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

2.2MiB live, 2.2MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.4s (19.2%)

Memory

-26.9MiB live, 1 386.7MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 758.0ms

ival-add: 289.0ms (38.1% of total)

ival-mult: 278.0ms (36.7% of total)

ival-div: 117.0ms (15.4% of total)

ival-sqrt: 61.0ms (8% of total)

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

exact: 5.0ms (0.7% of total)

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

Bogosity

explain130.0ms (1.7%)

Memory

37.6MiB live, 312.8MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
151	-	1	(-2.961797276432028e-160 -4.701018050446975e-194 -4.029643132655643e-204)	`(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	148	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	149
↳	`(*.f64 y y)`	overflow	56
↳	`(*.f64 x x)`	overflow	75
↳	`(*.f64 z z)`	overflow	66
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	119
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	148
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	2	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	2
↳	`(*.f64 y y)`	underflow	60
↳	`(*.f64 x x)`	underflow	66
↳	`(*.f64 z z)`	underflow	60
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	9
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2
`/.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	149
↳	`(*.f64 y y)`	overflow	56
↳	`(*.f64 x x)`	overflow	75
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	119
↳	`(*.f64 z z)`	overflow	66

Confusion

	Predicted +	Predicted -
+	151	1
-	0	104

Precision

1.0

Recall

0.993421052631579

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	151	0	1
-	0	0	104

Precision?

1.0

Recall?

0.993421052631579

Freqs

test

number	freq
0	105
1	151

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

42.0ms

512×

valid

Compiler

Compiled 134 to 37 computations (72.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 9.0ms (37.4% of total)

ival-add: 6.0ms (24.9% of total)

ival-sqrt: 4.0ms (16.6% of total)

ival-div: 3.0ms (12.5% of total)

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

exact: 0.0ms (0% of total)

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

preprocess142.0ms (1.9%)

Memory

-3.5MiB live, 71.7MiB 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	9

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 (hypot.f64 y 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: 0.6MiB live, 0.6MiB allocated
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.9%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 14 to 11 computations (21.4% saved)

simplify4.0ms (0.1%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f64 x x)
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 (.f64 x x) (.f64 y y)) (*.f64 z z))

Rules

24×	`lower-+.f32`
20×	`lower-+.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
12×	`lower-hypot.f32`

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	39

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 (hypot.f64 y 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 (hypot.f64 y x)) #s(literal 3 binary64))
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
(fma.f64 z z (hypot.f64 y x))
(+.f64 (.f64 x x) (.f64 y y))
(hypot.f64 y x)
(*.f64 x x)
x
(*.f64 y y)
y
(*.f64 z z)
z
#s(literal 3 binary64)

localize223.0ms (3%)

Memory

-4.7MiB live, 74.2MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0	(*.f64 x x)
accuracy	0.00390625	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
accuracy	0.2681973118413311	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	35.0347793232139	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

215.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 206.0ms

ival-add: 198.0ms (95.9% of total)

ival-mult: 5.0ms (2.4% of total)

ival-div: 2.0ms (1% of total)

ival-sqrt: 2.0ms (1% of total)

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

exact: 0.0ms (0% of total)

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

series194.0ms (2.6%)

Memory

-17.9MiB live, 28.0MiB allocated

Counts

4 → 120

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 (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>) () ())

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) (+ 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 (* 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 (* -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
181.0ms	y	@	0	((+ (+ (* x x) (* y y)) (* z z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	z	@	0	((+ (+ (* x x) (* y y)) (* z z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
2.0ms	z	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
1.0ms	y	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))
1.0ms	x	@	inf	((+ (+ (* x x) (* y y)) (* z z)) (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (* x x))

simplify902.0ms (12%)

Memory

7.8MiB live, 283.4MiB allocated

Algorithm

1×	egg-herbie

Rules

12 954×	`lower-fma.f64`
12 954×	`lower-fma.f32`
5 420×	`lower-*.f64`
5 420×	`lower-*.f32`
3 812×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	226	2334
1	659	2334
2	2233	2298
3	5624	2205
0	8102	1560

Stop Event

1×	iter limit
1×	node limit

Counts

120 → 120

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

rewrite219.0ms (2.9%)

Memory

16.0MiB live, 371.1MiB 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	41
0	18	41
1	65	41
2	486	41
3	6616	41
0	8497	26

Stop Event

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

Counts

4 → 289

Calls

Call 1

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

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

eval95.0ms (1.3%)

Memory: -45.2MiB live, 207.0MiB allocated
Compiler: Compiled 8 637 to 1 301 computations (84.9% saved)

prune7.0ms (0.1%)

Memory

36.6MiB live, 36.6MiB allocated

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	405	4	409
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	405	5	410

Accuracy

98.4%

Counts

410 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.4%	(/.f64 (sqrt.f64 (fma.f64 z z (hypot.f64 y x))) (sqrt.f64 #s(literal 3 binary64)))
✓	44.9%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
▶	44.1%	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
▶	44.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	97.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 43 to 43 computations (0% saved)

simplify7.0ms (0.1%)

Memory

-17.9MiB live, 21.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(hypot.f64 y x)
cost-diff	0	(fma.f64 z z (hypot.f64 y x))
cost-diff	0	(sqrt.f64 (fma.f64 z z (hypot.f64 y x)))
cost-diff	0	(/.f64 (sqrt.f64 (fma.f64 z z (hypot.f64 y 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	(/.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	(*.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))

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	163
0	39	133
1	51	133
2	59	133
3	61	133
0	61	133

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize58.0ms (0.8%)

Memory

-1.7MiB live, 157.3MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.359375	(/.f64 (sqrt.f64 (fma.f64 z z (hypot.f64 y x))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	35.183740304221935	(sqrt.f64 (fma.f64 z z (hypot.f64 y x)))
accuracy	59.824535850421604	(hypot.f64 y x)
accuracy	0	(*.f64 z z)
accuracy	0.2681973118413311	(/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64))
accuracy	0.5227421229412844	#s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z))
accuracy	35.0347793232139	(sqrt.f64 (/.f64 #s(approx (+ (+ (* x x) (* y y)) (* z z)) (*.f64 z z)) #s(literal 3 binary64)))
accuracy	0	(*.f64 z z)
accuracy	0.3033535618413311	(.f64 #s(literal 1/3 binary64) (.f64 z z))
accuracy	0.5228357552811462	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z)))
accuracy	35.0347793232139	(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	0.3984375	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
accuracy	1.290186941866845	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Samples

41.0ms

256×

valid

Compiler

Compiled 155 to 22 computations (85.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 28.0ms

ival-mult: 11.0ms (39.8% of total)

ival-sqrt: 6.0ms (21.7% of total)

ival-add: 4.0ms (14.5% of total)

ival-div: 3.0ms (10.9% of total)

const: 3.0ms (10.9% of total)

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

exact: 0.0ms (0% of total)

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

series35.0ms (0.5%)

Memory

0.6MiB live, 78.6MiB allocated

Counts

15 → 384

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	y	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt 1/3) (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) (+ (+ (* x x) (* y y)) (* 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 3))
3.0ms	z	@	0	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt 1/3) (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) (+ (+ (* x x) (* y y)) (* 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 3))
2.0ms	z	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt 1/3) (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) (+ (+ (* x x) (* y y)) (* 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 3))
2.0ms	z	@	-inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt 1/3) (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) (+ (+ (* x x) (* y y)) (* 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 3))
1.0ms	y	@	inf	((sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (* (sqrt 1/3) z) (sqrt 1/3) (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) (+ (+ (* x x) (* y y)) (* 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 3))

simplify258.0ms (3.4%)

Memory

2.4MiB live, 362.9MiB allocated

Algorithm

1×	egg-herbie

Rules

15 974×	`lower-fma.f64`
15 974×	`lower-fma.f32`
6 694×	`lower-*.f64`
6 694×	`lower-*.f32`
4 598×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	463	8598
1	1475	8556
2	5302	8445
0	8034	6030

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 381

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

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

rewrite219.0ms (2.9%)

Memory

13.6MiB live, 330.3MiB allocated

Rules

5 686×	`lower-fma.f32`
5 684×	`lower-fma.f64`
4 130×	`lower-/.f32`
4 126×	`lower-/.f64`
4 074×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	150
0	39	119
1	136	119
2	931	119
0	8171	119

Stop Event

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

Counts

15 → 362

Calls

Call 1

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

eval140.0ms (1.9%)

Memory: -21.2MiB live, 294.6MiB allocated
Compiler: Compiled 14 600 to 1 893 computations (87% saved)

prune16.0ms (0.2%)

Memory

18.4MiB live, 57.3MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	758	3	761
Fresh	0	0	0
Picked	2	2	4
Done	0	1	1
Total	760	6	766

Accuracy

98.8%

Counts

766 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	44.8%	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
✓	44.9%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
▶	44.4%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	44.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	97.4%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
✓	97.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 49 to 51 computations (-4.1% saved)

simplify6.0ms (0.1%)

Memory

12.4MiB live, 12.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 11 expressions of interest:

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

Rules

28×	`lower-+.f64`
28×	`lower-+.f32`
20×	`lower-fma.f32`
18×	`lower-fma.f64`
18×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	143
0	37	143
1	48	143
2	54	143
3	56	143
0	56	112

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize58.0ms (0.8%)

Memory

-26.3MiB live, 129.8MiB allocated

Localize:

Found 11 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.24992452051919237	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
accuracy	0.359375	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
accuracy	35.183740304221935	(sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y))))
accuracy	0.08203125	(.f64 (.f64 #s(literal 1/3 binary64) z) z)
accuracy	0.2890625	(*.f64 #s(literal 1/3 binary64) z)
accuracy	0.5228357552811462	#s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z))
accuracy	35.0347793232139	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
accuracy	0	(sqrt.f64 #s(literal 3 binary64))
accuracy	0.37109375	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
accuracy	1.290186941866845	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))

Samples

43.0ms

256×

valid

Compiler

Compiled 115 to 22 computations (80.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sqrt: 10.0ms (34.8% of total)

ival-mult: 7.0ms (24.4% of total)

ival-div: 4.0ms (13.9% of total)

ival-add: 4.0ms (13.9% of total)

const: 3.0ms (10.4% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.3%)

Memory

8.7MiB live, 55.0MiB allocated

Counts

11 → 276

Calls

Call 1

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

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

Calls

9 calls:

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

simplify593.0ms (7.9%)

Memory

14.6MiB live, 280.8MiB allocated

Algorithm

1×	egg-herbie

Rules

16 296×	`lower-fma.f64`
16 296×	`lower-fma.f32`
6 694×	`lower-*.f64`
6 694×	`lower-*.f32`
4 652×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	464	6378
1	1477	6294
2	5298	6252
0	8084	4524

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 273

Calls

Call 1

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

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

rewrite1.1s (14%)

Memory

14.5MiB live, 222.4MiB allocated

Rules

4 500×	`lower-/.f32`
4 496×	`lower-/.f64`
4 492×	`lower-fma.f32`
4 490×	`lower-fma.f64`
3 724×	`lower-*.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	131
0	37	129
1	146	129
2	1055	129
0	8185	98

Stop Event

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

Counts

11 → 146

Calls

Call 1

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

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

eval90.0ms (1.2%)

Memory: -22.4MiB live, 91.3MiB allocated
Compiler: Compiled 8 179 to 1 021 computations (87.5% saved)

prune12.0ms (0.2%)

Memory

-10.6MiB live, 35.6MiB allocated

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	0	0	0
Picked	0	3	3
Done	1	2	3
Total	431	9	440

Accuracy

98.8%

Counts

440 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	44.8%	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
▶	44.8%	(.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64)))
▶	44.9%	(sqrt.f64 (.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64)))
✓	44.4%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	44.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
▶	96.3%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	97.4%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
▶	89.0%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))))
✓	97.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 73 to 80 computations (-9.6% saved)

simplify18.0ms (0.2%)

Memory

28.1MiB live, 28.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score
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 1/3 binary64)))
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	(.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64))
cost-diff	0	(sqrt.f64 (.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64)))
cost-diff	0	(pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))
cost-diff	0	(/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
cost-diff	0	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
cost-diff	12288	(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
cost-diff	0	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
cost-diff	0	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))))
cost-diff	192	(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
cost-diff	12928	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Rules

144×	`lower-*.f32`
136×	`lower-*.f64`
84×	`lower-/.f32`
80×	`lower-/.f64`
60×	`times-frac`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	225
0	49	216
1	61	215
2	87	215
3	100	215
4	112	207
5	125	207
6	166	207
7	179	207
8	189	207
9	204	207
10	230	207
11	262	207
12	276	207
13	279	207
14	282	207
15	285	207
16	289	207
17	290	207
0	290	165

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize89.0ms (1.2%)

Memory

6.0MiB live, 158.7MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score
accuracy	0	(sqrt.f64 #s(literal 1/3 binary64))
accuracy	0.24992452051919237	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
accuracy	0.390625	(.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64)))
accuracy	35.183740304221935	(sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y))))
accuracy	0	(*.f64 y y)
accuracy	0.24992452051919237	#s(approx (+ (* y y) (* x x)) (*.f64 y y))
accuracy	0.3033535618413311	(.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64))
accuracy	35.0347793232139	(sqrt.f64 (.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64)))
accuracy	0	(pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))
accuracy	0.37109375	(/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
accuracy	1.0	(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
accuracy	1.290186941866845	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
accuracy	0.00390625	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
accuracy	0.359375	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
accuracy	1.290186941866845	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))))
accuracy	5.985554951440197	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Samples

70.0ms

256×

valid

Compiler

Compiled 184 to 29 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 54.0ms

ival-mult: 18.0ms (33.5% of total)

ival-sqrt: 10.0ms (18.6% of total)

ival-div: 5.0ms (9.3% of total)

ival-pow: 5.0ms (9.3% of total)

ival-exp: 3.0ms (5.6% of total)

ival-log: 3.0ms (5.6% of total)

const: 3.0ms (5.6% of total)

ival-add: 2.0ms (3.7% of total)

ival-pow2: 2.0ms (3.7% of total)

exact: 1.0ms (1.9% of total)

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

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

series107.0ms (1.4%)

Memory

-11.9MiB live, 163.5MiB allocated

Counts

17 → 348

Calls

Call 1

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

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

Calls

9 calls:

Time	Variable		Point	Expression
40.0ms	z	@	0	((exp (* (log (/ (sqrt 3) z)) -1)) (* (log (/ (sqrt 3) z)) -1) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (log (/ (sqrt 3) z)) (pow (pow 3 1/4) 2) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/ z (pow (pow 3 1/4) 2)) (pow 3 1/4) (sqrt (* (+ (* z z) (+ (* y y) (* x x))) 1/3)) (* (+ (* z z) (+ (* y y) (* x x))) 1/3) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 1/3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (/ (sqrt 3) z) (* y y) (sqrt 1/3))
26.0ms	z	@	-inf	((exp (* (log (/ (sqrt 3) z)) -1)) (* (log (/ (sqrt 3) z)) -1) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (log (/ (sqrt 3) z)) (pow (pow 3 1/4) 2) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/ z (pow (pow 3 1/4) 2)) (pow 3 1/4) (sqrt (* (+ (* z z) (+ (* y y) (* x x))) 1/3)) (* (+ (* z z) (+ (* y y) (* x x))) 1/3) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 1/3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (/ (sqrt 3) z) (* y y) (sqrt 1/3))
14.0ms	y	@	0	((exp (* (log (/ (sqrt 3) z)) -1)) (* (log (/ (sqrt 3) z)) -1) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (log (/ (sqrt 3) z)) (pow (pow 3 1/4) 2) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/ z (pow (pow 3 1/4) 2)) (pow 3 1/4) (sqrt (* (+ (* z z) (+ (* y y) (* x x))) 1/3)) (* (+ (* z z) (+ (* y y) (* x x))) 1/3) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 1/3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (/ (sqrt 3) z) (* y y) (sqrt 1/3))
8.0ms	z	@	inf	((exp (* (log (/ (sqrt 3) z)) -1)) (* (log (/ (sqrt 3) z)) -1) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (log (/ (sqrt 3) z)) (pow (pow 3 1/4) 2) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/ z (pow (pow 3 1/4) 2)) (pow 3 1/4) (sqrt (* (+ (* z z) (+ (* y y) (* x x))) 1/3)) (* (+ (* z z) (+ (* y y) (* x x))) 1/3) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 1/3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (/ (sqrt 3) z) (* y y) (sqrt 1/3))
1.0ms	y	@	inf	((exp (* (log (/ (sqrt 3) z)) -1)) (* (log (/ (sqrt 3) z)) -1) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (log (/ (sqrt 3) z)) (pow (pow 3 1/4) 2) (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/ z (pow (pow 3 1/4) 2)) (pow 3 1/4) (sqrt (* (+ (* z z) (+ (* y y) (* x x))) 1/3)) (* (+ (* z z) (+ (* y y) (* x x))) 1/3) (+ (* z z) (+ (* y y) (* x x))) (+ (* y y) (* x x)) (* (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 1/3)) (sqrt (+ (* z z) (+ (* y y) (* x x)))) (/ (sqrt 3) z) (* y y) (sqrt 1/3))

simplify280.0ms (3.7%)

Memory

-16.1MiB live, 334.6MiB allocated

Algorithm

1×	egg-herbie

Rules

16 034×	`lower-fma.f64`
16 034×	`lower-fma.f32`
6 740×	`lower-*.f64`
6 740×	`lower-*.f32`
4 622×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	479	7876
1	1515	7776
2	5350	7690
0	8107	5644

Stop Event

1×	iter limit
1×	node limit

Counts

348 → 345

Calls

Call 1

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

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

rewrite198.0ms (2.6%)

Memory

23.6MiB live, 249.6MiB allocated

Rules

5 514×	`lower-*.f32`
5 506×	`lower-*.f64`
5 390×	`lower-fma.f32`
5 388×	`lower-fma.f64`
3 840×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	182
0	49	170
1	142	161
2	837	160
0	8424	126

Stop Event

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

Counts

17 → 493

Calls

Call 1

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

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

eval209.0ms (2.8%)

Memory: 9.8MiB live, 211.5MiB allocated
Compiler: Compiled 17 687 to 2 388 computations (86.5% saved)

prune26.0ms (0.3%)

Memory

11.3MiB live, 87.0MiB allocated

Pruning

13 alts after pruning (5 fresh and 8 done)

	Pruned	Kept	Total
New	961	5	966
Fresh	0	0	0
Picked	1	3	4
Done	0	5	5
Total	962	13	975

Accuracy

98.8%

Counts

975 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	44.8%	(/.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ (* y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 3 binary64)))
✓	44.8%	(.f64 (sqrt.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64)))
✓	44.9%	(sqrt.f64 (.f64 (fma.f64 z z #s(approx (+ ( y y) (* x x)) (*.f64 y y))) #s(literal 1/3 binary64)))
✓	44.4%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 (.f64 #s(literal 1/3 binary64) z) z)))
✓	44.1%	(sqrt.f64 #s(approx (/ (+ (+ (* x x) (* y y)) (* z z)) 3) (.f64 #s(literal 1/3 binary64) (.f64 z z))))
	46.3%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (pow.f64 (*.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1/2 binary64)))
	96.7%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal -1 binary64) z)))
✓	96.3%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))))
✓	97.4%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
	88.5%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (-.f64 (log.f64 (.f64 z (pow.f64 #s(literal 9 binary64) #s(literal -1/8 binary64)))) (.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/4 binary64)))))
	89.0%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) z))) #s(literal -1 binary64))))
	89.0%	#s(approx (/ (sqrt (+ (* z z) (+ (* y y) (* x x)))) (sqrt 3)) (exp.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))))
✓	97.4%	#s(approx (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Compiler

Compiled 280 to 205 computations (26.8% saved)

regimes73.0ms (1%)

Memory

-22.3MiB live, 101.5MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

10 calls:

20.0ms	z
9.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(*.f64 z z)
5.0ms	y
5.0ms	x

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`y`
97.4%	1	`z`
97.4%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.4%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.4%	1	`(*.f64 x x)`
97.4%	1	`(*.f64 y y)`
97.4%	1	`(*.f64 z z)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

regimes32.0ms (0.4%)

Memory

-7.6MiB live, 30.8MiB allocated

Accuracy

Total -34.2b remaining (-2055.4%)

Threshold costs -34.2b (-2055.4%)

Counts

3 → 1

Calls

Call 1

Inputs

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

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

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

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

Calls

10 calls:

16.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
2.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))

Results

Accuracy	Segments	Branch
97.4%	1	`y`
97.4%	1	`z`
97.4%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.4%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.4%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.4%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.4%	1	`(*.f64 y y)`
97.4%	1	`(*.f64 z z)`
97.4%	1	`x`
97.4%	1	`(*.f64 x x)`

Compiler

Compiled 57 to 56 computations (1.8% saved)

simplify28.0ms (0.4%)

Memory

13.4MiB live, 50.6MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`-commutative-binary64-.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	39
1	24	39

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

Outputs

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

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

soundness460.0ms (6.1%)

Memory

-22.9MiB live, 384.2MiB allocated

Rules

15 974×	`lower-fma.f64`
15 974×	`lower-fma.f32`
12 954×	`lower-fma.f64`
12 954×	`lower-fma.f32`
6 694×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	226	2334
1	659	2334
2	2233	2298
3	5624	2205
0	8102	1560
0	463	8598
1	1475	8556
2	5302	8445
0	8034	6030
0	11	41
0	18	41
1	65	41
2	486	41
3	6616	41
0	8497	26

Stop Event

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

Compiler

Compiled 42 to 39 computations (7.1% saved)

preprocess72.0ms (1%)

Memory: 13.4MiB live, 131.7MiB allocated
Compiler: Compiled 152 to 146 computations (3.9% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	34	225
0	49	216
1	61	215
2	87	215
3	100	215
4	112	207
5	125	207
6	166	207
7	179	207
8	189	207
9	204	207
10	230	207
11	262	207
12	276	207
13	279	207
14	282	207
15	285	207
16	289	207
17	290	207
0	290	165

Iter	Nodes	Cost
0	34	225
0	49	216
1	61	215
2	87	215
3	100	215
4	112	207
5	125	207
6	166	207
7	179	207
8	189	207
9	204	207
10	230	207
11	262	207
12	276	207
13	279	207
14	282	207
15	285	207
16	289	207
17	290	207
0	290	165

start0.0ms (0%)

analyze1.0ms (0%)

sample1.4s (19.2%)

explain130.0ms (1.7%)

preprocess142.0ms (1.9%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify4.0ms (0.1%)

localize223.0ms (3%)

series194.0ms (2.6%)

simplify902.0ms (12%)

rewrite219.0ms (2.9%)

eval95.0ms (1.3%)

prune7.0ms (0.1%)

simplify7.0ms (0.1%)

localize58.0ms (0.8%)

series35.0ms (0.5%)

simplify258.0ms (3.4%)

rewrite219.0ms (2.9%)

eval140.0ms (1.9%)

prune16.0ms (0.2%)

simplify6.0ms (0.1%)

localize58.0ms (0.8%)

series21.0ms (0.3%)

simplify593.0ms (7.9%)

rewrite1.1s (14%)

eval90.0ms (1.2%)

prune12.0ms (0.2%)

simplify18.0ms (0.2%)

localize89.0ms (1.2%)

series107.0ms (1.4%)

simplify280.0ms (3.7%)

rewrite198.0ms (2.6%)

eval209.0ms (2.8%)

prune26.0ms (0.3%)

regimes73.0ms (1%)

regimes32.0ms (0.4%)

simplify28.0ms (0.4%)

soundness460.0ms (6.1%)

preprocess72.0ms (1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	34	225
0	49	216
1	61	215
2	87	215
3	100	215
4	112	207
5	125	207
6	166	207
7	179	207
8	189	207
9	204	207
10	230	207
11	262	207
12	276	207
13	279	207
14	282	207
15	285	207
16	289	207
17	290	207
0	290	165