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

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze1.0ms (0%)

Memory

2.6MiB live, 2.6MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample2.2s (33.1%)

Memory

-12.4MiB live, 1 934.5MiB allocated

Samples

1.7s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 676.0ms

ival-mult: 433.0ms (64.1% of total)

ival-div: 85.0ms (12.6% of total)

ival-add: 73.0ms (10.8% of total)

ival-sqrt: 70.0ms (10.4% of total)

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

exact: 5.0ms (0.7% of total)

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

Bogosity

explain688.0ms (10.3%)

Memory

2.9MiB live, 281.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
163	-	-	`(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	162	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	162
↳	`(*.f64 y y)`	overflow	75
↳	`(*.f64 x x)`	overflow	66
↳	`(*.f64 z z)`	overflow	77
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	125
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	162
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	1	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	1
↳	`(*.f64 y y)`	underflow	51
↳	`(*.f64 x x)`	underflow	58
↳	`(*.f64 z z)`	underflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	6
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	1

Confusion

	Predicted +	Predicted -
+	163	0
-	0	93

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	163	0	0
-	0	0	93

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	93
1	163

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

51.0ms

512×

valid

Compiler

Compiled 192 to 48 computations (75% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-add: 15.0ms (46.3% of total)

ival-mult: 10.0ms (30.8% of total)

ival-sqrt: 4.0ms (12.3% of total)

ival-div: 3.0ms (9.3% of total)

ival-true: 1.0ms (3.1% of total)

exact: 0.0ms (0% of total)

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

preprocess314.0ms (4.7%)

Memory

3.2MiB live, 51.1MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	129
1	76	129
2	155	129
3	321	129
4	583	129
5	941	129
6	1271	129
7	1286	129
0	11	14
0	18	14
1	22	14
2	29	14
3	31	14
0	31	12

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs z)

(abs y)

(abs x)

(sort x y z)

Compiler

Compiled 14 to 11 computations (21.4% saved)

eval0.0ms (0%)

Memory: 0.3MiB live, 0.3MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.0MiB live, 1.0MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.0%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify3.0ms (0.1%)

Memory

4.2MiB live, 4.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
cost-diff	0	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
cost-diff	128	(+.f64 (.f64 x x) (.f64 y y))
cost-diff	128	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
0	18	58
1	22	58
2	29	58
3	31	58
0	31	51

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize295.0ms (4.4%)

Memory

2.8MiB live, 41.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	0.1015625	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	37.71426106989376	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

288.0ms

256×

valid

Compiler

Compiled 118 to 24 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 279.0ms

ival-mult: 272.0ms (97.7% of total)

ival-div: 2.0ms (0.7% of total)

ival-add: 2.0ms (0.7% of total)

ival-sqrt: 2.0ms (0.7% of total)

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

exact: 0.0ms (0% of total)

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

series20.0ms (0.3%)

Memory

-4.0MiB live, 34.7MiB allocated

Counts

5 → 144

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	x	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	y	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	z	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	z	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	y	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))

simplify182.0ms (2.7%)

Memory

11.1MiB live, 285.9MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2478
1	673	2478
2	2273	2442
3	5705	2325
0	8205	2028

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

rewrite177.0ms (2.7%)

Memory

-7.8MiB live, 306.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
0	18	48
1	65	48
2	486	48
3	6616	48
0	8497	41

Stop Event

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

Counts

5 → 356

Calls

Call 1

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

Outputs
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eval62.0ms (0.9%)

Memory: 29.8MiB live, 144.7MiB allocated
Compiler: Compiled 14 663 to 1 644 computations (88.8% saved)

prune13.0ms (0.2%)

Memory

4.9MiB live, 43.0MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	493	7	500
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	494	7	501

Accuracy

99.6%

Counts

501 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.9%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
	41.0%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
▶	40.3%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
▶	97.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 270 to 198 computations (26.7% saved)

simplify6.0ms (0.1%)

Memory

-30.2MiB live, 9.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	231
0	44	222
1	60	222
2	75	222
3	78	222
0	78	213

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize64.0ms (1%)

Memory

14.6MiB live, 94.3MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 z z)
accuracy	0.1015625	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.4785272429954076	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	37.71426106989376	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
accuracy	0.16015625	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	37.71426106989376	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
accuracy	0	(*.f64 z z)
accuracy	0.1484375	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	0.48501289381499846	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	37.71426106989376	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.35546875	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	1.1883657379908845	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
accuracy	0	(hypot.f64 z y)
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.35546875	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))

Samples

50.0ms

256×

valid

Compiler

Compiled 422 to 52 computations (87.7% saved)

Precisions

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

ival-mult: 13.0ms (37.2% of total)

const: 9.0ms (25.8% of total)

ival-hypot: 4.0ms (11.5% of total)

ival-sqrt: 4.0ms (11.5% of total)

ival-add: 3.0ms (8.6% of total)

ival-div: 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)

series39.0ms (0.6%)

Memory

23.7MiB live, 61.3MiB allocated

Counts

18 → 468

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
4.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
3.0ms	z	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
2.0ms	z	@	-inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
2.0ms	y	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))

simplify188.0ms (2.8%)

Memory

-9.5MiB live, 213.7MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	394	10018
1	1212	10018
2	4138	9836
0	8342	8662

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 464

Calls

Call 1

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

Outputs
(*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))
(fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (.f64 (.f64 z z) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))))) (.f64 z z) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))))) (fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)
(fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y) #s(literal 1/2 binary64)) z) z (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(fma.f64 (fma.f64 (/.f64 (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) z) (pow.f64 y #s(literal 3 binary64))) #s(literal -1/8 binary64) (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y) #s(literal 1/2 binary64))) (.f64 z z) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 y #s(literal 5 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (.f64 (.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y) #s(literal 1/2 binary64)) z) z (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)))
y
(fma.f64 (/.f64 #s(literal 1/2 binary64) y) (*.f64 z z) y)
(fma.f64 (fma.f64 (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64))) (.f64 z z) (/.f64 #s(literal 1/2 binary64) y)) (.f64 z z) y)
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 z (/.f64 z (pow.f64 y #s(literal 5 binary64)))) #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) (pow.f64 y #s(literal 3 binary64)))) (fma.f64 (/.f64 #s(literal 1/2 binary64) y) (.f64 z z) y))
(*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))
(fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (.f64 (.f64 z z) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))))) (.f64 z z) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))))) (fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))
(fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (.f64 (.f64 z z) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))))) (.f64 z z) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))))) (fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))))
(.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(*.f64 z z)
(*.f64 z z)
(*.f64 z z)
(*.f64 z z)
(*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))
(fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (.f64 (.f64 z z) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))))) (.f64 z z) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))))) (fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))))
(.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64))
(*.f64 y y)
(fma.f64 z z (*.f64 y y))
(fma.f64 z z (*.f64 y y))
(fma.f64 z z (*.f64 y y))
(*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))
(fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (fma.f64 (.f64 (.f64 z z) (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))))) (.f64 z z) (*.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))))) (fma.f64 (.f64 (.f64 z z) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (hypot.f64 y x) (sqrt.f64 #s(literal 1/3 binary64)))))
(.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal 1/3 binary64))
(fma.f64 y y (*.f64 x x))
(fma.f64 z z (fma.f64 y y (*.f64 x x)))
(fma.f64 z z (fma.f64 y y (*.f64 x x)))
(fma.f64 z z (fma.f64 y y (*.f64 x x)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 y y (*.f64 x x))) z) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) (/.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) z) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 z #s(literal 4 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (.f64 y y)) (/.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) z) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(.f64 (fma.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 z #s(literal 4 binary64))) (fma.f64 (.f64 (pow.f64 y #s(literal 6 binary64)) #s(literal 1/16 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (.f64 #s(literal 1/2 binary64) (*.f64 y y)) (/.f64 (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) z) (sqrt.f64 #s(literal 1/3 binary64))))) z)
z
(fma.f64 (/.f64 z z) (.f64 (/.f64 (.f64 y y) z) #s(literal 1/2 binary64)) z)
(fma.f64 (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) z) y) (/.f64 y z) (/.f64 (.f64 (pow.f64 y #s(literal 4 binary64)) #s(literal -1/8 binary64)) (pow.f64 z #s(literal 4 binary64)))) z z)
(.f64 (fma.f64 (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))) #s(literal 1/16 binary64) (fma.f64 (/.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (fma.f64 (.f64 (/.f64 #s(literal 1/2 binary64) z) y) (/.f64 y z) #s(literal 1 binary64)))) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 y y (*.f64 x x))) z) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) (fma.f64 y y (*.f64 x x))) z) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64))) z)
(.f64 (fma.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1/8 binary64) (/.f64 (.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) #s(literal 1/2 binary64)) z)) (sqrt.f64 #s(literal 1/3 binary64)))) z)
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) (/.f64 #s(literal 1/3 binary64) z) #s(literal 1/3 binary64)) (*.f64 z z))
(.f64 (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) (/.f64 #s(literal 1/3 binary64) z) #s(literal 1/3 binary64)) (*.f64 z z))
(.f64 (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) z) (/.f64 #s(literal 1/3 binary64) z) #s(literal 1/3 binary64)) (*.f64 z z))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(*.f64 z z)
(*.f64 z z)
(*.f64 z z)
(*.f64 z z)
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(.f64 (fma.f64 (/.f64 y x) (/.f64 y x) (fma.f64 (/.f64 z x) (/.f64 z x) #s(literal 1 binary64))) (.f64 x x))
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rewrite184.0ms (2.8%)

Memory

4.1MiB live, 217.8MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Counts

18 → 284

Calls

Call 1

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

Outputs
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eval99.0ms (1.5%)

Memory: 10.9MiB live, 162.5MiB allocated
Compiler: Compiled 26 477 to 1 638 computations (93.8% saved)

prune27.0ms (0.4%)

Memory

-14.8MiB live, 60.1MiB allocated

Pruning

10 alts after pruning (5 fresh and 5 done)

	Pruned	Kept	Total
New	769	4	773
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	770	10	780

Accuracy

99.8%

Counts

780 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.2%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
▶	41.0%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
✓	40.3%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
▶	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	97.7%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	97.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 319 to 229 computations (28.2% saved)

simplify6.0ms (0.1%)

Memory

7.8MiB live, 7.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	294
0	53	277
1	72	269
2	87	267
3	89	267
0	89	256

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize93.0ms (1.4%)

Memory

2.6MiB live, 85.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.38671875	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.4785272429954076	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	37.67406234825523	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0	(*.f64 y y)
accuracy	0	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y)))
accuracy	0.1015625	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64))
accuracy	37.71426106989376	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
accuracy	0	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
accuracy	0.15234375	(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
accuracy	0.2890625	(.f64 (.f64 y y) #s(literal 1/3 binary64))
accuracy	37.71426106989376	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
accuracy	0.08984375	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.3515625	(*.f64 #s(literal 1/3 binary64) z)
accuracy	0.48501289381499846	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	37.71426106989376	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
accuracy	0.046875	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.265625	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
accuracy	1.1883657379908845	#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

54.0ms

256×

valid

Compiler

Compiled 515 to 63 computations (87.8% saved)

Precisions

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

ival-mult: 13.0ms (37.7% of total)

ival-sqrt: 5.0ms (14.5% of total)

ival-pow: 5.0ms (14.5% of total)

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

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

const: 3.0ms (8.7% of total)

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

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

exact: 0.0ms (0% of total)

series109.0ms (1.6%)

Memory

21.2MiB live, 129.8MiB allocated

Counts

22 → 528

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
46.0ms	z	@	0	((* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* z z) 1/3) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (+ (* z z) (* y y)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* (* y y) 1/3) (* y y) (sqrt 3))
14.0ms	z	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* z z) 1/3) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (+ (* z z) (* y y)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* (* y y) 1/3) (* y y) (sqrt 3))
9.0ms	z	@	-inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* z z) 1/3) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (+ (* z z) (* y y)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* (* y y) 1/3) (* y y) (sqrt 3))
6.0ms	x	@	-inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* z z) 1/3) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (+ (* z z) (* y y)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* (* y y) 1/3) (* y y) (sqrt 3))
3.0ms	y	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (+ (* (* z z) 1/3) (* (* y y) 1/3)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (+ (* z z) (* y y)) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* (* y y) 1/3) (* y y) (sqrt 3))

simplify248.0ms (3.7%)

Memory

-18.9MiB live, 204.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	474	10836
1	1508	10794
2	5380	10647
0	8185	9321

Stop Event

1×	iter limit
1×	node limit

Counts

528 → 525

Calls

Call 1

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

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

rewrite202.0ms (3%)

Memory

-22.7MiB live, 244.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	275
0	53	257
1	161	249
2	972	247
0	8200	236

Stop Event

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

Counts

22 → 286

Calls

Call 1

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

Outputs
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eval153.0ms (2.3%)

Memory: 14.7MiB live, 263.7MiB allocated
Compiler: Compiled 28 500 to 1 734 computations (93.9% saved)

prune21.0ms (0.3%)

Memory

-7.3MiB live, 69.2MiB allocated

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	856	2	858
Fresh	0	0	0
Picked	2	3	5
Done	1	4	5
Total	859	9	868

Accuracy

100.0%

Counts

868 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
✓	41.0%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
✓	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
✓	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	97.6%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	97.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 188 to 138 computations (26.6% saved)

simplify4.0ms (0.1%)

Memory

8.2MiB live, 8.2MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	71
0	23	71
1	27	71
2	33	71
3	34	71
0	34	65

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize40.0ms (0.6%)

Memory

7.0MiB live, 88.6MiB allocated

Localize:

Found 7 expressions of interest:

New	Metric	Score
accuracy	0	(hypot.f64 y z)
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z))
accuracy	0.38671875	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.37109375	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	1.1883657379908845	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Samples

32.0ms

256×

valid

Compiler

Compiled 136 to 35 computations (74.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 5.0ms (28.7% of total)

ival-hypot: 4.0ms (22.9% of total)

ival-div: 3.0ms (17.2% of total)

ival-sqrt: 3.0ms (17.2% of total)

ival-add: 2.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series42.0ms (0.6%)

Memory

-26.7MiB live, 11.9MiB allocated

Counts

6 → 144

Calls

Call 1

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

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

Calls

9 calls:

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

simplify390.0ms (5.9%)

Memory

4.5MiB live, 158.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	370	4172
1	1122	4088
2	4118	4077
3	7965	4077
0	8238	3548

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 137

Calls

Call 1

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

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

rewrite135.0ms (2%)

Memory

31.0MiB live, 113.0MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	64
0	23	63
1	87	63
2	635	63
0	8181	57

Stop Event

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

Counts

6 → 108

Calls

Call 1

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

Outputs
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eval38.0ms (0.6%)

Memory: -12.8MiB live, 60.1MiB allocated
Compiler: Compiled 9 017 to 791 computations (91.2% saved)

prune12.0ms (0.2%)

Memory

-4.2MiB live, 32.9MiB allocated

Pruning

10 alts after pruning (1 fresh and 9 done)

	Pruned	Kept	Total
New	260	1	261
Fresh	0	0	0
Picked	0	2	2
Done	0	7	7
Total	260	10	270

Accuracy

100.0%

Counts

270 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 y z)) (sqrt.f64 #s(literal 3 binary64)))
✓	41.0%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (fma.f64 z z (*.f64 y y))) #s(literal 3 binary64)))
✓	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))))
✓	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	41.0%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	40.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
✓	97.6%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	96.9%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) (neg.f64 z)))
✓	99.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	97.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 510 to 229 computations (55.1% saved)

regimes108.0ms (1.6%)

Memory

-9.2MiB live, 86.2MiB allocated

Counts

15 → 1

Calls

Call 1

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

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

Calls

10 calls:

44.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
16.0ms	(+.f64 (.f64 x x) (.f64 y y))
15.0ms	y
5.0ms	x
5.0ms	z

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes52.0ms (0.8%)

Memory

1.2MiB live, 72.8MiB allocated

Accuracy

Total -37.0b remaining (-2419.7%)

Threshold costs -37b (-2419.7%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

10 calls:

12.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
7.0ms	x
4.0ms	z
4.0ms	y
4.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
97.6%	1	`x`
97.6%	1	`y`
97.6%	1	`z`
97.6%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.6%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.6%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.6%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.6%	1	`(*.f64 x x)`
97.6%	1	`(*.f64 y y)`
97.6%	1	`(*.f64 z z)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify28.0ms (0.4%)

Memory

5.3MiB live, 49.8MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	40
1	20	40

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

Outputs

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

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

soundness177.0ms (2.7%)

Memory

5.1MiB live, 156.7MiB allocated

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2478
1	673	2478
2	2273	2442
3	5705	2325
0	8205	2028

Stop Event

1×	fuel
1×	iter limit
1×	node limit

Compiler

Compiled 50 to 31 computations (38% saved)

preprocess230.0ms (3.5%)

Memory: 8.8MiB live, 169.3MiB allocated
Compiler: Compiled 508 to 360 computations (29.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample2.2s (33.1%)

explain688.0ms (10.3%)

preprocess314.0ms (4.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify3.0ms (0.1%)

localize295.0ms (4.4%)

series20.0ms (0.3%)

simplify182.0ms (2.7%)

rewrite177.0ms (2.7%)

eval62.0ms (0.9%)

prune13.0ms (0.2%)

simplify6.0ms (0.1%)

localize64.0ms (1%)

series39.0ms (0.6%)

simplify188.0ms (2.8%)

rewrite184.0ms (2.8%)

eval99.0ms (1.5%)

prune27.0ms (0.4%)

simplify6.0ms (0.1%)

localize93.0ms (1.4%)

series109.0ms (1.6%)

simplify248.0ms (3.7%)

rewrite202.0ms (3%)

eval153.0ms (2.3%)

prune21.0ms (0.3%)

simplify4.0ms (0.1%)

localize40.0ms (0.6%)

series42.0ms (0.6%)

simplify390.0ms (5.9%)

rewrite135.0ms (2%)

eval38.0ms (0.6%)

prune12.0ms (0.2%)

regimes108.0ms (1.6%)

regimes52.0ms (0.8%)

simplify28.0ms (0.4%)

soundness177.0ms (2.7%)

preprocess230.0ms (3.5%)

end0.0ms (0%)

Profiling