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64)))) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64))))
(/.f64 (neg.f64 (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) (log.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(/.f64 (.f64 #s(literal -1 binary64) (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64)))) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(/.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) #s(literal -1 binary64)) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64))))
(/.f64 (.f64 (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))) #s(literal -1 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (exp.f64 #s(literal -1 binary64))))
(*.f64 #s(literal -1 binary64) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(+.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal 0 binary64))
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) (neg.f64 (log.f64 z)))
(+.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) (log.f64 (exp.f64 (neg.f64 (log.f64 z)))))
(+.f64 #s(literal 0 binary64) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (neg.f64 (log.f64 (neg.f64 z))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (log.f64 (/.f64 (/.f64 #s(literal -1 binary64) z) #s(literal 1 binary64))))
(+.f64 (log.f64 #s(literal -1 binary64)) (log.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))))
(+.f64 (neg.f64 (log.f64 z)) (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))))
(+.f64 (neg.f64 (log.f64 (neg.f64 z))) (log.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
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eval74.0ms (0.9%)

Memory: 19.2MiB live, 146.1MiB allocated
Compiler: Compiled 10 823 to 1 289 computations (88.1% saved)

prune109.0ms (1.3%)

Memory

1.1MiB live, 121.6MiB allocated

Pruning

14 alts after pruning (6 fresh and 8 done)

	Pruned	Kept	Total
New	646	6	652
Fresh	0	0	0
Picked	1	2	3
Done	0	6	6
Total	647	14	661

Accuracy

99.1%

Counts

661 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	43.7%	(sqrt.f64 (.f64 #s(approx (+ (+ ( x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 1/3 binary64)))
✓	44.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))))
✓	43.7%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 z (.f64 z #s(literal 1/3 binary64)))))
✓	96.9%	#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))))))
✓	98.0%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	89.3%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (neg.f64 (log.f64 z)))))
✓	97.2%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z))
	86.8%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (exp.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) (neg.f64 (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64)))))))
	87.0%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (exp.f64 (.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64)) (*.f64 (neg.f64 (log.f64 z)) (neg.f64 (log.f64 z)))) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) (/.f64 #s(literal 1 binary64) z)))) #s(literal -1 binary64))))
	88.3%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (exp.f64 (.f64 (/.f64 #s(literal 1 binary64) (/.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))))) #s(literal -1 binary64))))
	86.8%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (exp.f64 (.f64 (.f64 (-.f64 (pow.f64 (.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64))))) #s(literal -1 binary64))))
	89.6%	#s(approx (/ (sqrt (+ (* x x) (+ (* y y) (* z z)))) (sqrt 3)) (exp.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))))
✓	98.0%	#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)))
✓	97.8%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 472 to 244 computations (48.3% saved)

regimes326.0ms (3.9%)

Memory

-23.3MiB live, 91.8MiB allocated

Counts

18 → 1

Calls

Call 1

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

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

Calls

10 calls:

143.0ms	x
131.0ms	(*.f64 z z)
16.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
5.0ms	y
5.0ms	z

Results

Accuracy	Segments	Branch
98.0%	1	`x`
98.0%	1	`y`
98.0%	1	`z`
98.0%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.0%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.0%	1	`(*.f64 x x)`
98.0%	1	`(*.f64 y y)`
98.0%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes20.0ms (0.2%)

Memory

1.3MiB live, 44.6MiB allocated

Accuracy

Total -34.7b remaining (-2464.3%)

Threshold costs -34.7b (-2464.3%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

Calls

10 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 y y))
2.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
2.0ms	y
2.0ms	z
2.0ms	x

Results

Accuracy	Segments	Branch
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 y y)`
97.8%	1	`(*.f64 z z)`
97.8%	1	`x`
97.8%	1	`y`
97.8%	1	`z`
97.8%	1	`(*.f64 x x)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify7.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	24	39

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

Outputs

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

soundness523.0ms (6.3%)

Memory

-14.3MiB live, 412.7MiB allocated

Rules

15 994×	`lower-fma.f64`
15 994×	`lower-fma.f32`
13 366×	`lower-fma.f64`
13 366×	`lower-fma.f32`
6 910×	`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
0	471	10680
1	1504	10638
2	5373	10491
0	8180	9165
0	11	45
0	18	45
1	65	45
2	486	45
3	6616	45
0	8497	38

Stop Event

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

Compiler

Compiled 57 to 37 computations (35.1% saved)

preprocess79.0ms (0.9%)

Memory: 25.6MiB live, 185.8MiB allocated
Compiler: Compiled 194 to 134 computations (30.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	26	137
0	35	125
1	54	124
2	79	112
3	109	111
4	134	111
5	154	111
6	169	111
7	174	111
8	178	111
9	179	111
0	179	105

Iter	Nodes	Cost
0	26	137
0	35	125
1	54	124
2	79	112
3	109	111
4	134	111
5	154	111
6	169	111
7	174	111
8	178	111
9	179	111
0	179	105

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (15.4%)

explain135.0ms (1.6%)

preprocess342.0ms (4.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize132.0ms (1.6%)

series13.0ms (0.2%)

simplify1.0s (12.2%)

rewrite300.0ms (3.6%)

eval83.0ms (1%)

prune75.0ms (0.9%)

simplify10.0ms (0.1%)

localize79.0ms (0.9%)

series70.0ms (0.8%)

simplify343.0ms (4.1%)

rewrite1.2s (14.5%)

eval169.0ms (2%)

prune141.0ms (1.7%)

simplify10.0ms (0.1%)

localize75.0ms (0.9%)

series61.0ms (0.7%)

simplify320.0ms (3.8%)

rewrite415.0ms (5%)

eval43.0ms (0.5%)

prune71.0ms (0.8%)

simplify11.0ms (0.1%)

localize74.0ms (0.9%)

series68.0ms (0.8%)

simplify362.0ms (4.3%)

rewrite296.0ms (3.5%)

eval74.0ms (0.9%)

prune109.0ms (1.3%)

regimes326.0ms (3.9%)

regimes20.0ms (0.2%)

simplify7.0ms (0.1%)

soundness523.0ms (6.3%)

preprocess79.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	26	137
0	35	125
1	54	124
2	79	112
3	109	111
4	134	111
5	154	111
6	169	111
7	174	111
8	178	111
9	179	111
0	179	105