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

analyze1.0ms (0%)

Memory

3.1MiB live, 3.1MiB 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 (13.1%)

Memory

27.1MiB live, 1 247.8MiB allocated

Samples

866.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 582.0ms

ival-mult: 245.0ms (42.1% of total)

ival-add: 143.0ms (24.6% of total)

ival-div: 110.0ms (18.9% of total)

ival-sqrt: 72.0ms (12.4% of total)

ival-true: 6.0ms (1% of total)

exact: 4.0ms (0.7% of total)

ival-assert: 3.0ms (0.5% of total)

Bogosity

preprocess62.0ms (0.7%)

Memory

-11.8MiB live, 29.1MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

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

Calls

Call 1

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

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

Symmetry

(abs z)

(abs y)

(abs x)

(sort x y z)

explain980.0ms (10.5%)

Memory

14.4MiB live, 273.0MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	139	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	139
↳	`(*.f64 y y)`	overflow	44
↳	`(*.f64 x x)`	overflow	4
↳	`(*.f64 z z)`	overflow	139
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	44
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	139
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	4	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	4
↳	`(*.f64 y y)`	underflow	36
↳	`(*.f64 x x)`	underflow	152
↳	`(*.f64 z z)`	underflow	4
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	36
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	4

Confusion

	Predicted +	Predicted -
+	143	0
-	0	113

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	143	0	0
-	0	0	113

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	113
1	143

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

578.0ms

512×

valid

Compiler

Compiled 154 to 48 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 561.0ms

ival-mult: 549.0ms (97.9% of total)

ival-add: 4.0ms (0.7% of total)

ival-sqrt: 4.0ms (0.7% of total)

ival-div: 3.0ms (0.5% 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

1.9MiB live, 1.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	48.1%	(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)

simplify7.0ms (0.1%)

Memory

13.0MiB live, 13.0MiB 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×	`lower-+.f32`
20×	`lower-+.f64`
18×	`lower-fma.f64`
18×	`lower-fma.f32`
10×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize235.0ms (2.5%)

Memory

-29.0MiB live, 69.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 y y))
✓	accuracy	99.8%	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

224.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 216.0ms

ival-mult: 202.0ms (93.5% of total)

ival-div: 10.0ms (4.6% of total)

ival-add: 2.0ms (0.9% of total)

ival-sqrt: 2.0ms (0.9% of total)

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

exact: 0.0ms (0% of total)

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

series13.0ms (0.1%)

Memory

-1.5MiB live, 37.6MiB allocated

Counts

4 → 132

Calls

Call 1

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

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)))))>

Calls

33 calls:

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

rewrite374.0ms (4%)

Memory

-5.3MiB live, 646.8MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	45
0	18	45
1	65	45
2	486	45
3	6616	45
0	8497	38

Stop Event

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

Counts

4 → 350

Calls

Call 1

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

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

simplify559.0ms (6%)

Memory

1.9MiB live, 832.5MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	230	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

Outputs
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 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)))
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(*.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))))

eval61.0ms (0.7%)

Memory: -6.4MiB live, 148.3MiB allocated
Compiler: Compiled 18 234 to 1 563 computations (91.4% saved)

prune86.0ms (0.9%)

Memory

9.3MiB live, 131.3MiB allocated

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	476	6	482
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	477	6	483

Accuracy

98.4%

Counts

483 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
	47.9%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
▶	97.7%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	48.1%	(sqrt.f64 (fma.f64 (fma.f64 x x (.f64 z z)) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
▶	47.7%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
▶	48.1%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	47.7%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 140 to 96 computations (31.4% saved)

simplify9.0ms (0.1%)

Memory

20.4MiB live, 20.4MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

102×	`lower-fma.f32`
96×	`lower-fma.f64`
66×	`lower-*.f32`
52×	`lower-*.f64`
48×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	117
0	39	115
1	55	115
2	78	115
3	102	115
4	106	115
0	106	113

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize78.0ms (0.8%)

Memory

-3.3MiB live, 159.0MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	99.7%	(fma.f64 (fma.f64 x x (.f64 z z)) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 y y) #s(literal 1/3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (fma.f64 (fma.f64 x x (.f64 z z)) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.8%	(/.f64 (*.f64 z z) #s(literal 3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.7%	(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	accuracy	99.8%	(.f64 z (.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Samples

52.0ms

256×

valid

Compiler

Compiled 127 to 25 computations (80.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-mult: 16.0ms (42.3% of total)

ival-sqrt: 8.0ms (21.2% of total)

ival-add: 6.0ms (15.9% of total)

const: 5.0ms (13.2% of total)

ival-div: 2.0ms (5.3% of total)

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

exact: 0.0ms (0% of total)

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

series25.0ms (0.3%)

Memory

-28.9MiB live, 51.7MiB allocated

Counts

16 → 276

Calls

Call 1

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

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

69 calls:

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

rewrite496.0ms (5.3%)

Memory

45.7MiB live, 673.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 766×	`lower-fma.f32`
7 760×	`lower-fma.f64`
4 988×	`lower-*.f32`
4 974×	`lower-*.f64`
2 828×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
0	39	92
1	115	92
2	688	92
3	7019	92
0	8593	87

Stop Event

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

Counts

16 → 636

Calls

Call 1

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

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

simplify1.3s (14.3%)

Memory

-29.6MiB live, 733.8MiB allocated

Algorithm

1×	egg-herbie

Rules

11 080×	`lower-fma.f64`
11 080×	`lower-fma.f32`
6 062×	`lower-*.f64`
6 062×	`lower-*.f32`
4 734×	`lower-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	312	3620
1	949	3560
2	3478	3476
0	8326	3205

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(* 1/3 (pow x 2))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(* (pow x 2) (+ 1/3 (+ (* 1/3 (/ (pow y 2) (pow x 2))) (* 1/3 (/ (pow z 2) (pow x 2))))))
(+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(+ (* 1/3 (pow x 2)) (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 2))))))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 2))))))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 2))))))
(* 1/3 (pow z 2))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 2))))))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 2))))))
(* (pow z 2) (+ 1/3 (+ (* 1/3 (/ (pow x 2) (pow z 2))) (* 1/3 (/ (pow y 2) (pow z 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)))))
(sqrt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))
(+ (sqrt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))) (* 1/6 (* (pow x 2) (sqrt (/ 1 (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))))))))
(+ (sqrt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))) (* (pow x 2) (+ (* -1/72 (* (pow x 2) (sqrt (/ 1 (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 3))))) (* 1/6 (sqrt (/ 1 (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))))))))
(+ (sqrt (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))) (* (pow x 2) (+ (* 1/6 (sqrt (/ 1 (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))))) (* (pow x 2) (+ (* -1/72 (sqrt (/ 1 (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 3)))) (* 1/432 (* (pow x 2) (sqrt (/ 1 (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 5))))))))))
(* x (sqrt 1/3))
(* x (+ (sqrt 1/3) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3))))))
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 2) (* (pow x 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3)))))))
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 2) (* (pow x 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 3) (* (pow x 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3))))))))
(* -1 (* x (sqrt 1/3)))
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3)))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 2) (* (pow x 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3))))))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 2) (* (pow x 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) 3) (* (pow x 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2))) (* (pow x 2) (sqrt 1/3)))))))))
(sqrt (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))))
(+ (sqrt (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))) (* 1/6 (* (pow z 2) (sqrt (/ 1 (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))))))))
(+ (sqrt (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))) (* (pow z 2) (+ (* -1/72 (* (pow z 2) (sqrt (/ 1 (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3))))) (* 1/6 (sqrt (/ 1 (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))))))))
(+ (sqrt (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))) (* (pow z 2) (+ (* 1/6 (sqrt (/ 1 (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2)))))) (* (pow z 2) (+ (* -1/72 (sqrt (/ 1 (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3)))) (* 1/432 (* (pow z 2) (sqrt (/ 1 (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 5))))))))))
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3))))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3))))))))
(* -1 (* z (sqrt 1/3)))
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3))))))))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(+ (* 1/6 (* (/ (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) (+ (* -1/72 (* (/ (pow y 2) (pow (sqrt 1/3) 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/6 (* (/ 1 (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/6 (* (/ 1 (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/72 (* (/ 1 (pow (sqrt 1/3) 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/432 (* (/ (pow y 2) (pow (sqrt 1/3) 5)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(* y (sqrt 1/3))
(* y (+ (sqrt 1/3) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))))
(* -1 (* y (sqrt 1/3)))
(* -1 (* y (+ (sqrt 1/3) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))))
(pow z 2)
(+ (pow x 2) (pow z 2))
(+ (pow x 2) (pow z 2))
(+ (pow x 2) (pow z 2))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(pow x 2)
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(pow x 2)
(+ (pow x 2) (pow z 2))
(+ (pow x 2) (pow z 2))
(+ (pow x 2) (pow z 2))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(pow z 2)
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 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))
(* 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
(* 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)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* -1 (* z (sqrt 1/3)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* -1 (* z (sqrt 1/3)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* -1 (* z (sqrt 1/3)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* 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 (.f64 y y) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(+ (* 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 z (sqrt.f64 #s(literal 1/3 binary64)) (.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 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) 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))))))))
(fma.f64 z (sqrt.f64 #s(literal 1/3 binary64)) (.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 (.f64 #s(literal 1/16 binary64) (.f64 y y)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 z #s(literal 5 binary64))) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 z (.f64 z z)))) (*.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))))
(* 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)))))
(.f64 y (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))))
(* 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))))))
(.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))) (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (*.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64)))))
(* 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)))))))
(.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))) (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (.f64 y y)) (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 z #s(literal 6 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))))))
(* -1 (* y (sqrt 1/3)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) (pow y 2))))))
(.f64 (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 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)))))))
(.f64 (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))) (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (*.f64 y y)) (sqrt.f64 #s(literal 1/3 binary64)))) (neg.f64 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))))))))
(.f64 (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))) (fma.f64 (.f64 z z) (/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (.f64 y y)) (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 z #s(literal 6 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 y #s(literal 6 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))))) (neg.f64 y))
(* y (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)
(+ (* 1/2 (/ (* (pow z 2) (sqrt 1/3)) y)) (* y (sqrt 1/3)))
(fma.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)) (* (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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (.f64 y (.f64 y y))) (.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)) (* (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 (.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 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 y (.f64 y y)))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(* 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 (sqrt.f64 #s(literal 1/3 binary64)) y)) (.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 (.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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)) (*.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 1/2 binary64) (/.f64 (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)) (.f64 z z)) (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 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))))))
(* -1 (* z (sqrt 1/3)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) 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)))))))
(.f64 (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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) 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))) (+ (* 1/16 (/ (* (pow y 6) (sqrt 1/3)) (pow z 6))) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))))
(.f64 z (neg.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)) (.f64 z z)) (fma.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 y #s(literal 6 binary64)) (/.f64 (sqrt.f64 #s(literal 1/3 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)))))))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* (pow y 2) (+ 1/3 (* 1/3 (/ (pow z 2) (pow y 2)))))
(.f64 y (.f64 y (fma.f64 (.f64 z z) (/.f64 #s(literal 1/3 binary64) (.f64 y y)) #s(literal 1/3 binary64))))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(+ (* 1/3 (pow y 2)) (* 1/3 (pow z 2)))
(.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(* 1/3 (pow z 2))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(* (pow z 2) (+ 1/3 (* 1/3 (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (.f64 y y) (/.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/3 binary64)))
(pow z 2)
(*.f64 z z)
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(* (pow y 2) (+ 1 (/ (pow z 2) (pow y 2))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (*.f64 y y)) #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (/ (pow y 2) (pow z 2))))
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(.f64 z (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (*.f64 z z)))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))
(.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (.f64 z z))))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3))))))))
(.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/27 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 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (*.f64 z z)))))))
(* -1 (* z (sqrt 1/3)))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (neg.f64 z))
(* -1 (* z (+ (sqrt 1/3) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))
(.f64 (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (*.f64 z z)))) (neg.f64 z))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3))))))))
(.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (.f64 z z))))) (neg.f64 z))
(* -1 (* z (+ (sqrt 1/3) (+ (* -1/8 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 2) (* (pow z 4) (pow (sqrt 1/3) 3)))) (+ (* 1/16 (/ (pow (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) 3) (* (pow z 6) (pow (sqrt 1/3) 5)))) (* 1/2 (/ (+ (* 1/3 (pow x 2)) (* 1/3 (pow y 2))) (* (pow z 2) (sqrt 1/3)))))))))
(.f64 z (neg.f64 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (.f64 z z) (.f64 z z)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 #s(literal 1/27 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 (pow.f64 z #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64)))) (+.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 (.f64 #s(literal 1/6 binary64) (fma.f64 y y (.f64 x x))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (*.f64 z z))))))))
(* (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))))
(+ (* 1/6 (* (/ (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))))
(fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 #s(literal 1/6 binary64) (*.f64 y y))) (sqrt.f64 #s(literal 1/3 binary64))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/72 (* (/ (pow y 2) (pow (sqrt 1/3) 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/6 (* (/ 1 (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(fma.f64 (.f64 y y) (fma.f64 y (.f64 y (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))))) (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (sqrt.f64 #s(literal 1/3 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) (+ (* 1/6 (* (/ 1 (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/72 (* (/ 1 (pow (sqrt 1/3) 3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/432 (* (/ (pow y 2) (pow (sqrt 1/3) 5)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 #s(literal 1/432 binary64) (.f64 (/.f64 (.f64 y y) (pow.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 5 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 x x)) #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))))) (/.f64 #s(literal -1/24 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 #s(literal 1/6 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (*.f64 x x)))))
(* y (sqrt 1/3))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y)
(* y (+ (sqrt 1/3) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))
(.f64 y (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))
(.f64 y (fma.f64 #s(literal -1/72 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))))
(.f64 y (fma.f64 #s(literal 1/432 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))) (.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 -1/72 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64))))))
(* -1 (* y (sqrt 1/3)))
(neg.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))
(* -1 (* y (+ (sqrt 1/3) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))
(.f64 (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64))) (neg.f64 y))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3))))))))
(.f64 (fma.f64 #s(literal -1/72 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64)))) (neg.f64 y))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/72 (/ (pow (+ (pow x 2) (pow z 2)) 2) (* (pow y 4) (pow (sqrt 1/3) 3)))) (+ (* 1/432 (/ (pow (+ (pow x 2) (pow z 2)) 3) (* (pow y 6) (pow (sqrt 1/3) 5)))) (* 1/6 (/ (+ (pow x 2) (pow z 2)) (* (pow y 2) (sqrt 1/3)))))))))
(.f64 y (neg.f64 (fma.f64 #s(literal 1/432 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))) (.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 -1/72 binary64) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (.f64 (.f64 (.f64 y y) (.f64 y y)) (.f64 #s(literal 1/3 binary64) (sqrt.f64 #s(literal 1/3 binary64))))) (fma.f64 #s(literal 1/6 binary64) (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) y))) (sqrt.f64 #s(literal 1/3 binary64)))))))
(pow z 2)
(*.f64 z z)
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(* (pow x 2) (+ 1 (/ (pow z 2) (pow x 2))))
(.f64 (.f64 x x) (fma.f64 z (/.f64 z (*.f64 x x)) #s(literal 1 binary64)))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (/ (pow x 2) (pow z 2))))
(.f64 (.f64 z z) (fma.f64 x (/.f64 x (*.f64 z z)) #s(literal 1 binary64)))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(* 1/3 (pow y 2))
(.f64 #s(literal 1/3 binary64) (.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)
(pow y 2)
(*.f64 y y)

eval223.0ms (2.4%)

Memory: 22.3MiB live, 251.5MiB allocated
Compiler: Compiled 24 290 to 2 121 computations (91.3% saved)

prune122.0ms (1.3%)

Memory

-15.6MiB live, 276.4MiB allocated

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	966	6	972
Fresh	1	0	1
Picked	2	3	5
Done	0	0	0
Total	969	9	978

Accuracy

98.7%

Counts

978 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.7%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
▶	97.0%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
▶	97.7%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
	97.0%	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	97.7%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	48.1%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	48.1%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	47.7%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	47.7%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 152 to 117 computations (23% saved)

simplify8.0ms (0.1%)

Memory

19.9MiB live, 19.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

64×	`lower-*.f32`
50×	`lower-*.f64`
28×	`lower-fma.f32`
26×	`lower-fma.f64`
18×	`*-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	92
0	35	88
1	50	88
2	60	88
3	77	88
4	77	88
0	77	86

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

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

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

localize110.0ms (1.2%)

Memory

-29.1MiB live, 168.9MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	99.7%	(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
✓	accuracy	99.6%	(.f64 (.f64 y y) #s(literal 1/3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.4%	(*.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	99.7%	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	accuracy	48.1%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.9%	(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))

Samples

41.0ms

256×

valid

Compiler

Compiled 96 to 23 computations (76% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

ival-mult: 10.0ms (37.6% of total)

ival-sqrt: 8.0ms (30.1% of total)

const: 4.0ms (15% of total)

ival-div: 3.0ms (11.3% of total)

ival-add: 2.0ms (7.5% of total)

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

exact: 0.0ms (0% of total)

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

series9.0ms (0.1%)

Memory

28.0MiB live, 28.0MiB allocated

Counts

15 → 180

Calls

Call 1

Inputs
#<alt (.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))>
#<alt (sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))>
#<alt (*.f64 z #s(literal 1/3 binary64))>
#<alt (sqrt.f64 z)>
#<alt (sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))>
#<alt (.f64 (.f64 z z) #s(literal 1/3 binary64))>
#<alt (*.f64 z z)>
#<alt (/.f64 z (sqrt.f64 #s(literal 3 binary64)))>
#<alt (sqrt.f64 #s(literal 3 binary64))>
#<alt (*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))>
#<alt (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))>
#<alt (sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))>
#<alt (.f64 (.f64 y y) #s(literal 1/3 binary64))>
#<alt (*.f64 y y)>

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 (* -1 (* z (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* z (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* z (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* z (* (sqrt -1) (sqrt -1/3))))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* (sqrt z) (sqrt 1/3))>
#<alt (* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))>
#<alt (* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))>
#<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 (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 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
1.0ms	z	@	-inf	(* (sqrt (* z 1/3)) (sqrt z))
1.0ms	z	@	inf	(/ z (sqrt 3))
1.0ms	z	@	inf	(sqrt (+ (* (* z z) 1/3) (* (* y y) 1/3)))
0.0ms	z	@	0	(/ z (sqrt 3))
0.0ms	y	@	inf	(sqrt (+ (* (* z z) 1/3) (* (* y y) 1/3)))

rewrite349.0ms (3.8%)

Memory

-15.5MiB live, 739.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 492×	`lower-fma.f32`
5 490×	`lower-fma.f64`
4 588×	`lower-*.f32`
4 574×	`lower-*.f64`
2 442×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	75
0	35	70
1	89	67
2	398	65
3	3157	65
0	8658	60

Stop Event

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

Counts

15 → 533

Calls

Call 1

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

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 #s(literal 1/3 binary64) (*.f64 z z)))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))) (.f64 #s(literal 1/2 binary64) (log.f64 z))))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 z) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (*.f64 z z)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (log.f64 z) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (log.f64 z)))
(exp.f64 (fma.f64 (log.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z))) #s(literal 1/4 binary64) (.f64 (log.f64 (.f64 #s(literal 1/3 binary64) (*.f64 z z))) #s(literal 1/4 binary64))))
(sqrt.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 z z) (.f64 (.f64 z z) #s(literal 1/9 binary64))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z))))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
(.f64 (sqrt.f64 z) (sqrt.f64 (.f64 z #s(literal 1/3 binary64))))
(.f64 (.f64 z (sqrt.f64 #s(literal 1/3 binary64))) #s(literal 1 binary64))
(.f64 #s(literal 1 binary64) (.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)
(.f64 (pow.f64 z #s(literal 1/4 binary64)) (pow.f64 (.f64 z (.f64 (.f64 z z) #s(literal 1/9 binary64))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (.f64 z (.f64 #s(literal 1/3 binary64) (*.f64 z z))) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)) #s(literal 1/4 binary64)) (pow.f64 (.f64 #s(literal 1/3 binary64) (*.f64 z z)) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 z (.f64 (.f64 z z) #s(literal 1/9 binary64))) #s(literal 1/4 binary64)) (pow.f64 z #s(literal 1/4 binary64)))
(.f64 (pow.f64 (.f64 z (.f64 #s(literal 1/3 binary64) (.f64 z z))) #s(literal 1/4 binary64)) (pow.f64 (*.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))))
(exp.f64 (.f64 (log.f64 (pow.f64 (.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (*.f64 z z) #s(literal 1/9 binary64))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (*.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (fma.f64 #s(literal 1/2 binary64) (log.f64 z) (*.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))))
(exp.f64 (fma.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64) (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(exp.f64 (fma.f64 (log.f64 (.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64) (.f64 (log.f64 (*.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64))))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(pow.f64 (*.f64 z #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 z z) #s(literal 1/9 binary64)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (*.f64 z #s(literal 1/3 binary64))))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) #s(literal 1 binary64))
(*.f64 (sqrt.f64 z) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 z #s(literal 1/3 binary64))))
(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 z))
(.f64 (pow.f64 z #s(literal 1/4 binary64)) (.f64 (pow.f64 z #s(literal 1/4 binary64)) (sqrt.f64 #s(literal 1/3 binary64))))
(.f64 (pow.f64 (.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 z #s(literal 1/3 binary64)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (pow.f64 z #s(literal 1/4 binary64))) (pow.f64 z #s(literal 1/4 binary64)))
(exp.f64 (log.f64 (*.f64 z #s(literal 1/3 binary64))))
(*.f64 z #s(literal 1/3 binary64))
(*.f64 z (exp.f64 (log.f64 #s(literal 1/3 binary64))))
(*.f64 #s(literal 1/3 binary64) z)
(.f64 (.f64 z #s(literal 1/3 binary64)) #s(literal 1 binary64))
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(/.f64 (sqrt.f64 (.f64 (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z))))) #s(literal 1/3 binary64))) (sqrt.f64 (fma.f64 (.f64 y y) (-.f64 (.f64 y y) (.f64 z z)) (.f64 z (.f64 z (.f64 z z))))))
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(/.f64 (neg.f64 (sqrt.f64 (neg.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y))))))) (neg.f64 (sqrt.f64 (.f64 #s(literal -1/3 binary64) (.f64 (+.f64 z y) (-.f64 z y))))))
(/.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/9 binary64) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 z (.f64 z (.f64 z z))))))) (neg.f64 (sqrt.f64 (.f64 #s(literal 1/3 binary64) (-.f64 (.f64 y y) (.f64 z z))))))
(/.f64 (neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/27 binary64) (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z))))))))) (neg.f64 (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 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y))))))) (neg.f64 (neg.f64 (sqrt.f64 (.f64 #s(literal 1/3 binary64) (.f64 (+.f64 z y) (-.f64 z y)))))))
(pow.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) #s(literal -1/2 binary64))
(pow.f64 (pow.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) (.f64 #s(literal 1/3 binary64) (fma.f64 y y (*.f64 z z)))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))))) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))))
(.f64 #s(literal 1 binary64) (sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (*.f64 z z)))))
(.f64 (sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (sqrt.f64 (.f64 (.f64 #s(literal 1/3 binary64) (.f64 (+.f64 z y) (-.f64 z y))) (/.f64 #s(literal 3 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))))
(.f64 (sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z)))) (sqrt.f64 (/.f64 (.f64 #s(literal 1/3 binary64) (.f64 (+.f64 z y) (-.f64 z y))) (.f64 #s(literal 1/3 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
(.f64 (sqrt.f64 (fma.f64 y y (.f64 z z))) (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 (.f64 #s(literal 1/27 binary64) (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z))))))) (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 (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 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) (/.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 (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 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (.f64 z z))) (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 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y))))) (sqrt.f64 (/.f64 #s(literal 3 binary64) (.f64 (+.f64 z y) (-.f64 z y)))))
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(.f64 (sqrt.f64 (neg.f64 (.f64 #s(literal 1/27 binary64) (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z)))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (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 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal -1/3 binary64) (*.f64 (+.f64 z y) (-.f64 z y))))))
(.f64 (sqrt.f64 (.f64 #s(literal 1/9 binary64) (-.f64 (.f64 y (.f64 y (.f64 y y))) (.f64 z (.f64 z (.f64 z z)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 1/3 binary64) (-.f64 (.f64 y y) (*.f64 z z))))))
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(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y)))) (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y)))))) (sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 y y (*.f64 z z)))))
(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 1/27 binary64) (fma.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y))) (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z)))))) (fma.f64 (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (-.f64 (.f64 y y) (.f64 z z))) (.f64 (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (-.f64 (.f64 y y) (.f64 z z))) (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (-.f64 (.f64 y y) (.f64 z z)))) (.f64 (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z)))) (.f64 (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z)))) #s(literal 1/729 binary64)))))) (sqrt.f64 (fma.f64 (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (-.f64 (.f64 y y) (.f64 z z))) (-.f64 (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (-.f64 (.f64 y y) (.f64 z z))) (.f64 (.f64 z z) (.f64 (.f64 z z) #s(literal 1/9 binary64)))) (.f64 (.f64 (.f64 z (.f64 z (.f64 z z))) (.f64 z (.f64 z (*.f64 z z)))) #s(literal 1/81 binary64)))))
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(.f64 (sqrt.f64 (/.f64 (.f64 #s(literal 1/9 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (+.f64 z y) (-.f64 z y)))) (.f64 #s(literal 1/27 binary64) (-.f64 (.f64 (.f64 z z) (.f64 z (.f64 z (.f64 z z)))) (.f64 (.f64 y y) (.f64 y (.f64 y (.f64 y y)))))))) (sqrt.f64 (fma.f64 (.f64 z z) (.f64 (.f64 z z) #s(literal 1/9 binary64)) (.f64 (.f64 (.f64 y y) #s(literal 1/9 binary64)) (fma.f64 y y (*.f64 z z))))))
(exp.f64 (log.f64 (.f64 y (.f64 #s(literal 1/3 binary64) y))))
(exp.f64 (.f64 (log.f64 (.f64 y (*.f64 #s(literal 1/3 binary64) y))) #s(literal 1 binary64)))
(pow.f64 (.f64 y (.f64 #s(literal 1/3 binary64) y)) #s(literal 1 binary64))
(.f64 #s(literal 1/3 binary64) (.f64 y y))
(.f64 y (.f64 #s(literal 1/3 binary64) y))
(.f64 y (exp.f64 (log.f64 (.f64 #s(literal 1/3 binary64) y))))
(.f64 (.f64 y y) #s(literal 1/3 binary64))
(.f64 (.f64 y y) (exp.f64 (log.f64 #s(literal 1/3 binary64))))
(.f64 (.f64 #s(literal 1/3 binary64) y) y)
(.f64 (exp.f64 (log.f64 #s(literal 1/3 binary64))) (.f64 y y))
(.f64 (exp.f64 (log.f64 (.f64 #s(literal 1/3 binary64) y))) 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)))
(pow.f64 y #s(literal 2 binary64))
(pow.f64 (*.f64 y y) #s(literal 1 binary64))
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 y))
(*.f64 y y)

simplify464.0ms (5%)

Memory

8.0MiB live, 855.9MiB allocated

Algorithm

1×	egg-herbie

Rules

17 004×	`lower-fma.f64`
17 004×	`lower-fma.f32`
6 256×	`lower-*.f64`
6 256×	`lower-*.f32`
2 890×	`lower-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	142	1400
1	412	1400
2	1454	1376
3	5407	1346
0	8307	1298

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

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

eval92.0ms (1%)

Memory: 10.1MiB live, 239.2MiB allocated
Compiler: Compiled 17 028 to 1 578 computations (90.7% saved)

prune85.0ms (0.9%)

Memory

0.3MiB live, 237.7MiB allocated

Pruning

14 alts after pruning (6 fresh and 8 done)

	Pruned	Kept	Total
New	770	6	776
Fresh	1	0	1
Picked	0	5	5
Done	0	3	3
Total	771	14	785

Accuracy

98.7%

Counts

785 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.6%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	97.7%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
	90.2%	(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (sqrt.f64 z))
✓	97.0%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
▶	90.2%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
✓	97.7%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
▶	90.7%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
▶	91.0%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
✓	97.7%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	48.1%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	48.1%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	47.7%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	47.7%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
▶	89.5%	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Compiler

Compiled 225 to 185 computations (17.8% saved)

simplify37.0ms (0.4%)

Memory

-22.9MiB live, 56.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 z #s(literal 1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	cost-diff	640	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
✓	cost-diff	18624	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
✓	cost-diff	0	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
✓	cost-diff	320	(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
✓	cost-diff	12800	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
✓	cost-diff	0	(*.f64 z #s(literal 1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	cost-diff	640	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
✓	cost-diff	12480	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
✓	cost-diff	0	(log.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))
✓	cost-diff	640	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
✓	cost-diff	12480	(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #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))))

Rules

308×	`lower-*.f32`
304×	`lower-fma.f64`
304×	`lower-fma.f32`
298×	`lower-*.f64`
192×	`lower-pow.f32`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	28	147
0	50	135
1	68	122
2	89	116
3	106	115
4	144	115
5	172	115
6	200	115
7	230	112
8	299	112
9	380	112
10	500	112
11	665	112
12	752	112
13	763	112
0	763	112

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
z
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))))
(.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))
#s(literal 1/2 binary64)
(log.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(sqrt.f64 z)
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
(*.f64 #s(literal 1/2 binary64) (log.f64 z))
#s(literal 1/2 binary64)
(log.f64 z)
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
z
#s(literal -1 binary64)
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(exp.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(log.f64 z)

Outputs
(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
z
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(literal 3 binary64))
#s(literal 1 binary64)
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
(sqrt.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))
#s(literal 1/2 binary64)
(log.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(sqrt.f64 z)
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(sqrt.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
(sqrt.f64 z)
(*.f64 #s(literal 1/2 binary64) (log.f64 z))
#s(literal 1/2 binary64)
(log.f64 z)
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
(log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64))))
(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(sqrt.f64 #s(literal 3 binary64))
#s(literal 3 binary64)
z
#s(literal -1 binary64)
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
(sqrt.f64 (.f64 #s(literal 1/3 binary64) (.f64 z z)))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
z
#s(literal 1/3 binary64)
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(sqrt.f64 z)
(exp.f64 #s(literal 1/2 binary64))
#s(literal 1/2 binary64)
(log.f64 z)

localize164.0ms (1.8%)

Memory

11.4MiB live, 259.0MiB allocated

Localize:

Found 20 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.9%	(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
✓	accuracy	91.5%	(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	100.0%	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
✓	accuracy	90.8%	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
✓	accuracy	99.9%	(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	99.4%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
✓	accuracy	92.0%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
✓	accuracy	100.0%	(log.f64 (*.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	99.4%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
✓	accuracy	92.3%	(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #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)))

Samples

118.0ms

256×

valid

Compiler

Compiled 149 to 32 computations (78.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 100.0ms

ival-log: 56.0ms (56.2% of total)

ival-exp: 12.0ms (12% of total)

ival-mult: 10.0ms (10% of total)

ival-div: 6.0ms (6% of total)

ival-pow: 6.0ms (6% of total)

ival-sqrt: 5.0ms (5% of total)

const: 4.0ms (4% of total)

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

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

exact: 0.0ms (0% of total)

series193.0ms (2.1%)

Memory

20.4MiB live, 327.2MiB allocated

Counts

18 → 180

Calls

Call 1

Inputs
#<alt (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))>
#<alt (/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))>
#<alt (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))>
#<alt (sqrt.f64 #s(literal 3 binary64))>
#<alt (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))))>
#<alt (.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))>
#<alt (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))>
#<alt (log.f64 (*.f64 z #s(literal 1/3 binary64)))>
#<alt (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))>
#<alt (.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))>
#<alt (sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))>
#<alt (*.f64 z #s(literal 1/3 binary64))>
#<alt (exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))>
#<alt (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))>
#<alt (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))>
#<alt (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)>
#<alt (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))>
#<alt (.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))>

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

Calls

45 calls:

Time	Variable		Point	Expression
35.0ms	z	@	0	(* 1/2 (log (* z 1/3)))
34.0ms	z	@	0	(pow (exp 1/2) (log z))
31.0ms	z	@	-inf	(* (log (/ (sqrt 3) z)) -1)
25.0ms	z	@	inf	(* (log (/ (sqrt 3) z)) -1)
19.0ms	z	@	-inf	(* 1/2 (log (* z 1/3)))

rewrite516.0ms (5.5%)

Memory

11.0MiB live, 516.9MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

5 266×	`lower-*.f32`
5 256×	`lower-*.f64`
3 836×	`lower-fma.f64`
3 836×	`lower-fma.f32`
2 712×	`lower-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	108
0	50	81
1	111	67
2	344	66
3	1678	65
0	8441	65

Stop Event

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

Counts

18 → 1 365

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(sqrt.f64 #s(literal 3 binary64))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
(.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64))))
(log.f64 (*.f64 z #s(literal 1/3 binary64)))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z)))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(sqrt.f64 (*.f64 z #s(literal 1/3 binary64)))
(*.f64 z #s(literal 1/3 binary64))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))

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

simplify387.0ms (4.2%)

Memory

-15.3MiB live, 304.1MiB allocated

Algorithm

1×	egg-herbie

Rules

2 148×	`lower-fma.f64`
2 148×	`lower-fma.f32`
1 556×	`lower-*.f64`
1 556×	`lower-*.f32`
718×	`associate-r`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	58	936
1	148	912
2	329	904
3	716	904
4	1755	904
5	2475	880
6	3113	880
0	4265	880

Stop Event

1×	iter limit
1×	iter limit
1×	iter limit
1×	unsound

Counts

180 → 180

Calls

Call 1

Inputs
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (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) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* 1/2 (+ (log 1/3) (log z)))
(* 1/2 (+ (log 1/3) (log z)))
(* 1/2 (+ (log 1/3) (log z)))
(* 1/2 (+ (log 1/3) (log z)))
(* 1/2 (+ (log 1/3) (* -1 (log (/ 1 z)))))
(* 1/2 (+ (log 1/3) (* -1 (log (/ 1 z)))))
(* 1/2 (+ (log 1/3) (* -1 (log (/ 1 z)))))
(* 1/2 (+ (log 1/3) (* -1 (log (/ 1 z)))))
(* 1/2 (+ (log -1/3) (* -1 (log (/ -1 z)))))
(* 1/2 (+ (log -1/3) (* -1 (log (/ -1 z)))))
(* 1/2 (+ (log -1/3) (* -1 (log (/ -1 z)))))
(* 1/2 (+ (log -1/3) (* -1 (log (/ -1 z)))))
(+ (log 1/3) (log z))
(+ (log 1/3) (log z))
(+ (log 1/3) (log z))
(+ (log 1/3) (log z))
(+ (log 1/3) (* -1 (log (/ 1 z))))
(+ (log 1/3) (* -1 (log (/ 1 z))))
(+ (log 1/3) (* -1 (log (/ 1 z))))
(+ (log 1/3) (* -1 (log (/ 1 z))))
(+ (log -1/3) (* -1 (log (/ -1 z))))
(+ (log -1/3) (* -1 (log (/ -1 z))))
(+ (log -1/3) (* -1 (log (/ -1 z))))
(+ (log -1/3) (* -1 (log (/ -1 z))))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 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) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* -1 (* z (* (sqrt -1) (sqrt -1/3))))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* (sqrt z) (sqrt 1/3))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* -1 (* (sqrt z) (* (sqrt -1) (sqrt -1/3))))
(* 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 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(/ z (sqrt 3))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(+ (log (sqrt 3)) (* -1 (log z)))
(+ (log (sqrt 3)) (* -1 (log z)))
(+ (log (sqrt 3)) (* -1 (log z)))
(+ (log (sqrt 3)) (* -1 (log z)))
(+ (log (sqrt 3)) (log (/ 1 z)))
(+ (log (sqrt 3)) (log (/ 1 z)))
(+ (log (sqrt 3)) (log (/ 1 z)))
(+ (log (sqrt 3)) (log (/ 1 z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 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 z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z))))))
(exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z))))))
(exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z))))))
(exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z))))))
(* 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 (* (sqrt z) (* (exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z)))))) (* (sqrt -1) (sqrt -1/3)))))
(* -1 (* (sqrt z) (* (exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z)))))) (* (sqrt -1) (sqrt -1/3)))))
(* -1 (* (sqrt z) (* (exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z)))))) (* (sqrt -1) (sqrt -1/3)))))
(* -1 (* (sqrt z) (* (exp (* 1/2 (+ (log -1) (* -1 (log (/ -1 z)))))) (* (sqrt -1) (sqrt -1/3)))))

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

eval249.0ms (2.7%)

Memory: 40.9MiB live, 345.9MiB allocated
Compiler: Compiled 21 213 to 2 392 computations (88.7% saved)

prune189.0ms (2%)

Memory

-18.5MiB live, 286.6MiB allocated

Pruning

32 alts after pruning (21 fresh and 11 done)

	Pruned	Kept	Total
New	1 665	21	1 686
Fresh	1	0	1
Picked	2	3	5
Done	0	8	8
Total	1 668	32	1 700

Accuracy

98.7%

Counts

1 700 → 32

Alt Table

Click to see full alt table

Status	Accuracy	Program
	88.1%	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (log.f64 z)))
	89.0%	(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 #s(literal 2 binary64) (log.f64 z) (log.f64 #s(literal 1/3 binary64))))
	86.9%	(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 3 binary64)) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 3 binary64)) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))))
	87.0%	(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) z)))))
✓	96.6%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	97.7%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
	90.2%	(.f64 (pow.f64 (sqrt.f64 (E.f64)) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (sqrt.f64 z))
	87.7%	(*.f64 (/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
	88.1%	(.f64 (/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 z))))
✓	97.0%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
	97.1%	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64))))) (sqrt.f64 z))
	96.7%	(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (sqrt.f64 z))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (sqrt.f64 z))))
	86.2%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (*.f64 (log.f64 z) #s(literal 2 binary64))))
	90.2%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (E.f64)) (log.f64 z)))
	90.3%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (E.f64) (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
	90.2%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (E.f64)) (neg.f64 (log.f64 z)))))
✓	97.7%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
✓	90.7%	(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
	89.2%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (pow.f64 (log.f64 z) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1/3 binary64) z))))) (sqrt.f64 z))
	88.8%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))))) (sqrt.f64 z))
✓	91.0%	(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
✓	97.7%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	48.1%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	48.1%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	47.7%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	47.7%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
	89.0%	(exp.f64 (fma.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 3 binary64)) (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64))) z))))
	87.1%	(exp.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) (neg.f64 (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))))
	89.0%	(exp.f64 (/.f64 (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (neg.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))) (neg.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))))
	88.7%	(exp.f64 (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))))) #s(literal -1 binary64)))
	87.3%	(exp.f64 (.f64 (-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z))) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) #s(literal -1 binary64)))
	89.5%	(exp.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))

Compiler

Compiled 1 194 to 590 computations (50.6% saved)

regimes130.0ms (1.4%)

Memory

-4.0MiB live, 190.9MiB allocated

Counts

40 → 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)
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
(sqrt.f64 (fma.f64 (fma.f64 x x (.f64 z z)) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
(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)))))
(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64))))) (sqrt.f64 z))
(.f64 (.f64 (.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (sqrt.f64 z))) (.f64 (*.f64 (sqrt.f64 (sqrt.f64 z)) (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64)))) (sqrt.f64 (sqrt.f64 z))))
(exp.f64 (log.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 z #s(literal 1/3 binary64))))) (sqrt.f64 z))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (E.f64) (*.f64 #s(literal 1/2 binary64) (log.f64 z))))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (E.f64)) (log.f64 z)))
(.f64 (pow.f64 (sqrt.f64 (E.f64)) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (sqrt.f64 z))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 (sqrt.f64 (E.f64)) (neg.f64 (log.f64 z)))))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (sqrt.f64 (sqrt.f64 (E.f64))) (*.f64 (log.f64 z) #s(literal 2 binary64))))
(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 #s(literal 2 binary64) (log.f64 z) (log.f64 #s(literal 1/3 binary64))))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
(.f64 (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (sqrt.f64 z))
(pow.f64 (sqrt.f64 (E.f64)) (fma.f64 #s(literal 2 binary64) (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z #s(literal 1/3 binary64)))) (log.f64 z)))
(exp.f64 (fma.f64 #s(literal -1/4 binary64) (log.f64 #s(literal 3 binary64)) (log.f64 (*.f64 (sqrt.f64 (sqrt.f64 #s(literal 1/3 binary64))) z))))
(exp.f64 (/.f64 (.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (neg.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))) (neg.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (pow.f64 (log.f64 z) #s(literal 2 binary64))) (log.f64 (/.f64 #s(literal 1/3 binary64) z))))) (sqrt.f64 z))
(exp.f64 (.f64 (/.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #s(literal 3 binary64))) (+.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (log.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)) #s(literal 2 binary64)) (.f64 #s(literal 0 binary64) (log.f64 (*.f64 (sqrt.f64 #s(literal 1/3 binary64)) z)))))) #s(literal -1 binary64)))
(exp.f64 (.f64 (-.f64 (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z))) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) #s(literal -1 binary64)))
(.f64 (exp.f64 (.f64 #s(literal 1/2 binary64) (-.f64 (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))))) (sqrt.f64 z))
(exp.f64 (/.f64 (-.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 3 binary64)) (pow.f64 (log.f64 z) #s(literal 3 binary64))) (neg.f64 (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64)) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (*.f64 (sqrt.f64 #s(literal 3 binary64)) z)))))
(.f64 (/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))))) (exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 z))))
(*.f64 (/.f64 (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64))))) (pow.f64 (sqrt.f64 (E.f64)) (/.f64 (pow.f64 (log.f64 #s(literal 1/3 binary64)) #s(literal 2 binary64)) (log.f64 (/.f64 z #s(literal 1/3 binary64)))))) (pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 z)))
(/.f64 (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 3 binary64)) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))) (pow.f64 (exp.f64 #s(literal -1 binary64)) (/.f64 (pow.f64 (log.f64 z) #s(literal 3 binary64)) (fma.f64 (log.f64 z) (log.f64 (.f64 (sqrt.f64 #s(literal 3 binary64)) z)) (pow.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 #s(literal 1/3 binary64))) #s(literal 2 binary64))))))

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

Calls

10 calls:

21.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
17.0ms	y
13.0ms	(+.f64 (.f64 x x) (.f64 y y))
13.0ms	(*.f64 z z)
12.0ms	(*.f64 y y)

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`y`
97.7%	1	`z`
97.7%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.7%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.7%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.7%	1	`(*.f64 x x)`
97.7%	1	`(*.f64 y y)`
97.7%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes29.0ms (0.3%)

Memory

12.8MiB live, 50.5MiB allocated

Accuracy

Total -32.4b remaining (-2207%)

Threshold costs -32.4b (-2207%)

Counts

7 → 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)

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

Calls

10 calls:

5.0ms	(*.f64 y y)
3.0ms	y
3.0ms	x
3.0ms	z
3.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
97.7%	1	`x`
97.7%	1	`y`
97.7%	1	`z`
97.7%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
97.7%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
97.7%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
97.7%	1	`(+.f64 (.f64 x x) (.f64 y y))`
97.7%	1	`(*.f64 y y)`
97.7%	1	`(*.f64 z z)`
97.7%	1	`(*.f64 x x)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify36.0ms (0.4%)

Memory

-37.1MiB live, 6.6MiB allocated

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	11	11

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness290.0ms (3.1%)

Memory

9.2MiB live, 280.7MiB allocated

Rules

13 366×	`lower-fma.f64`
13 366×	`lower-fma.f32`
7 766×	`lower-fma.f32`
7 760×	`lower-fma.f64`
5 460×	`lower-*.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	98
0	39	92
1	115	92
2	688	92
3	7019	92
0	8593	87
0	230	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992

Stop Event

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

Compiler

Compiled 38 to 30 computations (21.1% saved)

preprocess84.0ms (0.9%)

Memory: 19.9MiB live, 226.7MiB allocated
Compiler: Compiled 212 to 152 computations (28.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	28	147
0	50	135
1	68	122
2	89	116
3	106	115
4	144	115
5	172	115
6	200	115
7	230	112
8	299	112
9	380	112
10	500	112
11	665	112
12	752	112
13	763	112
0	763	112

Iter	Nodes	Cost
0	28	147
0	50	135
1	68	122
2	89	116
3	106	115
4	144	115
5	172	115
6	200	115
7	230	112
8	299	112
9	380	112
10	500	112
11	665	112
12	752	112
13	763	112
0	763	112

analyze1.0ms (0%)

sample1.2s (13.1%)

preprocess62.0ms (0.7%)

explain980.0ms (10.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify7.0ms (0.1%)

localize235.0ms (2.5%)

series13.0ms (0.1%)

rewrite374.0ms (4%)

simplify559.0ms (6%)

eval61.0ms (0.7%)

prune86.0ms (0.9%)

simplify9.0ms (0.1%)

localize78.0ms (0.8%)

series25.0ms (0.3%)

rewrite496.0ms (5.3%)

simplify1.3s (14.3%)

eval223.0ms (2.4%)

prune122.0ms (1.3%)

simplify8.0ms (0.1%)

localize110.0ms (1.2%)

series9.0ms (0.1%)

rewrite349.0ms (3.8%)

simplify464.0ms (5%)

eval92.0ms (1%)

prune85.0ms (0.9%)

simplify37.0ms (0.4%)

localize164.0ms (1.8%)

series193.0ms (2.1%)

rewrite516.0ms (5.5%)

simplify387.0ms (4.2%)

eval249.0ms (2.7%)

prune189.0ms (2%)

regimes130.0ms (1.4%)

regimes29.0ms (0.3%)

simplify36.0ms (0.4%)

soundness290.0ms (3.1%)

preprocess84.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	28	147
0	50	135
1	68	122
2	89	116
3	106	115
4	144	115
5	172	115
6	200	115
7	230	112
8	299	112
9	380	112
10	500	112
11	665	112
12	752	112
13	763	112
0	763	112