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

analyze1.0ms (0%)

Memory

3.3MiB live, 3.3MiB 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)

sample1.2s (12.5%)

Memory

7.4MiB live, 1 954.3MiB allocated

Samples

796.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 411.0ms

ival-mult: 178.0ms (43.3% of total)

ival-sqrt: 81.0ms (19.7% of total)

ival-add: 75.0ms (18.2% of total)

ival-div: 62.0ms (15.1% of total)

ival-true: 6.0ms (1.5% of total)

exact: 5.0ms (1.2% of total)

ival-assert: 4.0ms (1% of total)

Bogosity

preprocess39.0ms (0.4%)

Memory

19.6MiB live, 58.5MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	143
1	78	143
2	157	143
3	317	143
4	581	143
5	938	143
6	1272	143
7	1289	143
0	11	14
1	15	14
2	22	14
3	24	14
0	24	12

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))

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

Call 2

Inputs
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
(sqrt (/ (+ (+ (* (neg x) (neg x)) (* y y)) (* z z)) 3))
(sqrt (/ (+ (+ (* x x) (* (neg y) (neg y))) (* z z)) 3))
(sqrt (/ (+ (+ (* x x) (* y y)) (* (neg z) (neg z))) 3))
(neg (sqrt (/ (+ (+ (* (neg x) (neg x)) (* y y)) (* z z)) 3)))
(neg (sqrt (/ (+ (+ (* x x) (* (neg y) (neg y))) (* z z)) 3)))
(neg (sqrt (/ (+ (+ (* x x) (* y y)) (* (neg z) (neg z))) 3)))
(sqrt (/ (+ (+ (* y y) (* x x)) (* z z)) 3))
(sqrt (/ (+ (+ (* z z) (* y y)) (* x x)) 3))
(sqrt (/ (+ (+ (* x x) (* z z)) (* y y)) 3))

Outputs
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(sqrt (/ (+ (+ (* (neg x) (neg x)) (* y y)) (* z z)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(sqrt (/ (+ (+ (* x x) (* (neg y) (neg y))) (* z z)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(sqrt (/ (+ (+ (* x x) (* y y)) (* (neg z) (neg z))) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(neg (sqrt (/ (+ (+ (* (neg x) (neg x)) (* y y)) (* z z)) 3)))
(neg (sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3)))
(neg (sqrt (/ (+ (+ (* x x) (* (neg y) (neg y))) (* z z)) 3)))
(neg (sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3)))
(neg (sqrt (/ (+ (+ (* x x) (* y y)) (* (neg z) (neg z))) 3)))
(neg (sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3)))
(sqrt (/ (+ (+ (* y y) (* x x)) (* z z)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(sqrt (/ (+ (+ (* z z) (* y y)) (* x x)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))
(sqrt (/ (+ (+ (* x x) (* z z)) (* y y)) 3))
(sqrt (* (+ (* x x) (+ (* y y) (* z z))) 1/3))

Symmetry

(abs x)

(abs y)

(abs z)

(sort x y z)

explain137.0ms (1.4%)

Memory

7.2MiB live, 400.6MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	151	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	152
↳	`(*.f64 y y)`	overflow	40
↳	`(*.f64 x x)`	overflow	4
↳	`(*.f64 z z)`	overflow	152
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	40
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	151
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	5	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	5
↳	`(*.f64 y y)`	underflow	33
↳	`(*.f64 x x)`	underflow	152
↳	`(*.f64 z z)`	underflow	5
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	33
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	5
`/.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	152
↳	`(*.f64 y y)`	overflow	40
↳	`(*.f64 x x)`	overflow	4
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	40
↳	`(*.f64 z z)`	overflow	152

Confusion

	Predicted +	Predicted -
+	157	0
-	0	99

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	157	0	0
-	0	0	99

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	99
1	157

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

40.0ms

512×

valid

Compiler

Compiled 154 to 48 computations (68.8% saved)

Precisions

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

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

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

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

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

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

Memory: 0.5MiB live, 0.5MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

2.3MiB live, 2.3MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	42.9%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify5.0ms (0%)

Memory

10.7MiB live, 10.7MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

24×	`+-lowering-+.f64`
24×	`+-lowering-+.f32`
18×	`accelerator-lowering-fma.f32`
18×	`accelerator-lowering-fma.f64`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	58
1	15	58
2	22	58
3	24	58
0	24	51

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
(/ (+ (+ (* x x) (* y y)) (* z z)) 3)
(+ (+ (* x x) (* y y)) (* z z))
(+ (* x x) (* y y))
(* x x)
x
(* y y)
y
(* z z)
z
3

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

localize38.0ms (0.4%)

Memory

-20.3MiB live, 106.1MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	accuracy	99.6%	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
✓	accuracy	43.4%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

25.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 11.0ms

ival-mult: 5.0ms (46.9% of total)

ival-div: 2.0ms (18.8% of total)

ival-add: 2.0ms (18.8% of total)

ival-sqrt: 2.0ms (18.8% of total)

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

exact: 0.0ms (0% of total)

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

series14.0ms (0.1%)

Memory

4.5MiB live, 42.4MiB allocated

Counts

5 → 144

Calls

Call 1

Inputs
#<alt (+ (+ (* x x) (* y y)) (* z z))>
#<alt (+ (* x x) (* y y))>
#<alt (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))>
#<alt (/ (+ (+ (* x x) (* y y)) (* z z)) 3)>
#<alt (* x x)>

Outputs
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))>
#<alt (+ (pow x 2) (pow z 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (+ (pow x 2) (+ (pow y 2) (pow z 2)))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))>
#<alt (pow y 2)>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))>
#<alt (pow x 2)>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (+ (pow x 2) (pow y 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))>
#<alt (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))>
#<alt (+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))))>
#<alt (+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))>
#<alt (+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))>
#<alt (* x (sqrt 1/3))>
#<alt (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* x (sqrt 1/3)))>
#<alt (* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))>
#<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)))))))>
#<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))))))))>
#<alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))>
#<alt (+ (* 1/2 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))))>
#<alt (+ (* (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)))))))))>
#<alt (+ (* (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))))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))>
#<alt (* 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))))))>
#<alt (* 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)))))))>
#<alt (* -1 (* y (sqrt 1/3)))>
#<alt (* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))>
#<alt (* -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)))))))>
#<alt (* -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))))))))>
#<alt (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))>
#<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)))))>
#<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)))))))))>
#<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))))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))>
#<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))))))>
#<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)))))))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))>
#<alt (* -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)))))))>
#<alt (* -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))))))))>
#<alt (* 1/3 (+ (pow y 2) (pow z 2)))>
#<alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))>
#<alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))>
#<alt (+ (* 1/3 (+ (pow y 2) (pow z 2))) (* 1/3 (pow x 2)))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* 1/3 (pow x 2))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* (pow x 2) (+ 1/3 (* 1/3 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))>
#<alt (* 1/3 (+ (pow x 2) (pow z 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow z 2))) (* 1/3 (pow y 2)))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))>
#<alt (* 1/3 (+ (pow x 2) (pow y 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (+ (pow x 2) (pow y 2))) (* 1/3 (pow z 2)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

36 calls:

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

rewrite623.0ms (6.5%)

Memory

-7.0MiB live, 563.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 524×	`accelerator-lowering-fma.f32`
4 524×	`accelerator-lowering-fma.f64`
4 260×	`-lowering-.f32`
4 260×	`-lowering-.f64`
3 048×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	58	48
2	479	48
3	6610	48
0	8491	41

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 356

Calls

Call 1

Inputs
(+ (+ (* x x) (* y y)) (* z z))
(+ (* x x) (* y y))
(sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3))
(/ (+ (+ (* x x) (* y y)) (* z z)) 3)
(* x x)

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

simplify1.2s (12.4%)

Memory

3.3MiB live, 674.3MiB allocated

Algorithm

1×	egg-herbie

Rules

13 366×	`accelerator-lowering-fma.f32`
13 366×	`accelerator-lowering-fma.f64`
5 460×	`-lowering-.f32`
5 460×	`-lowering-.f64`
3 804×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2478
1	673	2478
2	2272	2442
3	5706	2325
0	8198	2028

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval65.0ms (0.7%)

Memory: 10.6MiB live, 164.0MiB allocated
Compiler: Compiled 18 496 to 1 590 computations (91.4% saved)

prune67.0ms (0.7%)

Memory

-3.6MiB live, 195.8MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	494	6	500
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	495	6	501

Accuracy

98.7%

Counts

501 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	42.8%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
▶	42.9%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
▶	97.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	41.8%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
▶	42.9%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	42.2%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 132 to 94 computations (28.8% saved)

simplify6.0ms (0.1%)

Memory

17.3MiB live, 17.3MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Program
✓	cost-diff	(fma.f64 y y (*.f64 z z))
✓	cost-diff	(sqrt.f64 (fma.f64 y y (*.f64 z z)))
✓	cost-diff	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	cost-diff	(*.f64 z z)
✓	cost-diff	(/.f64 (*.f64 z z) #s(literal 3 binary64))
✓	cost-diff	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
✓	cost-diff	(*.f64 z z)
✓	cost-diff	(fma.f64 y y (*.f64 z z))
✓	cost-diff	(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
✓	cost-diff	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	cost-diff	(*.f64 z #s(literal 1/3 binary64))
✓	cost-diff	(.f64 z (.f64 z #s(literal 1/3 binary64)))
✓	cost-diff	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	cost-diff	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Rules

44×	`-lowering-.f32`
44×	`-lowering-.f64`
20×	`*-commutative`
20×	`accelerator-lowering-fma.f32`
20×	`accelerator-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	106
1	27	106
2	37	106
3	41	106
4	43	106
0	43	92

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* z (sqrt 1/3))
z
(sqrt 1/3)
1/3
(sqrt (* z (* z 1/3)))
(* z (* z 1/3))
z
(* z 1/3)
1/3
(sqrt (* (+ (* y y) (* z z)) 1/3))
(* (+ (* y y) (* z z)) 1/3)
(+ (* y y) (* z z))
y
(* z z)
z
1/3
(sqrt (/ (* z z) 3))
(/ (* z z) 3)
(* z z)
z
3
(* (sqrt 1/3) (sqrt (+ (* y y) (* z z))))
(sqrt 1/3)
1/3
(sqrt (+ (* y y) (* z z)))
(+ (* y y) (* z z))
y
(* z z)
z

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

localize79.0ms (0.8%)

Memory

-14.9MiB live, 133.5MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.4%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	accuracy	43.1%	(sqrt.f64 (fma.f64 y y (*.f64 z z)))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.6%	(/.f64 (*.f64 z z) #s(literal 3 binary64))
✓	accuracy	43.4%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.5%	(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
✓	accuracy	43.4%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	accuracy	99.9%	(.f64 z (.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.4%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	43.4%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.5%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Samples

41.0ms

256×

valid

Compiler

Compiled 102 to 21 computations (79.4% saved)

Precisions

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

ival-mult: 10.0ms (36.3% of total)

ival-sqrt: 8.0ms (29% of total)

const: 6.0ms (21.8% of total)

ival-div: 2.0ms (7.3% of total)

ival-add: 1.0ms (3.6% of total)

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

exact: 0.0ms (0% of total)

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

series11.0ms (0.1%)

Memory

22.4MiB live, 22.4MiB allocated

Counts

13 → 204

Calls

Call 1

Inputs
#<alt (* z (sqrt 1/3))>
#<alt (sqrt 1/3)>
#<alt (sqrt (* z (* z 1/3)))>
#<alt (* z (* z 1/3))>
#<alt (* z 1/3)>
#<alt (sqrt (* (+ (* y y) (* z z)) 1/3))>
#<alt (* (+ (* y y) (* z z)) 1/3)>
#<alt (+ (* y y) (* z z))>
#<alt (* z z)>
#<alt (sqrt (/ (* z z) 3))>
#<alt (/ (* z z) 3)>
#<alt (* (sqrt 1/3) (sqrt (+ (* y y) (* z z))))>
#<alt (sqrt (+ (* y y) (* z z)))>

Outputs
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* 1/3 z)>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/8 (/ (* (pow y 2) (sqrt 1/3)) (pow z 3))) (* 1/2 (/ (sqrt 1/3) z)))))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (* (pow y 2) (+ (* -1/8 (/ (sqrt 1/3) (pow z 3))) (* 1/16 (/ (* (pow y 2) (sqrt 1/3)) (pow z 5))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (sqrt 1/3)))>
#<alt (* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/8 (/ (* (pow z 2) (sqrt 1/3)) (pow y 3))) (* 1/2 (/ (sqrt 1/3) y)))))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (* (pow z 2) (+ (* -1/8 (/ (sqrt 1/3) (pow y 3))) (* 1/16 (/ (* (pow z 2) (sqrt 1/3)) (pow y 5))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))))>
#<alt (* 1/3 (pow z 2))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* 1/3 (pow y 2))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (pow z 2)>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))>
#<alt (pow y 2)>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (+ (pow y 2) (pow z 2))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (pow z 2)>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/8 (/ (* (pow y 2) (sqrt 1/3)) (pow z 3))) (* 1/2 (/ (sqrt 1/3) z)))))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (* (pow y 2) (+ (* -1/8 (/ (sqrt 1/3) (pow z 3))) (* 1/16 (/ (* (pow y 2) (sqrt 1/3)) (pow z 5))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (sqrt 1/3)))>
#<alt (* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/8 (/ (* (pow z 2) (sqrt 1/3)) (pow y 3))) (* 1/2 (/ (sqrt 1/3) y)))))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (* (pow z 2) (+ (* -1/8 (/ (sqrt 1/3) (pow y 3))) (* 1/16 (/ (* (pow z 2) (sqrt 1/3)) (pow y 5))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))>
#<alt (+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))>
#<alt y>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))>
#<alt (+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 z)>
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))>

Calls

51 calls:

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

rewrite775.0ms (8.1%)

Memory

-42.1MiB live, 486.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

3 442×	`-lowering-.f32`
3 442×	`-lowering-.f64`
3 316×	`accelerator-lowering-fma.f32`
3 316×	`accelerator-lowering-fma.f64`
2 490×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	74
1	63	74
2	318	74
3	2427	74
0	8203	59

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 839

Calls

Call 1

Inputs
(* z (sqrt 1/3))
(sqrt 1/3)
(sqrt (* z (* z 1/3)))
(* z (* z 1/3))
(* z 1/3)
(sqrt (* (+ (* y y) (* z z)) 1/3))
(* (+ (* y y) (* z z)) 1/3)
(+ (* y y) (* z z))
(* z z)
(sqrt (/ (* z z) 3))
(/ (* z z) 3)
(* (sqrt 1/3) (sqrt (+ (* y y) (* z z))))
(sqrt (+ (* y y) (* z z)))

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

simplify944.0ms (9.9%)

Memory

6.1MiB live, 520.5MiB allocated

Algorithm

1×	egg-herbie

Rules

12 064×	`accelerator-lowering-fma.f32`
12 064×	`accelerator-lowering-fma.f64`
5 150×	`-lowering-.f32`
5 150×	`-lowering-.f64`
2 578×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	200	2204
1	619	2204
2	2089	2202
3	6045	2178
0	8081	2048

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

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

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

eval156.0ms (1.6%)

Memory: 4.3MiB live, 326.1MiB allocated
Compiler: Compiled 32 602 to 2 511 computations (92.3% saved)

prune121.0ms (1.3%)

Memory

-2.0MiB live, 315.3MiB allocated

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	1 306	7	1 313
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	1 309	10	1 319

Accuracy

100.0%

Counts

1 319 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.3%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
▶	96.5%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
	96.7%	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
	7.4%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))
▶	99.4%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	97.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	42.9%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
✓	42.9%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	41.8%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	42.2%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 178 to 135 computations (24.2% saved)

simplify7.0ms (0.1%)

Memory

11.5MiB live, 11.5MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(.f64 #s(literal 1/3 binary64) (.f64 y y))
✓	cost-diff	0	(*.f64 z z)
✓	cost-diff	0	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
✓	cost-diff	320	(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y)))
✓	cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	320	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
✓	cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
✓	cost-diff	0	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(*.f64 z z)
✓	cost-diff	0	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	cost-diff	5120	(hypot.f64 z y)

Rules

64×	`-lowering-.f32`
64×	`-lowering-.f64`
28×	`accelerator-lowering-fma.f32`
28×	`accelerator-lowering-fma.f64`
20×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	98
1	34	94
2	44	94
3	60	94
4	60	94
0	60	82

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sqrt 1/3) (sqrt (+ (* z z) (* y y))))
(sqrt 1/3)
1/3
(sqrt (+ (* z z) (* y y)))
z
y
(sqrt (* (* z z) 1/3))
(* (* z z) 1/3)
(* z z)
z
1/3
(/ z (sqrt 3))
z
(sqrt 3)
3
(* (/ 1 (sqrt 3)) z)
(/ 1 (sqrt 3))
1
(sqrt 3)
3
z
(sqrt (+ (* (* z z) 1/3) (* 1/3 (* y y))))
(+ (* (* z z) 1/3) (* 1/3 (* y y)))
(* z z)
z
1/3
(* 1/3 (* y y))
(* y y)
y

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

localize75.0ms (0.8%)

Memory

14.8MiB live, 130.2MiB allocated

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	99.5%	(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y)))
✓	accuracy	99.3%	(.f64 #s(literal 1/3 binary64) (.f64 y y))
✓	accuracy	43.4%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.5%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.4%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.5%	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	accuracy	43.4%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(hypot.f64 z y)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.4%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))

Samples

51.0ms

256×

valid

Compiler

Compiled 90 to 22 computations (75.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

ival-div: 8.0ms (22.3% of total)

ival-mult: 8.0ms (22.3% of total)

ival-sqrt: 7.0ms (19.5% of total)

const: 7.0ms (19.5% of total)

ival-hypot: 4.0ms (11.2% of total)

ival-add: 1.0ms (2.8% of total)

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

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

exact: 0.0ms (0% of total)

series15.0ms (0.2%)

Memory

-19.8MiB live, 17.5MiB allocated

Counts

14 → 180

Calls

Call 1

Inputs
#<alt (sqrt (+ (* z z) (* y y)))>
#<alt (* (sqrt 1/3) (sqrt (+ (* z z) (* y y))))>
#<alt (sqrt 1/3)>
#<alt (sqrt (* (* z z) 1/3))>
#<alt (* (* z z) 1/3)>
#<alt (* z z)>
#<alt (/ z (sqrt 3))>
#<alt (sqrt 3)>
#<alt (* (/ 1 (sqrt 3)) z)>
#<alt (/ 1 (sqrt 3))>
#<alt (+ (* (* z z) 1/3) (* 1/3 (* y y)))>
#<alt (sqrt (+ (* (* z z) 1/3) (* 1/3 (* y y))))>
#<alt (* 1/3 (* y y))>
#<alt (* y y)>

Outputs
#<alt y>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))>
#<alt (+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 z)>
#<alt (* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))>
#<alt (* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))>
#<alt (+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 y)>
#<alt (* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))>
#<alt (* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/8 (/ (* (pow z 2) (sqrt 1/3)) (pow y 3))) (* 1/2 (/ (sqrt 1/3) y)))))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (* (pow z 2) (+ (* -1/8 (/ (sqrt 1/3) (pow y 3))) (* 1/16 (/ (* (pow z 2) (sqrt 1/3)) (pow y 5))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/8 (/ (* (pow y 2) (sqrt 1/3)) (pow z 3))) (* 1/2 (/ (sqrt 1/3) z)))))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (* (pow y 2) (+ (* -1/8 (/ (sqrt 1/3) (pow z 3))) (* 1/16 (/ (* (pow y 2) (sqrt 1/3)) (pow z 5))))))))>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (sqrt 1/3)))>
#<alt (* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow z 4) (sqrt 1/3)) (pow y 4))) (+ (* 1/16 (/ (* (pow z 6) (sqrt 1/3)) (pow y 6))) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (* 1/3 (pow z 2))>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (pow z 2)>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (* 1/3 (pow y 2))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* 1/3 (pow z 2))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))>
#<alt (* 1/3 (pow z 2))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* 1/3 (pow y 2))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (sqrt 1/3))>
#<alt (+ (* 1/6 (/ (pow z 2) (* y (sqrt 1/3)))) (* y (sqrt 1/3)))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/72 (/ (pow z 2) (* (pow y 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))>
#<alt (+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* (pow z 2) (- (* 1/432 (/ (pow z 2) (* (pow y 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow y 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* y (sqrt 1/3)))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))>
#<alt (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<alt (* -1 (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))))>
#<alt (* -1 (* z (+ (sqrt 1/3) (+ (* -1/72 (/ (pow y 4) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow y 6) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))))>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* -1/72 (/ (pow y 2) (* (pow z 3) (pow (sqrt 1/3) 3)))) (* 1/6 (/ 1 (* z (sqrt 1/3)))))))>
#<alt (+ (* z (sqrt 1/3)) (* (pow y 2) (+ (* (pow y 2) (- (* 1/432 (/ (pow y 2) (* (pow z 5) (pow (sqrt 1/3) 5)))) (* 1/72 (/ 1 (* (pow z 3) (pow (sqrt 1/3) 3)))))) (* 1/6 (/ 1 (* z (sqrt 1/3)))))))>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))>
#<alt (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow z 6) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))>
#<alt (* -1 (* y (sqrt 1/3)))>
#<alt (* -1 (* y (+ (sqrt 1/3) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))>
#<alt (* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow z 6) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (* 1/3 (pow y 2))>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>
#<alt (pow y 2)>

Calls

45 calls:

Time	Variable		Point	Expression
2.0ms	z	@	0	(+ (* (* z z) 1/3) (* 1/3 (* y y)))
1.0ms	z	@	inf	(/ z (sqrt 3))
1.0ms	z	@	0	(/ z (sqrt 3))
0.0ms	z	@	inf	(sqrt (+ (* (* z z) 1/3) (* 1/3 (* y y))))
0.0ms	y	@	0	(sqrt (+ (* (* z z) 1/3) (* 1/3 (* y y))))

rewrite692.0ms (7.2%)

Memory

29.0MiB live, 597.7MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 864×	`accelerator-lowering-fma.f32`
7 864×	`accelerator-lowering-fma.f64`
4 824×	`-lowering-.f32`
4 824×	`-lowering-.f64`
2 468×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	77
1	83	73
2	530	72
3	4813	72
0	9130	58

Stop Event

1×	iter limit
1×	node limit

Counts

14 → 484

Calls

Call 1

Inputs
(sqrt (+ (* z z) (* y y)))
(* (sqrt 1/3) (sqrt (+ (* z z) (* y y))))
(sqrt 1/3)
(sqrt (* (* z z) 1/3))
(* (* z z) 1/3)
(* z z)
(/ z (sqrt 3))
(sqrt 3)
(* (/ 1 (sqrt 3)) z)
(/ 1 (sqrt 3))
(+ (* (* z z) 1/3) (* 1/3 (* y y)))
(sqrt (+ (* (* z z) 1/3) (* 1/3 (* y y))))
(* 1/3 (* y y))
(* y y)

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

simplify474.0ms (5%)

Memory

9.1MiB live, 639.0MiB allocated

Algorithm

1×	egg-herbie

Rules

13 772×	`accelerator-lowering-fma.f32`
13 772×	`accelerator-lowering-fma.f64`
6 578×	`-lowering-.f32`
6 578×	`-lowering-.f64`
4 256×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	284	2164
1	878	2164
2	3181	2142
0	8462	2018

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

Outputs
y
(+ y (* 1/2 (/ (pow z 2) y)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 z z) y) y)
(+ y (* (pow z 2) (+ (* -1/8 (/ (pow z 2) (pow y 3))) (* 1/2 (/ 1 y)))))
(fma.f64 (.f64 z z) (fma.f64 (.f64 z z) (/.f64 #s(literal -1/8 binary64) (.f64 y (.f64 y y))) (/.f64 #s(literal 1/2 binary64) y)) y)
(+ y (* (pow z 2) (+ (* (pow z 2) (- (* 1/16 (/ (pow z 2) (pow y 5))) (* 1/8 (/ 1 (pow y 3))))) (* 1/2 (/ 1 y)))))
(fma.f64 (.f64 z z) (fma.f64 (.f64 z z) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 z z) (pow.f64 y #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 y (*.f64 y y)))) (/.f64 #s(literal 1/2 binary64) y)) y)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(fma.f64 (/.f64 (.f64 y y) (.f64 z z)) (*.f64 #s(literal 1/2 binary64) z) z)
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))))
(fma.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) (.f64 z z)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) (.f64 y y))) (.f64 (.f64 z z) (*.f64 z z)))) z)
(* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) (.f64 z z)) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 z #s(literal 6 binary64))))) z)
(* -1 z)
(neg.f64 z)
(* -1 (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2))))))
(fma.f64 (/.f64 (.f64 z (.f64 y y)) (*.f64 z z)) #s(literal -1/2 binary64) (neg.f64 z))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2)))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) (.f64 z z)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 z z) (*.f64 z z))) #s(literal 1 binary64))) (neg.f64 z))
(* -1 (* z (+ 1 (+ (* -1/8 (/ (pow y 4) (pow z 4))) (+ (* 1/16 (/ (pow y 6) (pow z 6))) (* 1/2 (/ (pow y 2) (pow z 2))))))))
(neg.f64 (fma.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) (.f64 z z)) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 y #s(literal 6 binary64))) (pow.f64 z #s(literal 6 binary64))))) z))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z)
(+ z (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 3))) (* 1/2 (/ 1 z)))))
(fma.f64 (.f64 y y) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 y y) (.f64 z (.f64 z z))) (/.f64 #s(literal 1/2 binary64) z)) z)
(+ z (* (pow y 2) (+ (* (pow y 2) (- (* 1/16 (/ (pow y 2) (pow z 5))) (* 1/8 (/ 1 (pow z 3))))) (* 1/2 (/ 1 z)))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 y y) (pow.f64 z #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 z (*.f64 z z)))) (/.f64 #s(literal 1/2 binary64) z)) z)
y
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
(fma.f64 y (/.f64 (.f64 #s(literal 1/2 binary64) (.f64 z z)) (*.f64 y y)) y)
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2))))))
(fma.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 z z) (.f64 y y)) (/.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 z z) (.f64 z z))) (.f64 (.f64 y y) (*.f64 y y)))) y)
(* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2)))))))
(fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (.f64 y y) (.f64 y y))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 z z) (.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64))))) y)
(* -1 y)
(neg.f64 y)
(* -1 (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2))))))
(fma.f64 (/.f64 (.f64 y (.f64 z z)) (*.f64 y y)) #s(literal -1/2 binary64) (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (* 1/2 (/ (pow z 2) (pow y 2)))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (.f64 y y) (.f64 y y))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 z z) (*.f64 y y)) #s(literal 1 binary64))) (neg.f64 y))
(* -1 (* y (+ 1 (+ (* -1/8 (/ (pow z 4) (pow y 4))) (+ (* 1/16 (/ (pow z 6) (pow y 6))) (* 1/2 (/ (pow z 2) (pow y 2))))))))
(neg.f64 (fma.f64 y (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (.f64 y y) (.f64 y y))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 z z) (.f64 y y)) (/.f64 (*.f64 #s(literal 1/16 binary64) (pow.f64 z #s(literal 6 binary64))) (pow.f64 y #s(literal 6 binary64))))) y))
(* y (sqrt 1/3))
(*.f64 y (sqrt.f64 #s(literal 1/3 binary64)))
(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
(fma.f64 y (sqrt.f64 #s(literal 1/3 binary64)) (.f64 (.f64 z z) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* -1/8 (/ (* (pow z 2) (sqrt 1/3)) (pow y 3))) (* 1/2 (/ (sqrt 1/3) y)))))
(fma.f64 (.f64 z z) (fma.f64 z (/.f64 (.f64 z (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 y (.f64 y y))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
(+ (* y (sqrt 1/3)) (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (* (pow z 2) (+ (* -1/8 (/ (sqrt 1/3) (pow y 3))) (* 1/16 (/ (* (pow z 2) (sqrt 1/3)) (pow y 5))))))))
(fma.f64 (.f64 z z) (fma.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y) (.f64 (.f64 z z) (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/16 binary64)) (pow.f64 y #s(literal 5 binary64))) (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 y (.f64 y y)))))) (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
(* z (sqrt 1/3))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 z z) (*.f64 z z))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))
(.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))))))
(* -1 (* z (sqrt 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(.f64 (neg.f64 z) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))))
(.f64 (neg.f64 z) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 z z) (*.f64 z z))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (pow y 4) (sqrt 1/3)) (pow z 4))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))))
(.f64 (neg.f64 z) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 z #s(literal 6 binary64)))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))))))
(* z (sqrt 1/3))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
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(neg.f64 (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (+ (sqrt 1/3) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))
(.f64 (neg.f64 y) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 z z) (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3))))))))
(.f64 y (neg.f64 (fma.f64 #s(literal -1/24 binary64) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64)))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 z z) (.f64 y (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow z 4) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow z 6) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (pow z 2) (* (pow y 2) (sqrt 1/3)))))))))
(.f64 (neg.f64 y) (fma.f64 #s(literal 1/6 binary64) (/.f64 (.f64 z z) (.f64 y (.f64 y (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/432 binary64) (/.f64 (pow.f64 z #s(literal 6 binary64)) (.f64 (pow.f64 y #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64)))) (fma.f64 #s(literal -1/24 binary64) (/.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 (.f64 (.f64 y y) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))))))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(* 1/3 (pow y 2))
(.f64 y (.f64 y #s(literal 1/3 binary64)))
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)
(pow y 2)
(*.f64 y y)

eval107.0ms (1.1%)

Memory: 2.5MiB live, 152.7MiB allocated
Compiler: Compiled 13 574 to 1 503 computations (88.9% saved)

prune80.0ms (0.8%)

Memory

-30.9MiB live, 179.5MiB allocated

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	731	2	733
Fresh	1	1	2
Picked	0	5	5
Done	0	3	3
Total	732	11	743

Accuracy

100.0%

Counts

743 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.0%	(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
▶	96.2%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	97.3%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	96.5%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
▶	7.4%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	97.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	42.9%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
✓	42.9%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	41.8%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	42.2%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 118 to 87 computations (26.3% saved)

simplify31.0ms (0.3%)

Memory

17.7MiB live, 56.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	cost-diff	0	(*.f64 y #s(literal 1/6 binary64))
✓	cost-diff	0	(/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
✓	cost-diff	0	(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
✓	cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	cost-diff	0	(/.f64 (*.f64 z #s(literal 1/2 binary64)) y)
✓	cost-diff	0	(fma.f64 z (/.f64 (*.f64 z #s(literal 1/2 binary64)) y) y)
✓	cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))

Rules

676×	`-lowering-.f32`
676×	`-lowering-.f64`
412×	`times-frac`
266×	`associate-l`
190×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	86
1	57	86
2	122	86
3	242	86
4	512	86
5	768	86
6	835	86
7	847	86
8	847	86
9	847	86
0	847	83

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (sqrt 1/3) (+ (* z (/ (* z 1/2) y)) y))
(sqrt 1/3)
1/3
(+ (* z (/ (* z 1/2) y)) y)
z
(/ (* z 1/2) y)
(* z 1/2)
1/2
y
(/ z (/ 1 (/ 1 (sqrt 3))))
z
(/ 1 (/ 1 (sqrt 3)))
1
(/ 1 (sqrt 3))
(sqrt 3)
3
(+ (* y (/ (* y 1/6) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
y
(/ (* y 1/6) (* z (sqrt 1/3)))
(* y 1/6)
1/6
(* z (sqrt 1/3))
z
(sqrt 1/3)
1/3

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

localize127.0ms (1.3%)

Memory

-0.8MiB live, 152.8MiB allocated

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(*.f64 y #s(literal 1/6 binary64))
✓	accuracy	99.5%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.4%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(*.f64 z #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.9%	(fma.f64 z (/.f64 (*.f64 z #s(literal 1/2 binary64)) y) y)
✓	accuracy	99.7%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))

Samples

43.0ms

256×

valid

Compiler

Compiled 93 to 25 computations (73.1% saved)

Precisions

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

ival-div: 8.0ms (27.5% of total)

ival-mult: 8.0ms (27.5% of total)

const: 6.0ms (20.6% of total)

ival-sqrt: 4.0ms (13.7% of total)

ival-add: 2.0ms (6.9% of total)

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

exact: 0.0ms (0% of total)

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

series20.0ms (0.2%)

Memory

3.6MiB live, 39.4MiB allocated

Counts

13 → 168

Calls

Call 1

Inputs
#<alt (* (sqrt 1/3) (+ (* z (/ (* z 1/2) y)) y))>
#<alt (sqrt 1/3)>
#<alt (+ (* z (/ (* z 1/2) y)) y)>
#<alt (/ (* z 1/2) y)>
#<alt (/ 1 (/ 1 (sqrt 3)))>
#<alt (/ z (/ 1 (/ 1 (sqrt 3))))>
#<alt (/ 1 (sqrt 3))>
#<alt (sqrt 3)>
#<alt (+ (* y (/ (* y 1/6) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))>
#<alt (/ (* y 1/6) (* z (sqrt 1/3)))>
#<alt (* y 1/6)>
#<alt (* z (sqrt 1/3))>
#<alt (* z 1/2)>

Outputs
#<alt (* y (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))>
#<alt (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))>
#<alt (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))>
#<alt (/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)>
#<alt (/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)>
#<alt (/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)>
#<alt (* y (sqrt 1/3))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))>
#<alt (* y (sqrt 1/3))>
#<alt (* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt (* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))>
#<alt y>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (+ y (* 1/2 (/ (pow z 2) y)))>
#<alt (* 1/2 (/ (pow z 2) y))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* 1/2 (/ (pow z 2) y))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))>
#<alt (* 1/2 (/ (pow z 2) y))>
#<alt (/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)>
#<alt (/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)>
#<alt (/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)>
#<alt y>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt (* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))>
#<alt y>
#<alt (* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))>
#<alt (* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))>
#<alt (* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (* 1/2 (/ z y))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (/ z (sqrt 3))>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))>
#<alt (+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))>
#<alt (+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))>
#<alt (* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))>
#<alt (/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (* z (sqrt 1/3))>
#<alt (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))>
#<alt (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))>
#<alt (* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 (/ y (* z (sqrt 1/3))))>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* 1/6 y)>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>
#<alt (* 1/2 z)>

Calls

42 calls:

Time	Variable		Point	Expression
6.0ms	y	@	inf	(/ (* y 1/6) (* z (sqrt 1/3)))
1.0ms	z	@	inf	(* (sqrt 1/3) (+ (* z (/ (* z 1/2) y)) y))
1.0ms	y	@	inf	(* (sqrt 1/3) (+ (* z (/ (* z 1/2) y)) y))
1.0ms	y	@	inf	(+ (* y (/ (* y 1/6) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
1.0ms	z	@	0	(/ (* y 1/6) (* z (sqrt 1/3)))

rewrite850.0ms (8.9%)

Memory

-21.7MiB live, 643.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

8 376×	`accelerator-lowering-fma.f32`
8 376×	`accelerator-lowering-fma.f64`
6 116×	`-lowering-.f32`
6 116×	`-lowering-.f64`
3 274×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	73
1	120	72
2	768	72
3	7443	72
0	8637	69

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 575

Calls

Call 1

Inputs
(* (sqrt 1/3) (+ (* z (/ (* z 1/2) y)) y))
(sqrt 1/3)
(+ (* z (/ (* z 1/2) y)) y)
(/ (* z 1/2) y)
(/ 1 (/ 1 (sqrt 3)))
(/ z (/ 1 (/ 1 (sqrt 3))))
(/ 1 (sqrt 3))
(sqrt 3)
(+ (* y (/ (* y 1/6) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(/ (* y 1/6) (* z (sqrt 1/3)))
(* y 1/6)
(* z (sqrt 1/3))
(* z 1/2)

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

simplify350.0ms (3.7%)

Memory

-5.6MiB live, 516.8MiB allocated

Algorithm

1×	egg-herbie

Rules

9 368×	`accelerator-lowering-fma.f32`
9 368×	`accelerator-lowering-fma.f64`
4 466×	`-lowering-.f32`
4 466×	`-lowering-.f64`
3 292×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	85	1308
1	233	1299
2	658	1299
3	2430	1254
4	4592	1254
0	8119	1200

Stop Event

1×	iter limit
1×	node limit

Counts

168 → 168

Calls

Call 1

Inputs
(* y (sqrt 1/3))
(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
(* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ (sqrt 1/3) y)) (/ (* y (sqrt 1/3)) (pow z 2))))
(* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y))
(/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)
(/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)
(/ (+ (* 1/2 (* (pow z 2) (sqrt 1/3))) (* (pow y 2) (sqrt 1/3))) y)
(* y (sqrt 1/3))
(* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))
(* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))
(* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2)))))
(* y (sqrt 1/3))
(* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))
(* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))
(* -1 (* y (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))
y
(+ y (* 1/2 (/ (pow z 2) y)))
(+ y (* 1/2 (/ (pow z 2) y)))
(+ y (* 1/2 (/ (pow z 2) y)))
(* 1/2 (/ (pow z 2) y))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* 1/2 (/ (pow z 2) y))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* (pow z 2) (+ (* 1/2 (/ 1 y)) (/ y (pow z 2))))
(* 1/2 (/ (pow z 2) y))
(/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)
(/ (+ (* 1/2 (pow z 2)) (pow y 2)) y)
y
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
(* y (+ 1 (* 1/2 (/ (pow z 2) (pow y 2)))))
y
(* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))
(* -1 (* y (- (* -1/2 (/ (pow z 2) (pow y 2))) 1)))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(* 1/2 (/ z y))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* z (sqrt 1/3))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(+ (* 1/6 (/ (pow y 2) (* z (sqrt 1/3)))) (* z (sqrt 1/3)))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/6 (/ 1 (* z (sqrt 1/3)))) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/6 (/ (pow y 2) (* z (sqrt 1/3))))
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/6 (/ (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (* 1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3))))))
(* z (sqrt 1/3))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/6 (/ (pow y 2) (* (pow z 2) (sqrt 1/3)))))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 (/ y (* z (sqrt 1/3))))
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* 1/6 y)
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)
(* 1/2 z)

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

eval134.0ms (1.4%)

Memory: 8.2MiB live, 199.5MiB allocated
Compiler: Compiled 17 590 to 1 632 computations (90.7% saved)

prune133.0ms (1.4%)

Memory

2.1MiB live, 213.6MiB allocated

Pruning

11 alts after pruning (1 fresh and 10 done)

	Pruned	Kept	Total
New	789	1	790
Fresh	0	0	0
Picked	1	2	3
Done	0	8	8
Total	790	11	801

Accuracy

100.0%

Counts

801 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.0%	(fma.f64 (/.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (.f64 y #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))
✓	96.2%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	97.3%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	96.5%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
✓	7.4%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))
✓	99.4%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	97.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	42.9%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
✓	42.9%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	41.8%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	42.2%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 273 to 143 computations (47.6% saved)

regimes80.0ms (0.8%)

Memory

-20.5MiB live, 96.1MiB allocated

Counts

17 → 1

Calls

Call 1

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

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

Calls

10 calls:

23.0ms	x
17.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
6.0ms	(*.f64 z z)
5.0ms	y
5.0ms	z

Results

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

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes50.0ms (0.5%)

Memory

19.4MiB live, 135.2MiB allocated

Counts

16 → 1

Calls

Call 1

Inputs
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 #s(literal 1/3 binary64) (*.f64 y y))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z (/.f64 (.f64 z #s(literal 1/2 binary64)) y) y))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 (/.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (.f64 y #s(literal 1/6 binary64)) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z))

Outputs
(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Calls

10 calls:

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

Results

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

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes50.0ms (0.5%)

Memory

-11.2MiB live, 101.6MiB allocated

Accuracy

Total -57.9b remaining (-3421.9%)

Threshold costs -57.9b (-3421.9%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

10 calls:

8.0ms	(*.f64 y y)
5.0ms	(*.f64 x x)
4.0ms	z
4.0ms	x
4.0ms	y

Results

Accuracy	Segments	Branch
97.4%	1	`x`
97.4%	1	`y`
97.4%	1	`z`
97.4%	1	`(*.f64 x x)`
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)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify7.0ms (0.1%)

Memory

19.0MiB live, 19.0MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	14	24

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

(fma.f64 y (/.f64 (*.f64 y #s(literal 1/6 binary64)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

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

Outputs
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.f64 z (sqrt.f64 #s(literal 1/3 binary64)))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(fma.f64 y (/.f64 (.f64 y #s(literal 1/6 binary64)) (.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 (sqrt.f64 #s(literal 1/3 binary64)) z)

soundness577.0ms (6%)

Memory

-9.9MiB live, 548.8MiB allocated

Rules

13 772×	`accelerator-lowering-fma.f32`
13 772×	`accelerator-lowering-fma.f64`
13 366×	`accelerator-lowering-fma.f32`
13 366×	`accelerator-lowering-fma.f64`
6 578×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	74
1	63	74
2	318	74
3	2427	74
0	8203	59
0	284	2164
1	878	2164
2	3181	2142
0	8462	2018
0	230	2478
1	673	2478
2	2272	2442
3	5706	2325
0	8198	2028

Stop Event

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

Compiler

Compiled 99 to 61 computations (38.4% saved)

preprocess247.0ms (2.6%)

Memory: 4.0MiB live, 160.0MiB allocated
Compiler: Compiled 374 to 260 computations (30.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	22	86
1	57	86
2	122	86
3	242	86
4	512	86
5	768	86
6	835	86
7	847	86
8	847	86
9	847	86
0	847	83

Iter	Nodes	Cost
0	22	86
1	57	86
2	122	86
3	242	86
4	512	86
5	768	86
6	835	86
7	847	86
8	847	86
9	847	86
0	847	83

analyze1.0ms (0%)

sample1.2s (12.5%)

preprocess39.0ms (0.4%)

explain137.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize38.0ms (0.4%)

series14.0ms (0.1%)

rewrite623.0ms (6.5%)

simplify1.2s (12.4%)

eval65.0ms (0.7%)

prune67.0ms (0.7%)

simplify6.0ms (0.1%)

localize79.0ms (0.8%)

series11.0ms (0.1%)

rewrite775.0ms (8.1%)

simplify944.0ms (9.9%)

eval156.0ms (1.6%)

prune121.0ms (1.3%)

simplify7.0ms (0.1%)

localize75.0ms (0.8%)

series15.0ms (0.2%)

rewrite692.0ms (7.2%)

simplify474.0ms (5%)

eval107.0ms (1.1%)

prune80.0ms (0.8%)

simplify31.0ms (0.3%)

localize127.0ms (1.3%)

series20.0ms (0.2%)

rewrite850.0ms (8.9%)

simplify350.0ms (3.7%)

eval134.0ms (1.4%)

prune133.0ms (1.4%)

regimes80.0ms (0.8%)

regimes50.0ms (0.5%)

regimes50.0ms (0.5%)

simplify7.0ms (0.1%)

soundness577.0ms (6%)

preprocess247.0ms (2.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	22	86
1	57	86
2	122	86
3	242	86
4	512	86
5	768	86
6	835	86
7	847	86
8	847	86
9	847	86
0	847	83