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

analyze1.0ms (0%)

Memory

3.3MiB live, 3.3MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample2.2s (21.2%)

Memory

-104.4MiB live, 1 836.3MiB allocated

Samples

1.2s

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 746.0ms

ival-mult: 497.0ms (66.6% of total)

ival-div: 89.0ms (11.9% of total)

ival-add: 74.0ms (9.9% of total)

ival-sqrt: 74.0ms (9.9% of total)

ival-true: 5.0ms (0.7% of total)

exact: 5.0ms (0.7% of total)

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

Bogosity

preprocess45.0ms (0.4%)

Memory

-6.3MiB live, 77.2MiB 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
1	15	14
2	22	14
3	24	14
0	24	12

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Symmetry

(abs z)

(abs y)

(abs x)

(sort x y z)

explain134.0ms (1.3%)

Memory

-3.6MiB live, 400.5MiB allocated

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
147	-	1	(3.291706993632703e-291 1.8048180878269285e-258 1.9316775498226967e-156)	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
0	-	0	-	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
0	-	0	-	`#s(literal 3 binary64)`
0	-	0	-	`z`
0	-	0	-	`(*.f64 x x)`
0	-	0	-	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0	-	0	-	`(+.f64 (.f64 x x) (.f64 y y))`
0	-	0	-	`(*.f64 z z)`
0	-	0	-	`y`
0	-	0	-	`(*.f64 y y)`
0	-	0	-	`x`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	143	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	143
↳	`(*.f64 y y)`	overflow	33
↳	`(*.f64 x x)`	overflow	4
↳	`(*.f64 z z)`	overflow	143
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	33
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	143
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	3	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	3
↳	`(*.f64 y y)`	underflow	36
↳	`(*.f64 x x)`	underflow	142
↳	`(*.f64 z z)`	underflow	3
↳	`(+.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	3

Confusion

	Predicted +	Predicted -
+	146	1
-	0	109

Precision

1.0

Recall

0.9931972789115646

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	146	0	1
-	0	0	109

Precision?

1.0

Recall?

0.9931972789115646

Freqs

test

number	freq
0	110
1	146

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

43.0ms

512×

valid

Compiler

Compiled 154 to 48 computations (68.8% saved)

Precisions

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

ival-mult: 9.0ms (42% of total)

ival-div: 4.0ms (18.7% of total)

ival-add: 4.0ms (18.7% of total)

ival-sqrt: 4.0ms (18.7% 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: 0.4MiB live, 0.4MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.8%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Compiler

Compiled 17 to 11 computations (35.3% saved)

simplify5.0ms (0%)

Memory

11.1MiB live, 11.1MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize34.0ms (0.3%)

Memory

-32.7MiB live, 86.7MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	accuracy	99.8%	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
✓	accuracy	46.8%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

21.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 6.0ms (48.7% of total)

ival-div: 2.0ms (16.2% of total)

ival-add: 2.0ms (16.2% of total)

ival-sqrt: 2.0ms (16.2% 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

-2.1MiB live, 36.9MiB allocated

Counts

5 → 144

Calls

Call 1

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

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

Calls

36 calls:

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

rewrite505.0ms (4.8%)

Memory

20.2MiB live, 649.0MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

5 → 356

Calls

Call 1

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

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

simplify405.0ms (3.8%)

Memory

12.5MiB live, 892.2MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

144 → 144

Calls

Call 1

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

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

eval66.0ms (0.6%)

Memory: -0.9MiB live, 165.2MiB allocated
Compiler: Compiled 18 496 to 1 590 computations (91.4% saved)

prune81.0ms (0.8%)

Memory

-5.7MiB live, 154.2MiB allocated

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	491	9	500
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	492	9	501

Accuracy

99.3%

Counts

501 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	87.2%	(fma.f64 z (sqrt.f64 #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) z))))
	46.7%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
▶	46.4%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (fma.f64 x x (fma.f64 y y (.f64 z z)))))
▶	46.7%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
▶	98.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
	46.8%	(sqrt.f64 (/.f64 (+.f64 (.f64 y y) (.f64 z z)) #s(literal 3 binary64)))
▶	45.7%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
	46.7%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	45.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 238 to 164 computations (31.1% saved)

simplify8.0ms (0.1%)

Memory

11.9MiB live, 11.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	135
1	40	133
2	53	133
3	62	133
4	62	133
0	62	115

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize82.0ms (0.8%)

Memory

-14.9MiB live, 180.1MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.5%	(.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (sqrt.f64 (fma.f64 x x (fma.f64 y y (.f64 z z)))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	46.9%	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	accuracy	46.9%	(sqrt.f64 (fma.f64 y y (*.f64 z z)))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.8%	(/.f64 (*.f64 z z) #s(literal 3 binary64))
✓	accuracy	46.8%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
✓	accuracy	99.9%	(.f64 z (.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	46.8%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.5%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Samples

51.0ms

256×

valid

Compiler

Compiled 127 to 26 computations (79.5% saved)

Precisions

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

ival-mult: 13.0ms (36.3% of total)

ival-sqrt: 12.0ms (33.5% of total)

const: 5.0ms (14% of total)

ival-div: 3.0ms (8.4% of total)

ival-add: 2.0ms (5.6% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.2%)

Memory

9.1MiB live, 47.0MiB allocated

Counts

15 → 228

Calls

Call 1

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

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

Calls

57 calls:

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

rewrite333.0ms (3.1%)

Memory

5.8MiB live, 710.6MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 564×	`accelerator-lowering-fma.f32`
4 564×	`accelerator-lowering-fma.f64`
4 368×	`-lowering-.f32`
4 368×	`-lowering-.f64`
3 036×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	90
1	97	87
2	597	86
3	6962	86
0	8777	72

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 509

Calls

Call 1

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

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

simplify1.6s (15%)

Memory

-13.1MiB live, 888.4MiB allocated

Algorithm

1×	egg-herbie

Rules

16 146×	`accelerator-lowering-fma.f32`
16 146×	`accelerator-lowering-fma.f64`
6 544×	`-lowering-.f32`
6 544×	`-lowering-.f64`
4 600×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	462	3900
1	1436	3858
2	5215	3855
0	8236	3432

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

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

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

eval113.0ms (1.1%)

Memory: 12.7MiB live, 321.2MiB allocated
Compiler: Compiled 19 717 to 1 900 computations (90.4% saved)

prune97.0ms (0.9%)

Memory

7.4MiB live, 257.8MiB allocated

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	893	9	902
Fresh	4	0	4
Picked	2	3	5
Done	0	0	0
Total	899	12	911

Accuracy

100.0%

Counts

911 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	46.7%	(/.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) (sqrt.f64 #s(literal 3 binary64)))
	98.0%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
	98.1%	(.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))
	97.3%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
▶	97.2%	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
▶	87.2%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) z))
▶	99.5%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	46.7%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	98.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	45.6%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	45.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
▶	46.7%	(sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))

Compiler

Compiled 225 to 168 computations (25.3% saved)

simplify45.0ms (0.4%)

Memory

-1.8MiB live, 77.0MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(sqrt.f64 z)
✓	cost-diff	320	(*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	cost-diff	1600	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	cost-diff	0	(/.f64 (*.f64 y y) z)
✓	cost-diff	0	(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z)
✓	cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	0	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) z))
✓	cost-diff	0	(*.f64 y y)
✓	cost-diff	0	(fma.f64 z z (*.f64 y y))
✓	cost-diff	0	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
✓	cost-diff	0	(sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
✓	cost-diff	0	(*.f64 z z)
✓	cost-diff	0	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	cost-diff	0	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	cost-diff	5120	(hypot.f64 z y)

Rules

830×	`-lowering-.f32`
830×	`-lowering-.f64`
636×	`times-frac`
338×	`associate-r`
282×	`associate-l`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	135
1	57	127
2	96	127
3	196	127
4	497	127
5	820	127
6	939	127
7	1090	127
8	1117	127
9	1138	127
10	1177	127
11	1177	127
12	1185	127
0	1185	112

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize108.0ms (1%)

Memory

9.7MiB live, 165.0MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.4%	(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	accuracy	99.4%	(*.f64 (sqrt.f64 z) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	100.0%	(fma.f64 #s(literal 1/2 binary64) (/.f64 (*.f64 y y) z) z)
✓	accuracy	99.5%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 #s(literal 1/2 binary64) (/.f64 (.f64 y y) z) z))
✓	accuracy	84.7%	(/.f64 (*.f64 y y) z)
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	100.0%	(fma.f64 z z (*.f64 y y))
✓	accuracy	99.8%	(.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y)))
✓	accuracy	46.8%	(sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.8%	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	accuracy	46.8%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	accuracy	100.0%	(hypot.f64 z y)
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.5%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))

Samples

73.0ms

256×

valid

Compiler

Compiled 122 to 28 computations (77% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-mult: 35.0ms (61.3% of total)

ival-sqrt: 8.0ms (14% of total)

ival-hypot: 4.0ms (7% of total)

const: 4.0ms (7% of total)

ival-div: 3.0ms (5.3% of total)

ival-add: 2.0ms (3.5% of total)

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

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

exact: 0.0ms (0% of total)

series19.0ms (0.2%)

Memory

-24.5MiB live, 16.7MiB allocated

Counts

18 → 276

Calls

Call 1

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

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

Calls

69 calls:

Time	Variable		Point	Expression
5.0ms	y	@	inf	(sqrt (+ (* z z) (* y y)))
1.0ms	z	@	-inf	(* (sqrt z) (* (sqrt z) (/ 1 (sqrt 3))))
1.0ms	z	@	0	(* (sqrt z) (/ 1 (sqrt 3)))
1.0ms	z	@	-inf	(* (sqrt z) (/ 1 (sqrt 3)))
1.0ms	y	@	inf	(* (sqrt 1/3) (+ (* 1/2 (/ (* y y) z)) z))

rewrite403.0ms (3.8%)

Memory

32.5MiB live, 540.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

7 318×	`accelerator-lowering-fma.f32`
7 318×	`accelerator-lowering-fma.f64`
4 730×	`-lowering-.f32`
4 730×	`-lowering-.f64`
2 498×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	108
1	107	102
2	645	102
3	6293	102
0	8028	85

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 696

Calls

Call 1

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

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

simplify450.0ms (4.2%)

Memory

-22.5MiB live, 608.7MiB allocated

Algorithm

1×	egg-herbie

Rules

11 740×	`accelerator-lowering-fma.f32`
11 740×	`accelerator-lowering-fma.f64`
5 566×	`-lowering-.f32`
5 566×	`-lowering-.f64`
3 186×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	236	3061
1	715	3028
2	2374	3024
3	7126	3017
0	8010	2854

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

Calls

Call 1

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

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

eval133.0ms (1.3%)

Memory: 33.4MiB live, 216.1MiB allocated
Compiler: Compiled 21 740 to 2 123 computations (90.2% saved)

prune117.0ms (1.1%)

Memory

-17.5MiB live, 288.7MiB allocated

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	1 026	5	1 031
Fresh	1	3	4
Picked	2	3	5
Done	0	3	3
Total	1 029	14	1 043

Accuracy

100.0%

Counts

1 043 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.8%	(fma.f64 (/.f64 y z) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
	46.7%	(/.f64 (sqrt.f64 (fma.f64 z z (*.f64 y y))) (sqrt.f64 #s(literal 3 binary64)))
▶	98.0%	(/.f64 (sqrt.f64 z) (sqrt.f64 (/.f64 #s(literal 3 binary64) z)))
▶	98.7%	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z)))
▶	98.0%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
	98.8%	(.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 1/2 binary64)) z) z) (sqrt.f64 #s(literal 1/3 binary64)))
	97.3%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
✓	99.5%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	46.7%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	98.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	46.8%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	45.6%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	45.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	46.7%	(sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))

Compiler

Compiled 259 to 190 computations (26.6% saved)

simplify27.0ms (0.3%)

Memory

4.1MiB live, 41.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z))
✓	cost-diff	0	(sqrt.f64 #s(literal 1/3 binary64))
✓	cost-diff	1088	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z)))
✓	cost-diff	0	(/.f64 #s(literal 3 binary64) z)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 3 binary64) z))
✓	cost-diff	0	(sqrt.f64 z)
✓	cost-diff	0	(/.f64 (sqrt.f64 z) (sqrt.f64 (/.f64 #s(literal 3 binary64) z)))
✓	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 z (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 y z)
✓	cost-diff	960	(fma.f64 (/.f64 y z) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))

Rules

424×	`-lowering-.f32`
424×	`-lowering-.f64`
294×	`associate-l`
142×	`associate-r`
120×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	147
1	62	147
2	113	141
3	188	141
4	259	141
5	290	141
6	344	141
7	436	141
8	460	141
9	515	141
10	546	141
11	547	141
0	547	135

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize157.0ms (1.5%)

Memory

10.4MiB live, 168.5MiB allocated

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 y #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z))
✓	accuracy	99.4%	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z)))
✓	accuracy	100.0%	(/.f64 #s(literal 3 binary64) z)
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 3 binary64) z))
✓	accuracy	99.5%	(/.f64 (sqrt.f64 z) (sqrt.f64 (/.f64 #s(literal 3 binary64) z)))
✓	accuracy	100.0%	(*.f64 y y)
✓	accuracy	99.8%	(fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64)))
✓	accuracy	99.3%	(.f64 (.f64 y y) #s(literal 1/3 binary64))
✓	accuracy	46.8%	(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 z (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	100.0%	(fma.f64 (/.f64 y z) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
✓	accuracy	99.5%	(.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.5%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Samples

92.0ms

256×

valid

Compiler

Compiled 146 to 34 computations (76.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 47.0ms (63.4% of total)

ival-div: 12.0ms (16.2% of total)

ival-sqrt: 8.0ms (10.8% of total)

ival-add: 3.0ms (4% of total)

const: 3.0ms (4% of total)

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

exact: 0.0ms (0% of total)

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

series150.0ms (1.4%)

Memory

3.5MiB live, 41.0MiB allocated

Counts

21 → 300

Calls

Call 1

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

Outputs
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<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) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (/ y z)>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<alt (* 1/2 (* y (sqrt 1/3)))>
#<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 (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 (* 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 (/ 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 (/ (* z (sqrt -1)) (sqrt -3)))>
#<alt (* -1 (/ (* z (sqrt -1)) (sqrt -3)))>
#<alt (* -1 (/ (* z (sqrt -1)) (sqrt -3)))>
#<alt (* -1 (/ (* z (sqrt -1)) (sqrt -3)))>
#<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 (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (sqrt 3))>
#<alt (* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))>
#<alt (* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))>
#<alt (* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))>
#<alt (* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (/ 3 z)>
#<alt (* z (sqrt 1/3))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))>
#<alt (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<alt (/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)>
#<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) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))>
#<alt (/ 1 z)>
#<alt (+ (* -1/2 (/ (pow y 2) (pow z 3))) (/ 1 z))>
#<alt (+ (* (pow y 2) (- (* 1/4 (/ (pow y 2) (pow z 5))) (* 1/2 (/ 1 (pow z 3))))) (/ 1 z))>
#<alt (+ (* (pow y 2) (- (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 7))) (* 1/4 (/ 1 (pow z 5))))) (* 1/2 (/ 1 (pow z 3))))) (/ 1 z))>
#<alt (* 2 (/ z (pow y 2)))>
#<alt (/ (+ (* -4 (/ (pow z 3) (pow y 2))) (* 2 z)) (pow y 2))>
#<alt (/ (- (+ (* 2 z) (* 8 (/ (pow z 5) (pow y 4)))) (* 4 (/ (pow z 3) (pow y 2)))) (pow y 2))>
#<alt (/ (- (+ (* -16 (/ (pow z 7) (pow y 6))) (* 2 z)) (+ (* -8 (/ (pow z 5) (pow y 4))) (* 4 (/ (pow z 3) (pow y 2))))) (pow y 2))>
#<alt (* 2 (/ z (pow y 2)))>
#<alt (/ (+ (* -4 (/ (pow z 3) (pow y 2))) (* 2 z)) (pow y 2))>
#<alt (/ (- (+ (* 2 z) (* 8 (/ (pow z 5) (pow y 4)))) (* 4 (/ (pow z 3) (pow y 2)))) (pow y 2))>
#<alt (/ (- (+ (* -16 (/ (pow z 7) (pow y 6))) (* 2 z)) (+ (* -8 (/ (pow z 5) (pow y 4))) (* 4 (/ (pow z 3) (pow y 2))))) (pow y 2))>
#<alt (* 2 (/ z (pow y 2)))>
#<alt (* z (+ (* -4 (/ (pow z 2) (pow y 4))) (* 2 (/ 1 (pow y 2)))))>
#<alt (* z (+ (* (pow z 2) (- (* 8 (/ (pow z 2) (pow y 6))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))>
#<alt (* z (+ (* (pow z 2) (- (* (pow z 2) (+ (* -16 (/ (pow z 2) (pow y 8))) (* 8 (/ 1 (pow y 6))))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))>
#<alt (/ 1 z)>
#<alt (/ (+ 1 (* -1/2 (/ (pow y 2) (pow z 2)))) z)>
#<alt (/ (- (+ 1 (* 1/4 (/ (pow y 4) (pow z 4)))) (* 1/2 (/ (pow y 2) (pow z 2)))) z)>
#<alt (/ (- (+ 1 (* -1/8 (/ (pow y 6) (pow z 6)))) (+ (* -1/4 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))) z)>
#<alt (/ 1 z)>
#<alt (* -1 (/ (- (* 1/2 (/ (pow y 2) (pow z 2))) 1) z))>
#<alt (* -1 (/ (- (* -1/4 (/ (pow y 4) (pow z 4))) (+ 1 (* -1/2 (/ (pow y 2) (pow z 2))))) z))>
#<alt (* -1 (/ (- (* 1/8 (/ (pow y 6) (pow z 6))) (+ 1 (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/4 (/ (pow y 4) (pow z 4)))))) z))>
#<alt z>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (+ z (* 1/2 (/ (pow y 2) z)))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))>
#<alt (* 1/2 (/ (pow y 2) z))>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt (/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)>
#<alt z>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt (* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))>
#<alt z>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<alt (* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))>
#<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 (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 (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>
#<alt (* 1/2 y)>

Calls

75 calls:

Time	Variable		Point	Expression
128.0ms	z	@	0	(+ (* (/ y z) (* y (* (sqrt 1/3) 1/2))) (* z (sqrt 1/3)))
5.0ms	z	@	0	(/ 3 z)
1.0ms	z	@	-inf	(/ (sqrt z) (sqrt (/ 3 z)))
1.0ms	y	@	0	(+ (* (/ y z) (* y (* (sqrt 1/3) 1/2))) (* z (sqrt 1/3)))
1.0ms	y	@	inf	(sqrt (+ (* (* z z) 1/3) (* (* y y) 1/3)))

rewrite597.0ms (5.6%)

Memory

-28.9MiB live, 722.3MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

13 938×	`accelerator-lowering-fma.f32`
13 938×	`accelerator-lowering-fma.f64`
7 304×	`-lowering-.f32`
7 304×	`-lowering-.f64`
2 578×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	121
1	154	121
2	1043	115
0	9039	106

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 878

Calls

Call 1

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

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

simplify417.0ms (3.9%)

Memory

47.6MiB live, 630.5MiB allocated

Algorithm

1×	egg-herbie

Rules

9 092×	`accelerator-lowering-fma.f32`
9 092×	`accelerator-lowering-fma.f64`
5 334×	`-lowering-.f32`
5 334×	`-lowering-.f64`
4 012×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	285	2917
1	820	2899
2	2559	2875
3	7436	2862
0	8136	2731

Stop Event

1×	iter limit
1×	node limit

Counts

300 → 300

Calls

Call 1

Inputs
(* z (sqrt 1/3))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (sqrt 1/3))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(/ y z)
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(* 1/2 (* y (sqrt 1/3)))
(/ 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)))))))))
(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)
(* 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))
(/ 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 (/ (* z (sqrt -1)) (sqrt -3)))
(* -1 (/ (* z (sqrt -1)) (sqrt -3)))
(* -1 (/ (* z (sqrt -1)) (sqrt -3)))
(* -1 (/ (* z (sqrt -1)) (sqrt -3)))
(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)))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (sqrt 3))
(* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))
(* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))
(* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))
(* (sqrt (/ 1 z)) (* (sqrt -3) (sqrt -1)))
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(/ 3 z)
(* z (sqrt 1/3))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(+ (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z)) (* z (sqrt 1/3)))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ (sqrt 1/3) z)) (/ (* z (sqrt 1/3)) (pow y 2))))
(* 1/2 (/ (* (pow y 2) (sqrt 1/3)) z))
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(/ (+ (* 1/2 (* (pow y 2) (sqrt 1/3))) (* (pow z 2) (sqrt 1/3))) z)
(* z (sqrt 1/3))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2)))))
(* z (sqrt 1/3))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(* -1 (* z (+ (* -1 (sqrt 1/3)) (* -1/2 (/ (* (pow y 2) (sqrt 1/3)) (pow z 2))))))
(/ 1 z)
(+ (* -1/2 (/ (pow y 2) (pow z 3))) (/ 1 z))
(+ (* (pow y 2) (- (* 1/4 (/ (pow y 2) (pow z 5))) (* 1/2 (/ 1 (pow z 3))))) (/ 1 z))
(+ (* (pow y 2) (- (* (pow y 2) (+ (* -1/8 (/ (pow y 2) (pow z 7))) (* 1/4 (/ 1 (pow z 5))))) (* 1/2 (/ 1 (pow z 3))))) (/ 1 z))
(* 2 (/ z (pow y 2)))
(/ (+ (* -4 (/ (pow z 3) (pow y 2))) (* 2 z)) (pow y 2))
(/ (- (+ (* 2 z) (* 8 (/ (pow z 5) (pow y 4)))) (* 4 (/ (pow z 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* -16 (/ (pow z 7) (pow y 6))) (* 2 z)) (+ (* -8 (/ (pow z 5) (pow y 4))) (* 4 (/ (pow z 3) (pow y 2))))) (pow y 2))
(* 2 (/ z (pow y 2)))
(/ (+ (* -4 (/ (pow z 3) (pow y 2))) (* 2 z)) (pow y 2))
(/ (- (+ (* 2 z) (* 8 (/ (pow z 5) (pow y 4)))) (* 4 (/ (pow z 3) (pow y 2)))) (pow y 2))
(/ (- (+ (* -16 (/ (pow z 7) (pow y 6))) (* 2 z)) (+ (* -8 (/ (pow z 5) (pow y 4))) (* 4 (/ (pow z 3) (pow y 2))))) (pow y 2))
(* 2 (/ z (pow y 2)))
(* z (+ (* -4 (/ (pow z 2) (pow y 4))) (* 2 (/ 1 (pow y 2)))))
(* z (+ (* (pow z 2) (- (* 8 (/ (pow z 2) (pow y 6))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(* z (+ (* (pow z 2) (- (* (pow z 2) (+ (* -16 (/ (pow z 2) (pow y 8))) (* 8 (/ 1 (pow y 6))))) (* 4 (/ 1 (pow y 4))))) (* 2 (/ 1 (pow y 2)))))
(/ 1 z)
(/ (+ 1 (* -1/2 (/ (pow y 2) (pow z 2)))) z)
(/ (- (+ 1 (* 1/4 (/ (pow y 4) (pow z 4)))) (* 1/2 (/ (pow y 2) (pow z 2)))) z)
(/ (- (+ 1 (* -1/8 (/ (pow y 6) (pow z 6)))) (+ (* -1/4 (/ (pow y 4) (pow z 4))) (* 1/2 (/ (pow y 2) (pow z 2))))) z)
(/ 1 z)
(* -1 (/ (- (* 1/2 (/ (pow y 2) (pow z 2))) 1) z))
(* -1 (/ (- (* -1/4 (/ (pow y 4) (pow z 4))) (+ 1 (* -1/2 (/ (pow y 2) (pow z 2))))) z))
(* -1 (/ (- (* 1/8 (/ (pow y 6) (pow z 6))) (+ 1 (+ (* -1/2 (/ (pow y 2) (pow z 2))) (* 1/4 (/ (pow y 4) (pow z 4)))))) z))
z
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(+ z (* 1/2 (/ (pow y 2) z)))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* (pow y 2) (+ (* 1/2 (/ 1 z)) (/ z (pow y 2))))
(* 1/2 (/ (pow y 2) z))
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
(/ (+ (* 1/2 (pow y 2)) (pow z 2)) z)
z
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
(* z (+ 1 (* 1/2 (/ (pow y 2) (pow z 2)))))
z
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* -1 (* z (- (* -1/2 (/ (pow y 2) (pow z 2))) 1)))
(* 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))
(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)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)
(* 1/2 y)

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

eval364.0ms (3.4%)

Memory: -5.3MiB live, 288.8MiB allocated
Compiler: Compiled 25 188 to 2 031 computations (91.9% saved)

prune192.0ms (1.8%)

Memory

-8.0MiB live, 305.2MiB allocated

Pruning

14 alts after pruning (3 fresh and 11 done)

	Pruned	Kept	Total
New	1 217	1	1 218
Fresh	1	2	3
Picked	0	5	5
Done	0	6	6
Total	1 218	14	1 232

Accuracy

100.0%

Counts

1 232 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.8%	(fma.f64 (/.f64 y z) (.f64 y (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (*.f64 z (sqrt.f64 #s(literal 1/3 binary64))))
	46.1%	(/.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 z z (.f64 #s(literal 1/2 binary64) (*.f64 y y)))) z)
✓	98.0%	(/.f64 (sqrt.f64 z) (sqrt.f64 (/.f64 #s(literal 3 binary64) z)))
✓	98.7%	(/.f64 (sqrt.f64 #s(literal 1/3 binary64)) (/.f64 #s(literal 1 binary64) (fma.f64 y (/.f64 (*.f64 y #s(literal 1/2 binary64)) z) z)))
✓	98.0%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
	98.8%	(.f64 (fma.f64 y (/.f64 (.f64 y #s(literal 1/2 binary64)) z) z) (sqrt.f64 #s(literal 1/3 binary64)))
	97.3%	(*.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) z)
✓	99.5%	(*.f64 (sqrt.f64 #s(literal 1/3 binary64)) (hypot.f64 z y))
✓	46.7%	(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
✓	98.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	46.8%	(sqrt.f64 (fma.f64 (.f64 z z) #s(literal 1/3 binary64) (.f64 (*.f64 y y) #s(literal 1/3 binary64))))
✓	45.6%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	45.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	46.7%	(sqrt.f64 (.f64 #s(literal 1/3 binary64) (fma.f64 z z (.f64 y y))))

Compiler

Compiled 411 to 201 computations (51.1% saved)

regimes264.0ms (2.5%)

Memory

-3.4MiB live, 154.6MiB allocated

Counts

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

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

Calls

10 calls:

200.0ms	x
8.0ms	(*.f64 z z)
7.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))
7.0ms	z

Results

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

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes174.0ms (1.6%)

Memory

4.8MiB live, 81.8MiB allocated

Counts

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

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

Calls

10 calls:

85.0ms	(+.f64 (.f64 x x) (.f64 y y))
37.0ms	y
7.0ms	x
7.0ms	z
6.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`z`
98.8%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.8%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.8%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.8%	1	`(*.f64 x x)`
98.8%	1	`(*.f64 y y)`
98.8%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes65.0ms (0.6%)

Memory

-47.1MiB live, 107.1MiB allocated

Counts

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

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

Calls

10 calls:

13.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
7.0ms	x
6.0ms	(*.f64 y y)
6.0ms	y
6.0ms	z

Results

Accuracy	Segments	Branch
98.8%	1	`x`
98.8%	1	`y`
98.8%	1	`z`
98.8%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
98.8%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
98.8%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
98.8%	1	`(+.f64 (.f64 x x) (.f64 y y))`
98.8%	1	`(*.f64 x x)`
98.8%	1	`(*.f64 y y)`
98.8%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes42.0ms (0.4%)

Memory

15.7MiB live, 90.6MiB allocated

Accuracy

Total -33.8b remaining (-2627.8%)

Threshold costs -33.8b (-2627.8%)

Counts

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

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

Calls

10 calls:

6.0ms	z
5.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	y
4.0ms	x
4.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Results

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

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify8.0ms (0.1%)

Memory

20.8MiB live, 20.8MiB allocated

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	22	35

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness875.0ms (8.2%)

Memory

-32.3MiB live, 651.9MiB allocated

Rules

16 146×	`accelerator-lowering-fma.f32`
16 146×	`accelerator-lowering-fma.f64`
13 366×	`accelerator-lowering-fma.f32`
13 366×	`accelerator-lowering-fma.f64`
7 318×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	108
1	107	102
2	645	102
3	6293	102
0	8028	85
0	230	2478
1	673	2478
2	2272	2442
3	5706	2325
0	8198	2028
0	462	3900
1	1436	3858
2	5215	3855
0	8236	3432
0	24	90
1	97	87
2	597	86
3	6962	86
0	8777	72

Stop Event

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

Compiler

Compiled 152 to 98 computations (35.5% saved)

preprocess229.0ms (2.2%)

Memory: 23.0MiB live, 175.7MiB allocated
Compiler: Compiled 468 to 326 computations (30.3% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	31	147
1	62	147
2	113	141
3	188	141
4	259	141
5	290	141
6	344	141
7	436	141
8	460	141
9	515	141
10	546	141
11	547	141
0	547	135

Iter	Nodes	Cost
0	31	147
1	62	147
2	113	141
3	188	141
4	259	141
5	290	141
6	344	141
7	436	141
8	460	141
9	515	141
10	546	141
11	547	141
0	547	135

analyze1.0ms (0%)

sample2.2s (21.2%)

preprocess45.0ms (0.4%)

explain134.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0%)

localize34.0ms (0.3%)

series13.0ms (0.1%)

rewrite505.0ms (4.8%)

simplify405.0ms (3.8%)

eval66.0ms (0.6%)

prune81.0ms (0.8%)

simplify8.0ms (0.1%)

localize82.0ms (0.8%)

series21.0ms (0.2%)

rewrite333.0ms (3.1%)

simplify1.6s (15%)

eval113.0ms (1.1%)

prune97.0ms (0.9%)

simplify45.0ms (0.4%)

localize108.0ms (1%)

series19.0ms (0.2%)

rewrite403.0ms (3.8%)

simplify450.0ms (4.2%)

eval133.0ms (1.3%)

prune117.0ms (1.1%)

simplify27.0ms (0.3%)

localize157.0ms (1.5%)

series150.0ms (1.4%)

rewrite597.0ms (5.6%)

simplify417.0ms (3.9%)

eval364.0ms (3.4%)

prune192.0ms (1.8%)

regimes264.0ms (2.5%)

regimes174.0ms (1.6%)

regimes65.0ms (0.6%)

regimes42.0ms (0.4%)

simplify8.0ms (0.1%)

soundness875.0ms (8.2%)

preprocess229.0ms (2.2%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	31	147
1	62	147
2	113	141
3	188	141
4	259	141
5	290	141
6	344	141
7	436	141
8	460	141
9	515	141
10	546	141
11	547	141
0	547	135