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

start0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze1.0ms (0%)

Memory

0.5MiB live, 0.5MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.3s (17.7%)

Memory

51.8MiB live, 1 343.6MiB allocated

Samples

905.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 481.0ms

ival-mult: 222.0ms (46.1% of total)

ival-add: 116.0ms (24.1% of total)

ival-sqrt: 77.0ms (16% of total)

ival-div: 51.0ms (10.6% of total)

ival-true: 7.0ms (1.5% of total)

exact: 5.0ms (1% of total)

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

Bogosity

explain632.0ms (8.4%)

Memory

-39.8MiB live, 213.4MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
148	-	1	(-1.1135192249359759e-155 2.7693892538491165e-158 4.961350135490226e-306)	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
1	-	0	-	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
0	-	0	-	`#s(literal 3 binary64)`
0	-	0	-	`z`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`(*.f64 z z)`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	143	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	144
↳	`(*.f64 y y)`	overflow	66
↳	`(*.f64 x x)`	overflow	66
↳	`(*.f64 z z)`	overflow	68
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	109
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	143
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	4	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	4
↳	`(*.f64 y y)`	underflow	66
↳	`(*.f64 x x)`	underflow	68
↳	`(*.f64 z z)`	underflow	60
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	23
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	4
`/.f64`	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	o/n	1	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	144
↳	`(*.f64 y y)`	overflow	66
↳	`(*.f64 x x)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	109
↳	`(*.f64 z z)`	overflow	68

Confusion

	Predicted +	Predicted -
+	148	1
-	0	107

Precision

1.0

Recall

0.9932885906040269

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	148	0	1
-	0	0	107

Precision?

1.0

Recall?

0.9932885906040269

Freqs

test

number	freq
0	108
1	148

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

233.0ms

512×

valid

Compiler

Compiled 134 to 37 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

ival-mult: 10.0ms (46.9% of total)

ival-add: 4.0ms (18.8% of total)

ival-div: 3.0ms (14.1% of total)

ival-sqrt: 3.0ms (14.1% of total)

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

exact: 0.0ms (0% of total)

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

preprocess206.0ms (2.7%)

Memory

4.3MiB live, 53.1MiB allocated

Algorithm

1×	egg-herbie

Rules

224×	`div-sub`
222×	`cancel-sign-sub`
216×	`sub-neg`
132×	`associate-/l*`
132×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

Outputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(sqrt.f64 (/.f64 (fma.f64 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: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune1.0ms (0%)

Memory

1.4MiB live, 1.4MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.2%	(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)

simplify4.0ms (0.1%)

Memory

4.0MiB live, 4.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

24×	`lower-+.f32`
20×	`lower-+.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize195.0ms (2.6%)

Memory

-8.7MiB live, 30.5MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 y y)
accuracy	0	(*.f64 x x)
accuracy	0.3196693304114102	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	34.133266272395076	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

188.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

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

ival-mult: 4.0ms (40% of total)

ival-div: 2.0ms (20% of total)

ival-add: 2.0ms (20% of total)

ival-sqrt: 2.0ms (20% of total)

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

exact: 0.0ms (0% of total)

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

series18.0ms (0.2%)

Memory

1.1MiB live, 39.9MiB allocated

Counts

6 → 156

Calls

Call 1

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

Outputs
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (+ (pow y 2) (pow z 2))) (taylor 0 z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* -1/8 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (pow z 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/16 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5)))))))))) (taylor 0 z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (+ (pow x 2) (pow y 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2))) (taylor 0 z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow z 2) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* z (sqrt 1/3)) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 3)) (pow z 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))) (taylor inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow z 2)) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))) (taylor inf z) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow z 2) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2))))) (taylor -inf z) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (sqrt 1/3))) (taylor -inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))) (taylor -inf z) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
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#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (+ (pow x 2) (pow y 2)) (taylor 0 x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5)))))))))) (taylor 0 x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (+ (pow y 2) (pow z 2))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2))) (taylor 0 x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor 0 x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* x (sqrt 1/3)) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))) (taylor inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2))))) (taylor -inf x) (#s(alt (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (patch (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2)))) (taylor -inf x) (#s(alt (+.f64 (.f64 x x) (.f64 y y)) (patch (+.f64 (.f64 x x) (.f64 y y)) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (sqrt 1/3))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))))) (taylor -inf x) (#s(alt (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) (patch (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64))) #<representation binary64>) () ())) ())
#s(alt (* 1/3 (pow x 2)) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))) (taylor -inf x) (#s(alt (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) (patch (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) #s(literal 3 binary64)) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (patch (.f64 x x) #<representation binary64>) () ())) ())
#s(alt (pow x 2) (taylor -inf x) (#s(alt (.f64 x x) (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) (* y y))
2.0ms	y	@	0	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
2.0ms	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) (* y y))
2.0ms	y	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))
2.0ms	z	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (+ (* x x) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x) (* y y))

simplify303.0ms (4%)

Memory

3.4MiB live, 279.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 366×	`lower-fma.f64`
13 366×	`lower-fma.f32`
5 460×	`lower-*.f64`
5 460×	`lower-*.f32`
3 804×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2514
1	673	2514
2	2273	2478
3	5705	2361
0	8205	2064

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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

rewrite197.0ms (2.6%)

Memory

-0.7MiB live, 239.6MiB allocated

Rules

4 524×	`lower-fma.f64`
4 524×	`lower-fma.f32`
4 260×	`lower-*.f32`
4 254×	`lower-*.f64`
3 048×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	51
0	18	51
1	65	51
2	486	51
3	6616	51
0	8497	44

Stop Event

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

Counts

6 → 362

Calls

Call 1

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

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 (.f64 z z) (fma.f64 z z (fma.f64 y y (.f64 x x))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))))
(.f64 (/.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 4 binary64)) (pow.f64 (fma.f64 (.f64 z (fma.f64 y y (.f64 x x))) (neg.f64 z) (pow.f64 z #s(literal 4 binary64))) #s(literal 2 binary64)))) (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (.f64 z (fma.f64 y y (.f64 x x))) (neg.f64 z) (pow.f64 z #s(literal 4 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (fma.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)))) (fma.f64 (fma.f64 (.f64 z (fma.f64 y y (.f64 x x))) (neg.f64 z) (pow.f64 z #s(literal 4 binary64))) (-.f64 (fma.f64 (.f64 z (fma.f64 y y (.f64 x x))) (neg.f64 z) (pow.f64 z #s(literal 4 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64)))) (fma.f64 z z (fma.f64 y y (.f64 x x))))
(.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 z z) (fma.f64 y y (.f64 x x)))))
(.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) (fma.f64 z z (.f64 y y)))))
(.f64 (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64)) (-.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))))
(.f64 (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)) (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))))
(.f64 (+.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (/.f64 #s(literal 1 binary64) (fma.f64 (fma.f64 z z (.f64 y y)) (-.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))))
(.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (/.f64 #s(literal 1 binary64) (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))))))
(.f64 #s(literal -1 binary64) (neg.f64 (fma.f64 z z (fma.f64 y y (.f64 x x)))))
(.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64)))
(.f64 #s(literal 1 binary64) (fma.f64 z z (fma.f64 y y (.f64 x x))))
(.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) (.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) (/.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64)))))
(.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal -1 binary64))))
(.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) (/.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))))
(pow.f64 (pow.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal -1 binary64)) #s(literal -1 binary64))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64))) (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal -1 binary64))) (+.f64 (fma.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))) (-.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64))))
(/.f64 (.f64 (+.f64 (pow.f64 z #s(literal 18 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 9 binary64))) (pow.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))) (fma.f64 (pow.f64 z #s(literal 6 binary64)) (-.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64))))
(/.f64 (.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 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))
(/.f64 (.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) #s(literal 1 binary64)) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))) (.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))))) (+.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))))
(/.f64 (-.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (pow.f64 y #s(literal 4 binary64))) (-.f64 (fma.f64 z z (.f64 x x)) (*.f64 y y)))
(/.f64 (-.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (pow.f64 x #s(literal 4 binary64))) (-.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)))
(/.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))) (-.f64 (.f64 y y) (fma.f64 z z (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (fma.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))))))
(/.f64 (+.f64 (pow.f64 (fma.f64 z z (.f64 x x)) #s(literal 3 binary64)) (pow.f64 y #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)) (-.f64 (pow.f64 y #s(literal 4 binary64)) (.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)))))
(/.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (fma.f64 z z (.f64 x x)) #s(literal 3 binary64))) (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (.f64 (.f64 y y) (fma.f64 z z (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 z z) (fma.f64 y y (*.f64 x x)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)))) (neg.f64 (-.f64 (.f64 x x) (fma.f64 z z (*.f64 y y)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64)))) (neg.f64 (fma.f64 (fma.f64 z z (.f64 y y)) (-.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))))) (neg.f64 (neg.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))))) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))))) (neg.f64 (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) (pow.f64 z #s(literal 4 binary64))))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (fma.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 4 binary64))) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))))
(/.f64 (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64)))))
(/.f64 (.f64 (+.f64 (pow.f64 z #s(literal 18 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 9 binary64))) #s(literal 1 binary64)) (.f64 (fma.f64 (pow.f64 z #s(literal 6 binary64)) (-.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64))) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) (pow.f64 z #s(literal 4 binary64)))))
(/.f64 (-.f64 (.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64)))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 4 binary64)) (pow.f64 z #s(literal 8 binary64))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (+.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (+.f64 (fma.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 8 binary64))) (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)) (pow.f64 z #s(literal 12 binary64))) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) (-.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 3 binary64)) (pow.f64 z #s(literal 6 binary64)))))
(/.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64))) (-.f64 (.f64 z z) (fma.f64 y y (*.f64 x x))))
(/.f64 (-.f64 (pow.f64 x #s(literal 4 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64))) (-.f64 (.f64 x x) (fma.f64 z z (*.f64 y y))))
(/.f64 (+.f64 (pow.f64 z #s(literal 18 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 9 binary64))) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) (fma.f64 (pow.f64 z #s(literal 6 binary64)) (-.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 6 binary64)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 2 binary64)) (-.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 3 binary64)) (pow.f64 x #s(literal 6 binary64))) (fma.f64 (fma.f64 z z (.f64 y y)) (-.f64 (fma.f64 z z (.f64 y y)) (.f64 x x)) (pow.f64 x #s(literal 4 binary64))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64)))) (neg.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))))
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(/.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 #s(literal -3 binary64) (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64)))))
(/.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (.f64 #s(literal 3 binary64) (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64)))) (neg.f64 (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal 3 binary64))))
(/.f64 #s(literal -1 binary64) (/.f64 #s(literal -3 binary64) (fma.f64 z z (fma.f64 y y (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (.f64 #s(literal -3 binary64) (neg.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)))))
(/.f64 (-.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal 3 binary64)))
(/.f64 #s(literal 1/3 binary64) (pow.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal -1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (.f64 (-.f64 (pow.f64 (fma.f64 y y (*.f64 x x)) #s(literal 2 binary64)) (pow.f64 z #s(literal 4 binary64))) #s(literal 1/3 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) (.f64 #s(literal 1/3 binary64) (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 3 binary64) (fma.f64 z z (fma.f64 y y (*.f64 x x)))))
(/.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (.f64 #s(literal -3 binary64) (neg.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 3 binary64))) (.f64 (fma.f64 (fma.f64 y y (.f64 x x)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) (pow.f64 z #s(literal 4 binary64))) #s(literal 3 binary64)))
(/.f64 (neg.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))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 #s(literal 3 binary64) (fma.f64 z z (fma.f64 y y (*.f64 x x))))))
(neg.f64 (.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))) #s(literal -1/3 binary64))))
(neg.f64 (.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal -1/3 binary64)))
(fma.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64) (.f64 (*.f64 x x) #s(literal 1/3 binary64)))
(fma.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 x x)) (.f64 #s(literal 1/3 binary64) (*.f64 y y)))
(fma.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)) (.f64 #s(literal 1/3 binary64) (*.f64 x x)))
(fma.f64 #s(literal 1/3 binary64) (.f64 z z) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (*.f64 x x))))
(fma.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 x x)) (.f64 #s(literal 1/3 binary64) (*.f64 z z)))
(fma.f64 #s(literal 1/3 binary64) (.f64 y y) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (*.f64 x x))))
(fma.f64 #s(literal 1/3 binary64) (.f64 x x) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (*.f64 y y))))
(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (fma.f64 y y (*.f64 x x)) #s(literal 1/3 binary64)))
(fma.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64) (.f64 (*.f64 z z) #s(literal 1/3 binary64)))
(fma.f64 (.f64 y y) #s(literal 1/3 binary64) (.f64 (fma.f64 z z (*.f64 x x)) #s(literal 1/3 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/3 binary64) (.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/3 binary64)))
(-.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x)) #s(literal 3 binary64))) (/.f64 (pow.f64 z #s(literal 4 binary64)) (.f64 (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x)) #s(literal 3 binary64))))
(-.f64 (/.f64 (/.f64 (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 2 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (.f64 x x))) #s(literal 3 binary64)) (/.f64 (/.f64 (pow.f64 z #s(literal 4 binary64)) (fma.f64 (+.f64 y z) (-.f64 y z) (*.f64 x x))) #s(literal 3 binary64)))
(-.f64 #s(literal 0 binary64) (.f64 (fma.f64 z z (fma.f64 y y (.f64 x x))) #s(literal -1/3 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 #s(literal 3 binary64) (fma.f64 z z (fma.f64 y y (.f64 x x))))) #s(literal -1 binary64)))
(+.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)) (.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64)))
(+.f64 (.f64 (fma.f64 y y (.f64 x x)) #s(literal 1/3 binary64)) (.f64 (.f64 z z) #s(literal 1/3 binary64)))
(+.f64 (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64)) (.f64 (.f64 y y) #s(literal 1/3 binary64)))
(+.f64 (.f64 (.f64 y y) #s(literal 1/3 binary64)) (.f64 (fma.f64 z z (.f64 x x)) #s(literal 1/3 binary64)))
(+.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)) (.f64 (.f64 x x) #s(literal 1/3 binary64)))
(+.f64 (.f64 (.f64 x x) #s(literal 1/3 binary64)) (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 x x))) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 x x))) (.f64 #s(literal 1/3 binary64) (.f64 y y)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 x x))))
(+.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))) (.f64 #s(literal 1/3 binary64) (.f64 x x)))
(+.f64 (.f64 #s(literal 1/3 binary64) (.f64 x x)) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(*.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 y)))
(*.f64 y y)
(pow.f64 (exp.f64 (log.f64 y)) #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 y #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 y) #s(literal 2 binary64)))

eval64.0ms (0.9%)

Memory: 29.2MiB live, 146.8MiB allocated
Compiler: Compiled 13 365 to 1 667 computations (87.5% saved)

prune16.0ms (0.2%)

Memory

-41.6MiB live, 46.6MiB allocated

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	511	7	518
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	512	7	519

Accuracy

99.7%

Counts

519 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.1%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
	46.2%	(.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64)))
▶	45.9%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	46.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
▶	45.9%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
▶	98.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 124 to 120 computations (3.2% saved)

simplify6.0ms (0.1%)

Memory

12.1MiB live, 12.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize62.0ms (0.8%)

Memory

-3.6MiB live, 108.2MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 z z)
accuracy	0.21232960997120676	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	0.3196693304114102	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	34.133266272395076	(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	0.3274818304114102	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
accuracy	34.133266272395076	(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	0.2077595903394903	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	0.3313880804114102	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	34.133266272395076	(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	0.5725435686485784	#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	0.3515625	(*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64)))

Samples

45.0ms

256×

valid

Compiler

Compiled 191 to 21 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-mult: 15.0ms (48.2% of total)

ival-add: 4.0ms (12.9% of total)

ival-hypot: 4.0ms (12.9% of total)

ival-sqrt: 3.0ms (9.6% of total)

const: 3.0ms (9.6% of total)

ival-div: 2.0ms (6.4% of total)

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

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

exact: 0.0ms (0% of total)

series38.0ms (0.5%)

Memory

27.3MiB live, 67.4MiB allocated

Counts

18 → 468

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
2.0ms	z	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
2.0ms	z	@	-inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
2.0ms	y	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (* z z)) (* z z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* 1/3 (+ (* z z) (* y y))) (+ (* z z) (* y y)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (+ (+ (* x x) (* y y)) (* z z)) (* y y))
1.0ms	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))

simplify209.0ms (2.8%)

Memory

-22.6MiB live, 337.9MiB allocated

Algorithm

1×	egg-herbie

Rules

12 468×	`lower-fma.f64`
12 468×	`lower-fma.f32`
6 866×	`lower-*.f64`
6 866×	`lower-*.f32`
3 486×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 464

Calls

Call 1

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

rewrite528.0ms (7%)

Memory

0.6MiB live, 231.8MiB allocated

Rules

5 812×	`lower-fma.f32`
5 810×	`lower-fma.f64`
5 806×	`lower-*.f32`
5 794×	`lower-*.f64`
4 192×	`lower-/.f32`

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

eval410.0ms (5.5%)

Memory: 13.1MiB live, 169.5MiB allocated
Compiler: Compiled 15 233 to 1 622 computations (89.4% saved)

prune72.0ms (1%)

Memory

18.4MiB live, 106.5MiB allocated

Pruning

11 alts after pruning (6 fresh and 5 done)

	Pruned	Kept	Total
New	768	5	773
Fresh	1	1	2
Picked	0	5	5
Done	0	0	0
Total	769	11	780

Accuracy

99.8%

Counts

780 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.1%	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
▶	45.8%	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
✓	45.9%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	46.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	46.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	45.9%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
	98.6%	#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)))
✓	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
▶	46.2%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 158 to 152 computations (3.8% saved)

simplify30.0ms (0.4%)

Memory

-28.3MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	251
0	60	247
1	75	231
2	87	227
3	87	227
0	87	227

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize88.0ms (1.2%)

Memory

17.1MiB live, 134.9MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.40234375	(/.f64 (sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x)))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	34.28535788431696	(sqrt.f64 (fma.f64 z z (fma.f64 y y (*.f64 x x))))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.21232960997120676	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	0.40234375	(/.f64 (sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	34.28535788431696	(sqrt.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)))
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.3515625	(.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	34.28535788431696	(sqrt.f64 (fma.f64 z z (*.f64 y y)))
accuracy	0.12890625	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.2077595903394903	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	0.29296875	(*.f64 #s(literal 1/3 binary64) z)
accuracy	34.133266272395076	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0	(hypot.f64 z y)
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))))
accuracy	0.078125	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y))
accuracy	0.26171875	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (hypot.f64 z y)))

Samples

68.0ms

256×

valid

Compiler

Compiled 243 to 31 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-mult: 11.0ms (21.6% of total)

ival-div: 10.0ms (19.7% of total)

ival-add: 9.0ms (17.7% of total)

ival-sqrt: 7.0ms (13.8% of total)

ival-pow: 5.0ms (9.8% of total)

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

const: 4.0ms (7.9% of total)

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

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

exact: 0.0ms (0% of total)

series50.0ms (0.7%)

Memory

6.1MiB live, 124.2MiB allocated

Counts

25 → 588

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	z	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (+ (* z z) (* y y)) (* y y) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (sqrt (+ (* z z) (* y y))) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt 3) (* x x))
5.0ms	z	@	0	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (+ (* z z) (* y y)) (* y y) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (sqrt (+ (* z z) (* y y))) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt 3) (* x x))
3.0ms	y	@	inf	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (+ (* z z) (* y y)) (* y y) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (sqrt (+ (* z z) (* y y))) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt 3) (* x x))
2.0ms	x	@	0	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (+ (* z z) (* y y)) (* y y) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (sqrt (+ (* z z) (* y y))) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt 3) (* x x))
2.0ms	y	@	0	((* (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y))))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (pow 1/3 1/4) (* (pow 1/3 1/4) (sqrt (+ (* z z) (* y y)))) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* (* 1/3 z) z) (* 1/3 z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (+ (* z z) (* y y)) (* y y) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (+ (+ (* x x) (* y y)) (* z z)) (* z z) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (sqrt (+ (* z z) (* y y))) (sqrt (+ (* z z) (* y y))) (sqrt 1/3) (sqrt 3) (* x x))

simplify240.0ms (3.2%)

Memory

-9.8MiB live, 426.8MiB allocated

Algorithm

1×	egg-herbie

Rules

14 598×	`lower-fma.f64`
14 598×	`lower-fma.f32`
8 934×	`lower-*.f64`
8 934×	`lower-*.f32`
5 132×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	787	13330
1	2552	13234
0	8389	11697

Stop Event

1×	iter limit
1×	node limit

Counts

588 → 574

Calls

Call 1

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

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

rewrite156.0ms (2.1%)

Memory

1.0MiB live, 314.4MiB allocated

Rules

4 622×	`lower-fma.f32`
4 616×	`lower-fma.f64`
4 394×	`lower-/.f32`
4 390×	`lower-/.f64`
3 762×	`lower-*.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	234
0	60	228
1	178	208
2	1084	208
0	8202	208

Stop Event

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

Counts

25 → 544

Calls

Call 1

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

Outputs
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64))) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(.f64 (pow.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (*.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 y z))
(*.f64 (hypot.f64 y z) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(pow.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/3 binary64))) (sqrt.f64 (.f64 (+.f64 z y) (-.f64 z y))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))))
(sqrt.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 (fma.f64 z z (*.f64 y y))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64) (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (.f64 (log.f64 (.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/3 binary64))) #s(literal 1/2 binary64)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 y z)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 1/3 binary64)))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64))) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (hypot.f64 y z)))
(*.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (hypot.f64 y z))
(exp.f64 (fma.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64))))
(.f64 (pow.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)) #s(literal 1/4 binary64)) (pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)) #s(literal 1/4 binary64)))
(pow.f64 (exp.f64 (log.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)))) #s(literal 1/2 binary64))
(pow.f64 (.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)) #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)) #s(literal 1/2 binary64))
(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z)))
(exp.f64 (.f64 (log.f64 #s(approx (/ (+ (+ ( x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z))) #s(literal 1/2 binary64)))
#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 z #s(literal 1/3 binary64)) z))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 (.f64 z #s(literal 1/3 binary64)) z)
(.f64 z (.f64 z #s(literal 1/3 binary64)))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(*.f64 z #s(literal 1/3 binary64))
(*.f64 #s(literal 1/3 binary64) z)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 y z)))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64))) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64))))
(.f64 (.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(.f64 (pow.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (*.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (*.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 y z))
(*.f64 (hypot.f64 y z) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (.f64 (hypot.f64 y z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))))
(pow.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(/.f64 (sqrt.f64 (.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))) #s(literal 1/3 binary64))) (sqrt.f64 (.f64 (+.f64 z y) (-.f64 z y))))
(/.f64 (sqrt.f64 (.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))) #s(literal 1/3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))))
(sqrt.f64 (.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/3 binary64)))
(exp.f64 (+.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))) (.f64 (log.f64 (fma.f64 z z (*.f64 y y))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64) (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))))
(exp.f64 (fma.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64) (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
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(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 z y) (-.f64 z y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 z z (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y z) (-.f64 y z))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 z y)) (-.f64 z y))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))) (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y)))))
(sqrt.f64 (fma.f64 z z (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 z)))
(hypot.f64 (exp.f64 (log.f64 y)) z)
(hypot.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 z)) y)
(hypot.f64 y (exp.f64 (log.f64 z)))
(hypot.f64 y z)
(hypot.f64 z (exp.f64 (log.f64 y)))
(hypot.f64 z y)
(exp.f64 (.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 z y) (-.f64 z y)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 z y) (-.f64 z y)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 z y) (-.f64 z y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 z z (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 y z) (-.f64 y z))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (*.f64 (neg.f64 (+.f64 z y)) (-.f64 z y))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 z #s(literal 6 binary64)) (pow.f64 y #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (+.f64 (pow.f64 y #s(literal 4 binary64)) (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))))))
(/.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))) (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64)))) (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (*.f64 y y)))))
(sqrt.f64 (fma.f64 z z (*.f64 y y)))
(hypot.f64 (exp.f64 (log.f64 y)) (exp.f64 (log.f64 z)))
(hypot.f64 (exp.f64 (log.f64 y)) z)
(hypot.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 y)))
(hypot.f64 (exp.f64 (log.f64 z)) y)
(hypot.f64 y (exp.f64 (log.f64 z)))
(hypot.f64 y z)
(hypot.f64 z (exp.f64 (log.f64 y)))
(hypot.f64 z y)
(exp.f64 (.f64 (log.f64 (fma.f64 z z (.f64 y y))) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)) (pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/27 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(pow.f64 #s(literal 1/81 binary64) #s(literal 1/8 binary64))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 4 binary64))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/2 binary64))
(sqrt.f64 #s(literal 1/3 binary64))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))) #s(literal 2 binary64)))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(*.f64 #s(literal -1 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(*.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 #s(literal 3 binary64))) #s(literal 1/2 binary64))
(pow.f64 #s(literal 9 binary64) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 3 binary64) #s(literal 1/2 binary64))
(/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))) #s(literal -1 binary64))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(neg.f64 (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(literal 3 binary64))
(-.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(exp.f64 (*.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))
(*.f64 x x)
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 x #s(literal 2 binary64))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))

eval175.0ms (2.3%)

Memory: 26.9MiB live, 381.5MiB allocated
Compiler: Compiled 26 814 to 3 221 computations (88% saved)

prune27.0ms (0.4%)

Memory

9.0MiB live, 87.2MiB allocated

Pruning

11 alts after pruning (5 fresh and 6 done)

	Pruned	Kept	Total
New	1 140	4	1 144
Fresh	0	1	1
Picked	3	2	5
Done	1	4	5
Total	1 144	11	1 155

Accuracy

100.0%

Counts

1 155 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.1%	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
▶	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
✓	46.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	46.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	45.9%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	98.5%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
▶	98.6%	#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)))
✓	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	46.2%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
▶	99.1%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 147 to 144 computations (2% saved)

simplify142.0ms (1.9%)

Memory

-10.0MiB live, 150.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
cost-diff	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
cost-diff	12608	(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
cost-diff	0	#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z))
cost-diff	0	(.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64)))
cost-diff	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64))))
cost-diff	1024	(fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)
cost-diff	0	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
cost-diff	0	(fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
cost-diff	0	(sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y))))
cost-diff	0	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
cost-diff	0	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
cost-diff	0	(hypot.f64 z y)
cost-diff	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
cost-diff	0	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))

Rules

5 928×	`lower-fma.f32`
5 924×	`lower-fma.f64`
3 766×	`lower-*.f32`
3 754×	`lower-*.f64`
2 936×	`associate-/l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	281
0	61	281
1	83	273
2	127	271
3	201	271
4	302	259
5	389	259
6	685	259
7	2083	259
8	2810	259
9	2870	259
10	2896	259
11	2899	259
12	2899	259
13	3596	259
14	3618	259
15	3620	259
16	3620	259
17	3620	259
18	5434	259
19	5665	259
20	6081	259
21	6410	259
22	6872	259
0	8054	241

Stop Event

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

Calls

Call 1

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

Outputs
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(hypot.f64 z y)
z
y
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
#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 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y))))
(fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))
z
#s(approx (+ (* y y) (* x x)) (*.f64 y y))
(*.f64 y y)
y
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (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)) #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z))))
(.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z)))
#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z))
#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z))
(fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)
(fma.f64 (/.f64 #s(literal 1/2 binary64) z) (*.f64 y y) z)
(*.f64 z #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) z)
z
#s(literal 1/2 binary64)
(*.f64 (/.f64 y z) (/.f64 y z))
(*.f64 (/.f64 (/.f64 y z) z) y)
(/.f64 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 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
#s(literal 1/3 binary64)
#s(literal 1/4 binary64)
(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
z

localize184.0ms (2.5%)

Memory

-18.0MiB live, 234.6MiB allocated

Localize:

Found 19 expressions of interest:

New	Metric	Score
accuracy	0	(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
accuracy	0.0703125	(*.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)
accuracy	0.265625	(.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	0.5725435686485784	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) (.f64 (pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64)) z)))
accuracy	0	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64))))
accuracy	0.21545787887375717	#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z))
accuracy	0.27962875976844204	(*.f64 (/.f64 y z) (/.f64 y z))
accuracy	0.3515625	(.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.40234375	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.6631011458985527	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
accuracy	34.28535788431696	(sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y))))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.40234375	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	0.5725435686485784	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
accuracy	0	(hypot.f64 z y)
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0	#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
accuracy	0.40234375	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))

Samples

125.0ms

256×

valid

Compiler

Compiled 217 to 35 computations (83.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

ival-div: 22.0ms (35.5% of total)

ival-mult: 13.0ms (21% of total)

ival-sqrt: 8.0ms (12.9% of total)

ival-pow: 6.0ms (9.7% of total)

ival-add: 5.0ms (8.1% of total)

ival-hypot: 4.0ms (6.5% of total)

const: 4.0ms (6.5% of total)

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

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

exact: 0.0ms (0% of total)

series117.0ms (1.6%)

Memory

-0.0MiB live, 194.3MiB allocated

Counts

19 → 468

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
63.0ms	z	@	0	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* z z) (* y y))) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (+ (* (* z 1/2) (* (/ y z) (/ y z))) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (* (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) (* (/ y z) (/ y z)))
13.0ms	z	@	-inf	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* z z) (* y y))) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (+ (* (* z 1/2) (* (/ y z) (/ y z))) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (* (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) (* (/ y z) (/ y z)))
10.0ms	z	@	inf	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* z z) (* y y))) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (+ (* (* z 1/2) (* (/ y z) (/ y z))) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (* (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) (* (/ y z) (/ y z)))
2.0ms	y	@	inf	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* z z) (* y y))) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (+ (* (* z 1/2) (* (/ y z) (/ y z))) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (* (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) (* (/ y z) (/ y z)))
2.0ms	y	@	0	((/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt (+ (* z z) (* y y))) (sqrt 3) (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/ z (sqrt 3)) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (+ (* (* z 1/2) (* (/ y z) (/ y z))) z) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt (+ (* z z) (* y y))) (sqrt 1/3)) (sqrt (+ (* z z) (* y y))) (* (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) (* (/ y z) (/ y z)))

simplify227.0ms (3%)

Memory

18.6MiB live, 293.7MiB allocated

Algorithm

1×	egg-herbie

Rules

14 696×	`lower-fma.f64`
14 696×	`lower-fma.f32`
8 400×	`lower-*.f64`
8 400×	`lower-*.f32`
3 988×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	614	11295
1	1940	11169
2	6846	11169
0	8113	9814

Stop Event

1×	iter limit
1×	node limit

Counts

468 → 451

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

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

rewrite192.0ms (2.6%)

Memory

-9.7MiB live, 302.2MiB allocated

Rules

4 460×	`lower-/.f32`
4 452×	`lower-/.f64`
4 276×	`lower-fma.f32`
4 272×	`lower-fma.f64`
3 856×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	251
0	61	239
1	203	229
2	1386	229
0	8250	215

Stop Event

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

Counts

19 → 341

Calls

Call 1

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

Outputs
(.f64 (/.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y))))))
(.f64 #s(literal -1 binary64) (/.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) #s(literal -1 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)) #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)))
(.f64 #s(literal 1 binary64) (/.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (neg.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y))) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) (pow.f64 #s(literal 3 binary64) #s(literal -1/2 binary64)))
(pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))) #s(literal -1 binary64))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))))
(/.f64 (neg.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))) (neg.f64 (sqrt.f64 #s(literal 3 binary64))))
(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
(neg.f64 (/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))) (/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
(-.f64 #s(literal 0 binary64) (/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (neg.f64 (sqrt.f64 #s(literal 3 binary64)))))
(exp.f64 (.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)))) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (neg.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y))))
(.f64 #s(approx (sqrt (+ (+ ( x x) (* y y)) (* z z))) (hypot.f64 z y)) #s(literal 1 binary64))
#s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))
(neg.f64 (neg.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))))
(-.f64 #s(literal 0 binary64) (neg.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y))))
(.f64 (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 (+.f64 z y) (-.f64 z y)))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (pow.f64 (.f64 (+.f64 z y) (-.f64 z y)) #s(literal -1 binary64))))
(.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (pow.f64 (pow.f64 (.f64 (+.f64 z y) (-.f64 z y)) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (sqrt.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64))))
(.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64))) (pow.f64 (pow.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))) #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(pow.f64 (exp.f64 (log.f64 (fma.f64 z z (*.f64 y y)))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 2 binary64)) #s(literal 1/4 binary64))
(pow.f64 (fma.f64 z z (*.f64 y y)) #s(literal 1/2 binary64))
(/.f64 (neg.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (neg.f64 (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y)))))
(/.f64 (neg.f64 (hypot.f64 (pow.f64 y #s(literal 3 binary64)) (pow.f64 z #s(literal 3 binary64)))) (neg.f64 (sqrt.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 z #s(literal 4 binary64)))) (sqrt.f64 (fma.f64 y y (neg.f64 (*.f64 z z)))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64))))) (sqrt.f64 (neg.f64 (*.f64 (+.f64 z y) (-.f64 z y)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 (pow.f64 y #s(literal 4 binary64)) (pow.f64 (*.f64 y z) #s(literal 2 binary64))) (pow.f64 z #s(literal 4 binary64))))))
(/.f64 (sqrt.f64 (-.f64 (pow.f64 z #s(literal 4 binary64)) (pow.f64 y #s(literal 4 binary64)))) (sqrt.f64 (*.f64 (+.f64 z y) (-.f64 z y))))
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(fma.f64 (/.f64 (.f64 (/.f64 y z) (.f64 #s(literal 1/2 binary64) z)) #s(literal -1 binary64)) (/.f64 (neg.f64 y) z) z)
(fma.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) z) z) (/.f64 (/.f64 y z) (pow.f64 y #s(literal -1 binary64))) z)
(fma.f64 (/.f64 (.f64 #s(literal 1/2 binary64) z) z) (.f64 (/.f64 y z) y) z)
(fma.f64 (/.f64 z z) (/.f64 (*.f64 #s(literal 1/2 binary64) (/.f64 y z)) (pow.f64 y #s(literal -1 binary64))) z)
(fma.f64 (/.f64 #s(literal 1/2 binary64) z) (/.f64 (*.f64 z (/.f64 y z)) (pow.f64 y #s(literal -1 binary64))) z)
(fma.f64 (/.f64 (/.f64 y z) z) (/.f64 (*.f64 #s(literal 1/2 binary64) z) (pow.f64 y #s(literal -1 binary64))) z)
(fma.f64 (.f64 (.f64 (/.f64 y z) y) (*.f64 #s(literal 1/2 binary64) z)) (pow.f64 z #s(literal -1 binary64)) z)
(fma.f64 (.f64 (.f64 y y) (*.f64 #s(literal 1/2 binary64) z)) (pow.f64 z #s(literal -2 binary64)) z)
(fma.f64 (.f64 (.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) (neg.f64 y)) (/.f64 #s(literal -1 binary64) z) z)
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) z) (*.f64 (/.f64 y z) y)) (pow.f64 z #s(literal -1 binary64)) z)
(fma.f64 (.f64 (.f64 #s(literal 1/2 binary64) z) (*.f64 y y)) (pow.f64 z #s(literal -2 binary64)) z)
(fma.f64 (.f64 (.f64 (/.f64 y z) (*.f64 #s(literal 1/2 binary64) z)) y) (pow.f64 z #s(literal -1 binary64)) z)
(fma.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) z)
(fma.f64 #s(literal -1 binary64) (neg.f64 z) (.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)))
(fma.f64 (.f64 (/.f64 y z) y) (/.f64 (.f64 #s(literal 1/2 binary64) z) z) z)
(fma.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) #s(literal 1/2 binary64)) z z)
(fma.f64 (.f64 (/.f64 y z) (.f64 #s(literal 1/2 binary64) z)) (/.f64 (pow.f64 z #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))) z)
(fma.f64 (.f64 (/.f64 y z) (.f64 #s(literal 1/2 binary64) z)) (/.f64 y z) z)
(fma.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (pow.f64 (fma.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z)) #s(literal -1 binary64)) (neg.f64 (/.f64 (.f64 z z) (fma.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z)))))
(fma.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) z) z)
(fma.f64 (/.f64 y z) (.f64 (/.f64 y z) (.f64 #s(literal 1/2 binary64) z)) z)
(fma.f64 (*.f64 #s(literal 1/2 binary64) z) (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z)
(fma.f64 #s(literal 1/2 binary64) (*.f64 z (pow.f64 (/.f64 y z) #s(literal 2 binary64))) z)
(fma.f64 z (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) #s(literal 1/2 binary64)) z)
(fma.f64 z #s(literal 1 binary64) (.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)))
(-.f64 (/.f64 (.f64 z z) (-.f64 z (.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)))) (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (-.f64 z (.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)))))
(-.f64 (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z))) (/.f64 (.f64 z z) (fma.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z))))
(+.f64 (/.f64 (.f64 (pow.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 2 binary64)) #s(literal 1/4 binary64)) (fma.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z))) (neg.f64 (/.f64 (.f64 z z) (fma.f64 (*.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64) (neg.f64 z)))))
(+.f64 (.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)) z)
(+.f64 z (.f64 (.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) z) #s(literal 1/2 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) z) z))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) z) z)))
(.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) z) z)) (sqrt.f64 #s(literal 1/3 binary64)))
#s(approx (sqrt (+ (* z z) (* y y))) (fma.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) (*.f64 #s(literal 1/2 binary64) z) z))
(.f64 (.f64 (*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)))
(.f64 (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(pow.f64 (exp.f64 #s(literal 1/4 binary64)) (log.f64 #s(literal 1/3 binary64)))
(pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64))
(pow.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) #s(literal 2 binary64))
(pow.f64 #s(literal 1/3 binary64) #s(literal 1/4 binary64))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64))))
(exp.f64 (.f64 (.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/8 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/9 binary64)) #s(literal 1/8 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)))
(.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/16 binary64)) z))
(*.f64 (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)) z)
(*.f64 z (pow.f64 #s(literal 1/9 binary64) #s(literal 1/8 binary64)))
(*.f64 (/.f64 (neg.f64 y) #s(literal -1 binary64)) (/.f64 (/.f64 y z) z))
(*.f64 (/.f64 (/.f64 y z) #s(literal -1 binary64)) (/.f64 (neg.f64 y) z))
(*.f64 (exp.f64 (log.f64 (/.f64 y z))) (exp.f64 (log.f64 (/.f64 y z))))
(*.f64 (/.f64 (/.f64 y z) z) (/.f64 #s(literal 1 binary64) (pow.f64 y #s(literal -1 binary64))))
(.f64 (.f64 (neg.f64 y) (/.f64 y z)) (/.f64 #s(literal -1 binary64) z))
(.f64 (.f64 (/.f64 y z) (neg.f64 y)) (/.f64 #s(literal -1 binary64) z))
(*.f64 (/.f64 (neg.f64 y) z) (/.f64 (/.f64 #s(literal -1 binary64) z) (pow.f64 y #s(literal -1 binary64))))
(*.f64 (/.f64 (neg.f64 y) z) (/.f64 (neg.f64 y) z))
(.f64 (neg.f64 (.f64 (/.f64 y z) y)) (/.f64 #s(literal -1 binary64) z))
(.f64 (neg.f64 (.f64 y y)) (/.f64 #s(literal 1 binary64) (neg.f64 (*.f64 z z))))
(.f64 (.f64 (neg.f64 y) y) (/.f64 #s(literal 1 binary64) (*.f64 (neg.f64 z) z)))
(.f64 (.f64 y (neg.f64 y)) (/.f64 #s(literal 1 binary64) (*.f64 z (neg.f64 z))))
(*.f64 (pow.f64 z #s(literal -2 binary64)) (/.f64 y (pow.f64 y #s(literal -1 binary64))))
(.f64 (pow.f64 z #s(literal -2 binary64)) (.f64 y y))
(.f64 (.f64 (/.f64 y z) y) (pow.f64 z #s(literal -1 binary64)))
(*.f64 (pow.f64 z #s(literal -1 binary64)) (/.f64 (/.f64 y z) (pow.f64 y #s(literal -1 binary64))))
(*.f64 #s(literal 1 binary64) (pow.f64 (/.f64 y z) #s(literal 2 binary64)))
(.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 z y) (neg.f64 z))))
(.f64 (neg.f64 y) (/.f64 #s(literal 1 binary64) (.f64 (neg.f64 z) (/.f64 z y))))
(*.f64 (/.f64 y z) (/.f64 (pow.f64 z #s(literal -1 binary64)) (pow.f64 y #s(literal -1 binary64))))
(*.f64 (/.f64 y z) (/.f64 y z))
(.f64 (.f64 y y) (pow.f64 (/.f64 #s(literal -1 binary64) z) #s(literal 2 binary64)))
(.f64 (.f64 y y) (pow.f64 z #s(literal -2 binary64)))
(.f64 y (/.f64 #s(literal 1 binary64) (.f64 (/.f64 z y) z)))
(*.f64 y (/.f64 (/.f64 y z) z))
(.f64 y (.f64 y (pow.f64 z #s(literal -2 binary64))))
(.f64 y (pow.f64 (.f64 z (/.f64 z y)) #s(literal -1 binary64)))
(pow.f64 (exp.f64 (log.f64 (/.f64 y z))) #s(literal 2 binary64))
(pow.f64 (pow.f64 (/.f64 z y) #s(literal 2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 z y) #s(literal -2 binary64))
(pow.f64 (pow.f64 (/.f64 y z) #s(literal 2 binary64)) #s(literal 1 binary64))
(pow.f64 (/.f64 y z) #s(literal 2 binary64))
(/.f64 (neg.f64 (*.f64 (neg.f64 y) (/.f64 y z))) z)
(/.f64 (neg.f64 (*.f64 (/.f64 y z) (neg.f64 y))) z)
(/.f64 (neg.f64 (neg.f64 (*.f64 (/.f64 y z) y))) z)
(/.f64 (neg.f64 (neg.f64 (.f64 y y))) (neg.f64 (neg.f64 (.f64 z z))))
(/.f64 (neg.f64 (.f64 (neg.f64 y) y)) (neg.f64 (.f64 (neg.f64 z) z)))
(/.f64 (neg.f64 (.f64 y (neg.f64 y))) (neg.f64 (.f64 z (neg.f64 z))))
(/.f64 (neg.f64 (/.f64 y z)) (neg.f64 (/.f64 z y)))
(/.f64 (*.f64 (neg.f64 y) (/.f64 y z)) (neg.f64 z))
(/.f64 (*.f64 (/.f64 y z) (neg.f64 y)) (neg.f64 z))
(/.f64 (neg.f64 (*.f64 (/.f64 y z) y)) (neg.f64 z))
(/.f64 (neg.f64 (.f64 y y)) (neg.f64 (.f64 z z)))
(/.f64 (.f64 (neg.f64 y) y) (.f64 (neg.f64 z) z))
(/.f64 (.f64 y (neg.f64 y)) (.f64 z (neg.f64 z)))
(/.f64 #s(literal -1 binary64) (neg.f64 (pow.f64 (/.f64 z y) #s(literal 2 binary64))))
(/.f64 (*.f64 (/.f64 y z) y) z)
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 z) (*.f64 (neg.f64 y) (/.f64 y z))))
(/.f64 #s(literal 1 binary64) (/.f64 (neg.f64 z) (*.f64 (/.f64 y z) (neg.f64 y))))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 z y) (neg.f64 z)) (neg.f64 y)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (/.f64 z y) z) y))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 (neg.f64 z) (/.f64 z y)) (neg.f64 y)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (neg.f64 z) z) (.f64 (neg.f64 y) y)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 z (/.f64 z y)) y))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 z (neg.f64 z)) (.f64 y (neg.f64 y))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (/.f64 z y) #s(literal 2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (pow.f64 (/.f64 z y) #s(literal 2 binary64)))
(/.f64 (neg.f64 y) (neg.f64 (*.f64 (/.f64 z y) z)))
(/.f64 (neg.f64 y) (neg.f64 (*.f64 z (/.f64 z y))))
(/.f64 (neg.f64 y) (*.f64 (/.f64 z y) (neg.f64 z)))
(/.f64 (neg.f64 y) (*.f64 (neg.f64 z) (/.f64 z y)))
(/.f64 (/.f64 y z) (/.f64 z y))
(/.f64 (.f64 y y) (.f64 z z))
(/.f64 y (neg.f64 (*.f64 (/.f64 z y) (neg.f64 z))))
(/.f64 y (neg.f64 (*.f64 (neg.f64 z) (/.f64 z y))))
(/.f64 y (*.f64 (/.f64 z y) z))
(/.f64 y (*.f64 z (/.f64 z y)))
(exp.f64 (-.f64 (.f64 (log.f64 y) #s(literal 2 binary64)) (.f64 (log.f64 z) #s(literal 2 binary64))))
(exp.f64 (*.f64 (log.f64 (/.f64 y z)) #s(literal 2 binary64)))

eval364.0ms (4.8%)

Memory: -121.6MiB live, 302.0MiB allocated
Compiler: Compiled 18 558 to 2 391 computations (87.1% saved)

prune28.0ms (0.4%)

Memory

4.7MiB live, 80.9MiB allocated

Pruning

12 alts after pruning (2 fresh and 10 done)

	Pruned	Kept	Total
New	828	2	830
Fresh	0	0	0
Picked	1	4	5
Done	0	6	6
Total	829	12	841

Accuracy

100.0%

Counts

841 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	46.1%	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
✓	99.4%	(/.f64 #s(approx (sqrt (+ (+ (* x x) (* y y)) (* z z))) (hypot.f64 z y)) (sqrt.f64 #s(literal 3 binary64)))
✓	46.3%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	46.2%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))))
✓	45.9%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
✓	98.5%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	98.5%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
	97.8%	#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (*.f64 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	99.5%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (hypot.f64 z y) (sqrt.f64 #s(literal 1/3 binary64))))
✓	46.2%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64))))
✓	98.6%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
✓	99.1%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64))))

Compiler

Compiled 281 to 183 computations (34.9% saved)

regimes64.0ms (0.9%)

Memory

-34.7MiB live, 132.4MiB allocated

Counts

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

Outputs

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

Calls

10 calls:

11.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
7.0ms	(*.f64 z z)
7.0ms	x
6.0ms	(+.f64 (.f64 x x) (.f64 y y))
6.0ms	z

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes58.0ms (0.8%)

Memory

14.7MiB live, 133.1MiB allocated

Counts

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

Outputs
#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:

8.0ms	y
7.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
6.0ms	(*.f64 x x)
6.0ms	z
5.0ms	x

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes91.0ms (1.2%)

Memory

11.8MiB live, 126.6MiB 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 (neg.f64 z) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
#s(approx (/ (sqrt (+ (+ (* x x) (* y y)) (* z z))) (sqrt 3)) (/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (.f64 (sqrt.f64 (fma.f64 z z (.f64 y y))) (sqrt.f64 #s(literal 1/3 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 1/3 binary64)))
(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #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 #s(approx (sqrt (+ ( z z) (* y y))) (fma.f64 (.f64 z #s(literal 1/2 binary64)) (.f64 (/.f64 y z) (/.f64 y z)) z)) (sqrt.f64 #s(literal 1/3 binary64))))

Outputs

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

Calls

10 calls:

27.0ms	(*.f64 x x)
24.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
7.0ms	y
5.0ms	z
5.0ms	x

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`z`
99.1%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.1%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.1%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`
99.1%	1	`(*.f64 z z)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes71.0ms (0.9%)

Memory

-8.5MiB live, 107.8MiB allocated

Accuracy

Total -34.0b remaining (-3713%)

Threshold costs -34b (-3713%)

Counts

14 → 1

Calls

Call 1

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

24.0ms	y
9.0ms	(*.f64 z z)
7.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
5.0ms	z
4.0ms	x

Results

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

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify42.0ms (0.6%)

Memory

19.7MiB live, 58.3MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	105
1	39	105

Stop Event

1×

saturated

Calls

Call 1

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

soundness695.0ms (9.3%)

Memory

-29.2MiB live, 416.1MiB allocated

Rules

14 598×	`lower-fma.f64`
14 598×	`lower-fma.f32`
13 366×	`lower-fma.f64`
13 366×	`lower-fma.f32`
8 934×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	787	13330
1	2552	13234
0	8389	11697
0	30	214
0	44	205
1	124	205
2	726	205
0	8336	196
0	230	2514
1	673	2514
2	2273	2478
3	5705	2361
0	8205	2064

Stop Event

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

Compiler

Compiled 77 to 69 computations (10.4% saved)

preprocess176.0ms (2.3%)

Memory: 9.2MiB live, 247.3MiB allocated
Compiler: Compiled 558 to 434 computations (22.2% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze1.0ms (0%)

sample1.3s (17.7%)

explain632.0ms (8.4%)

preprocess206.0ms (2.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0.1%)

localize195.0ms (2.6%)

series18.0ms (0.2%)

simplify303.0ms (4%)

rewrite197.0ms (2.6%)

eval64.0ms (0.9%)

prune16.0ms (0.2%)

simplify6.0ms (0.1%)

localize62.0ms (0.8%)

series38.0ms (0.5%)

simplify209.0ms (2.8%)

rewrite528.0ms (7%)

eval410.0ms (5.5%)

prune72.0ms (1%)

simplify30.0ms (0.4%)

localize88.0ms (1.2%)

series50.0ms (0.7%)

simplify240.0ms (3.2%)

rewrite156.0ms (2.1%)

eval175.0ms (2.3%)

prune27.0ms (0.4%)

simplify142.0ms (1.9%)

localize184.0ms (2.5%)

series117.0ms (1.6%)

simplify227.0ms (3%)

rewrite192.0ms (2.6%)

eval364.0ms (4.8%)

prune28.0ms (0.4%)

regimes64.0ms (0.9%)

regimes58.0ms (0.8%)

regimes91.0ms (1.2%)

regimes71.0ms (0.9%)

simplify42.0ms (0.6%)

soundness695.0ms (9.3%)

preprocess176.0ms (2.3%)

end0.0ms (0%)

Profiling