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

analyze1.0ms (0%)

Memory

2.1MiB live, 2.1MiB allocated

Algorithm

1×

Search

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

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample1.1s (14.9%)

Memory

-1.2MiB live, 1 485.1MiB allocated

Samples

752.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 489.0ms

ival-mult: 201.0ms (41.1% of total)

ival-add: 115.0ms (23.5% of total)

ival-sqrt: 99.0ms (20.3% of total)

ival-div: 59.0ms (12.1% of total)

ival-true: 7.0ms (1.4% of total)

exact: 5.0ms (1% of total)

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

Bogosity

preprocess47.0ms (0.6%)

Memory

15.1MiB live, 59.7MiB allocated

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

Symmetry

(abs x)

(abs y)

(abs z)

(sort x y z)

explain257.0ms (3.5%)

Memory

-14.9MiB live, 225.1MiB allocated

FPErrors

Click to see full error table

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

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	oflow-rescue	161	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	162
↳	`(*.f64 y y)`	overflow	45
↳	`(*.f64 x x)`	overflow	5
↳	`(*.f64 z z)`	overflow	162
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	45
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	overflow	161
`sqrt.f64`	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`	uflow-rescue	2	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	underflow	2
↳	`(*.f64 y y)`	underflow	34
↳	`(*.f64 x x)`	underflow	146
↳	`(*.f64 z z)`	underflow	2
↳	`(+.f64 (.f64 x x) (.f64 y y))`	underflow	34
↳	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	underflow	2
`/.f64`	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`	o/n	1	0
↳	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`	overflow	162
↳	`(*.f64 y y)`	overflow	45
↳	`(*.f64 x x)`	overflow	5
↳	`(+.f64 (.f64 x x) (.f64 y y))`	overflow	45
↳	`(*.f64 z z)`	overflow	162

Confusion

	Predicted +	Predicted -
+	164	0
-	0	92

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	164	0	0
-	0	0	92

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	92
1	164

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

80.0ms

512×

valid

Compiler

Compiled 154 to 48 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 28.0ms (69.4% of total)

ival-add: 4.0ms (9.9% of total)

ival-sqrt: 4.0ms (9.9% of total)

ival-div: 3.0ms (7.4% of total)

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

exact: 0.0ms (0% of total)

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

eval0.0ms (0%)

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

prune1.0ms (0%)

Memory

1.7MiB live, 1.7MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.5%	(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 (0.1%)

Memory

10.2MiB live, 10.2MiB 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)

localize60.0ms (0.8%)

Memory

-8.7MiB live, 67.4MiB allocated

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	accuracy	100.0%	(+.f64 (.f64 x x) (.f64 y y))
✓	accuracy	99.5%	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))
✓	accuracy	41.0%	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))

Samples

22.0ms

256×

valid

Compiler

Compiled 60 to 13 computations (78.3% saved)

Precisions

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

ival-mult: 5.0ms (45.4% of total)

ival-div: 2.0ms (18.2% of total)

ival-add: 2.0ms (18.2% of total)

ival-sqrt: 2.0ms (18.2% of total)

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

exact: 0.0ms (0% of total)

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

series12.0ms (0.2%)

Memory

13.1MiB live, 13.1MiB allocated

Counts

4 → 132

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)>

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

Calls

33 calls:

Time	Variable		Point	Expression
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))

rewrite853.0ms (11.8%)

Memory

-65.8MiB live, 619.7MiB 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	45
1	58	45
2	479	45
3	6610	45
0	8491	38

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 350

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)

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

simplify782.0ms (10.8%)

Memory

-11.0MiB live, 815.1MiB 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	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

Outputs
(+ (pow y 2) (pow z 2))
(fma.f64 y y (*.f64 z z))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(fma.f64 (.f64 x x) (fma.f64 z (/.f64 z (.f64 x x)) #s(literal 1 binary64)) (*.f64 y y))
(+ (pow x 2) (pow z 2))
(fma.f64 z z (*.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(fma.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) #s(literal 1 binary64)) (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 y y (fma.f64 z z (*.f64 x x)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 (/.f64 #s(literal 1 binary64) (.f64 z z)) (fma.f64 y y (.f64 x x)) #s(literal 1 binary64)))
(pow y 2)
(*.f64 y y)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(* (pow x 2) (+ 1 (/ (pow y 2) (pow x 2))))
(fma.f64 y y (*.f64 x x))
(pow x 2)
(*.f64 x x)
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(+ (pow x 2) (pow y 2))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (pow y 2) (+ 1 (/ (pow x 2) (pow y 2))))
(fma.f64 y y (*.f64 x x))
(* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z))))
(+ (* 1/2 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))))
(fma.f64 (.f64 x x) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z)))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* -1/8 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z)))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z))))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow y 2) (pow z 2)))) (* (pow x 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow y 2) (pow z 2)))))) (* (pow x 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow x 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow y 2) (pow z 2)) 5))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 z z)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))))))))) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 z z))))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 z z)))))
(* x (sqrt 1/3))
(*.f64 x (sqrt.f64 #s(literal 1/3 binary64)))
(* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) (.f64 x (sqrt.f64 #s(literal 1/3 binary64))))
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(.f64 x (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64))))
(* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))))
(.f64 x (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (*.f64 z z)))) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* x (sqrt 1/3)))
(*.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* x (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) x)) (.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 1/3 binary64)))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2)))))))
(-.f64 #s(literal 0 binary64) (.f64 x (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 #s(literal 1/3 binary64)))))
(* -1 (* x (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 2)) (pow x 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow y 2) (pow z 2)) 3)) (pow x 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow y 2) (pow z 2))) (pow x 2))))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (.f64 z z))) (.f64 (.f64 x x) (.f64 x x))) #s(literal -1/8 binary64) (fma.f64 (/.f64 (fma.f64 y y (.f64 z z)) (.f64 x x)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 y y (.f64 z z)) (.f64 (fma.f64 y y (.f64 z z)) (fma.f64 y y (*.f64 z z)))) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))))) (sqrt.f64 #s(literal 1/3 binary64))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x))))
(+ (* 1/2 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))))
(fma.f64 (.f64 y y) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* -1/8 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))))))
(fma.f64 (.f64 y y) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x)))))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)) (.f64 y y)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow z 2)))) (* (pow y 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow z 2)))))) (* (pow y 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 3))))) (* 1/16 (* (* (pow y 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow z 2)) 5))))))))))
(fma.f64 (.f64 y y) (fma.f64 (.f64 y y) (fma.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 x x)) (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 x x)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 y y)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 z z (.f64 x x)))))
(* y (sqrt 1/3))
(*.f64 y (sqrt.f64 #s(literal 1/3 binary64)))
(* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))
(fma.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) y)) (.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
(* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
(.f64 y (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64))))
(* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
(.f64 y (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (fma.f64 (.f64 (fma.f64 z z (.f64 x x)) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (*.f64 y y))))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (sqrt 1/3)))
(-.f64 #s(literal 0 binary64) (*.f64 y (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* y (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))
(fma.f64 #s(literal -1 binary64) (.f64 (.f64 (fma.f64 z z (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) y)) (-.f64 #s(literal 0 binary64) (.f64 y (sqrt.f64 #s(literal 1/3 binary64)))))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2)))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (.f64 y y)))) (sqrt.f64 #s(literal 1/3 binary64))) (-.f64 #s(literal 0 binary64) y))
(* -1 (* y (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 2)) (pow y 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow z 2)) 3)) (pow y 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow z 2))) (pow y 2))))))))
(.f64 (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 z z (.f64 x x)) (.f64 y y)) #s(literal 1/2 binary64) (fma.f64 (.f64 (fma.f64 z z (.f64 x x)) (/.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) (pow.f64 y #s(literal 6 binary64)))) #s(literal 1/16 binary64) (/.f64 (.f64 (.f64 (fma.f64 z z (.f64 x x)) (fma.f64 z z (.f64 x x))) #s(literal -1/8 binary64)) (.f64 (.f64 y y) (*.f64 y y))))) (sqrt.f64 #s(literal 1/3 binary64))) (-.f64 #s(literal 0 binary64) y))
(* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2))))
(.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x))))
(+ (* 1/2 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))))
(fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (.f64 (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)) (.f64 z z)) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* -1/8 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))))))
(fma.f64 (.f64 z z) (fma.f64 (.f64 z z) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 x x)) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x)))))
(+ (* (sqrt 1/3) (sqrt (+ (pow x 2) (pow y 2)))) (* (pow z 2) (+ (* 1/2 (* (sqrt 1/3) (sqrt (/ 1 (+ (pow x 2) (pow y 2)))))) (* (pow z 2) (+ (* -1/8 (* (sqrt 1/3) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 3))))) (* 1/16 (* (* (pow z 2) (sqrt 1/3)) (sqrt (/ 1 (pow (+ (pow x 2) (pow y 2)) 5))))))))))
(fma.f64 (.f64 z z) (fma.f64 (.f64 z z) (fma.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 y y (.f64 x x)) #s(literal 5 binary64)))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 z z)) (sqrt.f64 #s(literal 1/3 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 y y (.f64 x x)) (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x)))))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal -1/8 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 y y (.f64 x x)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) #s(literal 1/2 binary64)))) (.f64 (sqrt.f64 #s(literal 1/3 binary64)) (sqrt.f64 (fma.f64 y y (.f64 x x)))))
(* z (sqrt 1/3))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(* z (+ (sqrt 1/3) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))
(fma.f64 z (sqrt.f64 #s(literal 1/3 binary64)) (.f64 #s(literal 1 binary64) (.f64 (.f64 (fma.f64 y y (.f64 x x)) (sqrt.f64 #s(literal 1/3 binary64))) (/.f64 #s(literal 1/2 binary64) z))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2))))))
(.f64 z (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (.f64 z z) (.f64 z z))) #s(literal -1/8 binary64) (.f64 (/.f64 (fma.f64 y y (.f64 x x)) (.f64 z z)) #s(literal 1/2 binary64))) (sqrt.f64 #s(literal 1/3 binary64))))
(* z (+ (sqrt 1/3) (+ (* -1/8 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 2)) (pow z 4))) (+ (* 1/16 (/ (* (sqrt 1/3) (pow (+ (pow x 2) (pow y 2)) 3)) (pow z 6))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))))
(.f64 z (fma.f64 (sqrt.f64 #s(literal 1/3 binary64)) (fma.f64 (/.f64 (fma.f64 y y (.f64 x x)) (.f64 z z)) #s(literal 1/2 binary64) (fma.f64 (/.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (.f64 (.f64 z z) (.f64 z z))) #s(literal -1/8 binary64) (.f64 (.f64 (.f64 (fma.f64 y y (.f64 x x)) (fma.f64 y y (.f64 x x))) (/.f64 (fma.f64 y y (*.f64 x x)) (pow.f64 z #s(literal 6 binary64)))) #s(literal 1/16 binary64)))) (sqrt.f64 #s(literal 1/3 binary64))))
(* -1 (* z (sqrt 1/3)))
(*.f64 z (-.f64 #s(literal 0 binary64) (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 (-.f64 #s(literal 0 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))) (* 1/2 (/ (* (sqrt 1/3) (+ (pow x 2) (pow y 2))) (pow z 2)))))))
(.f64 z (-.f64 #s(literal 0 binary64) (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))) (-.f64 #s(literal 0 binary64) 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))))

eval202.0ms (2.8%)

Memory: 13.7MiB live, 124.3MiB allocated
Compiler: Compiled 18 353 to 1 565 computations (91.5% saved)

prune66.0ms (0.9%)

Memory

22.9MiB live, 177.8MiB allocated

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	477	5	482
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	478	5	483

Accuracy

99.5%

Counts

483 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.4%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
▶	99.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
▶	40.3%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
▶	40.5%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	40.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify17.0ms (0.2%)

Memory

-64.7MiB live, 15.9MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

42×	`-lowering-.f32`
42×	`-lowering-.f64`
34×	`accelerator-lowering-fma.f32`
34×	`accelerator-lowering-fma.f64`
28×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	126
1	33	126
2	50	126
3	56	126
4	57	126
0	57	116

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize83.0ms (1.1%)

Memory

7.2MiB live, 198.3MiB allocated

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.5%	(/.f64 (sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z)))) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	40.6%	(sqrt.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.5%	(/.f64 (*.f64 z z) #s(literal 3 binary64))
✓	accuracy	41.0%	(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	100.0%	(fma.f64 y y (*.f64 z z))
✓	accuracy	99.4%	(.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64))
✓	accuracy	41.0%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	accuracy	99.9%	(.f64 z (.f64 z #s(literal 1/3 binary64)))
✓	accuracy	99.5%	(*.f64 z #s(literal 1/3 binary64))
✓	accuracy	41.0%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 1/3 binary64))
✓	accuracy	99.4%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))

Samples

55.0ms

256×

valid

Compiler

Compiled 118 to 24 computations (79.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 40.0ms

ival-mult: 18.0ms (44.6% of total)

ival-sqrt: 11.0ms (27.2% of total)

const: 6.0ms (14.9% of total)

ival-div: 3.0ms (7.4% of total)

ival-add: 2.0ms (5% of total)

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

exact: 0.0ms (0% of total)

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

series21.0ms (0.3%)

Memory

15.1MiB live, 53.3MiB allocated

Counts

15 → 264

Calls

Call 1

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

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

Calls

66 calls:

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

rewrite1.0s (14%)

Memory

15.5MiB live, 813.1MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

4 584×	`accelerator-lowering-fma.f32`
4 584×	`accelerator-lowering-fma.f64`
4 458×	`-lowering-.f32`
4 458×	`-lowering-.f64`
3 230×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	95
1	92	95
2	597	95
3	7151	95
0	9077	83

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 583

Calls

Call 1

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

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

simplify552.0ms (7.6%)

Memory

-13.1MiB live, 1 214.4MiB allocated

Algorithm

1×	egg-herbie

Rules

14 820×	`accelerator-lowering-fma.f32`
14 820×	`accelerator-lowering-fma.f64`
6 634×	`-lowering-.f32`
6 634×	`-lowering-.f64`
4 124×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	411	4276
1	1284	4234
2	4677	4228
0	8192	3769

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

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

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))
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(+ (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))))))))))
(fma.f64 (.f64 x x) (fma.f64 (.f64 x x) (fma.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 z z (.f64 y y)) (.f64 (fma.f64 z z (.f64 y y)) (fma.f64 z z (.f64 y y)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 z z (.f64 y y)) #s(literal 5 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 z z (.f64 y y)))))) (sqrt.f64 (fma.f64 z z (.f64 y y))))
x
(* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))
(.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64)))
(* 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 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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64))))
(* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(.f64 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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x 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))) #s(literal 1 binary64)))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2)))))))
(.f64 x (-.f64 #s(literal 0 binary64) (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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (*.f64 x x)) #s(literal 1 binary64)))))
(* -1 (* x (+ 1 (+ (* -1/8 (/ (pow (+ (pow y 2) (pow z 2)) 2) (pow x 4))) (+ (* 1/16 (/ (pow (+ (pow y 2) (pow z 2)) 3) (pow x 6))) (* 1/2 (/ (+ (pow y 2) (pow z 2)) (pow x 2))))))))
(.f64 (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))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 z z (.f64 y y)) (.f64 x 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))) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) x))
(sqrt (+ (pow x 2) (pow z 2)))
(sqrt.f64 (fma.f64 x x (*.f64 z z)))
(+ (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 x x (.f64 z z))))) (sqrt.f64 (fma.f64 x x (.f64 z z))))
(+ (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 x x (.f64 z z)))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 z z)) (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))))))))) (sqrt.f64 (fma.f64 x x (*.f64 z z))))
(+ (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 (.f64 y y) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 y y) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 z z)) #s(literal 5 binary64))))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 z z)) (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z)))))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 z z)))))) (sqrt.f64 (fma.f64 x x (.f64 z z))))
y
(* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2)))))
(.f64 y (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (*.f64 y y)) #s(literal 1 binary64)))
(* 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 y (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (.f64 (.f64 y y) (*.f64 y y))) #s(literal 1 binary64))))
(* 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 y (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (.f64 (.f64 y y) (.f64 y y))) #s(literal 1 binary64)))))
(* -1 y)
(-.f64 #s(literal 0 binary64) y)
(* -1 (* y (+ 1 (* 1/2 (/ (+ (pow x 2) (pow z 2)) (pow y 2))))))
(.f64 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (*.f64 y y)) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) 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 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (.f64 (.f64 y y) (*.f64 y y))) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) y))
(* -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 (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 z z)) (.f64 y y)) (fma.f64 #s(literal 1/16 binary64) (.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (/.f64 (fma.f64 x x (.f64 z z)) (pow.f64 y #s(literal 6 binary64)))) (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 z z)) (fma.f64 x x (.f64 z z))) (.f64 (.f64 y y) (.f64 y y))) #s(literal 1 binary64)))) (-.f64 #s(literal 0 binary64) y))
(sqrt (+ (pow x 2) (pow y 2)))
(sqrt.f64 (fma.f64 x x (*.f64 y y)))
(+ (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 x x (.f64 y y)))) (.f64 (.f64 z z) #s(literal 1/2 binary64)) (sqrt.f64 (fma.f64 x x (.f64 y y))))
(+ (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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.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) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y)))))) (sqrt.f64 (fma.f64 x x (*.f64 y y))))
(+ (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 z (.f64 z (fma.f64 (.f64 z z) (fma.f64 (.f64 z z) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 (fma.f64 x x (.f64 y y)) #s(literal 5 binary64)))) #s(literal 1/16 binary64)) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))))))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (fma.f64 x x (.f64 y y))))))) (sqrt.f64 (fma.f64 x x (.f64 y y))))
z
(* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2)))))
(.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (*.f64 z z)) #s(literal 1 binary64)))
(* 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 -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (*.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)))))))
(.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))) (pow.f64 z #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1 binary64)))))
(* -1 z)
(-.f64 #s(literal 0 binary64) z)
(* -1 (* z (+ 1 (* 1/2 (/ (+ (pow x 2) (pow y 2)) (pow z 2))))))
(-.f64 #s(literal 0 binary64) (.f64 z (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (*.f64 z z)) #s(literal 1 binary64))))
(* -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 (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (*.f64 z z)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) z))
(* -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 #s(literal 0 binary64) (.f64 z (fma.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y))) (.f64 (.f64 z z) (.f64 z z))) (fma.f64 #s(literal 1/16 binary64) (/.f64 (.f64 (fma.f64 x x (.f64 y y)) (.f64 (fma.f64 x x (.f64 y y)) (fma.f64 x x (.f64 y y)))) (pow.f64 z #s(literal 6 binary64))) (fma.f64 #s(literal 1/2 binary64) (/.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) #s(literal 1 binary64))))))
(+ (pow y 2) (pow z 2))
(fma.f64 z z (*.f64 y y))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.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)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(* (pow x 2) (+ 1 (+ (/ (pow y 2) (pow x 2)) (/ (pow z 2) (pow x 2)))))
(.f64 x (.f64 x (fma.f64 z (/.f64 z (.f64 x x)) (fma.f64 y (/.f64 y (.f64 x x)) #s(literal 1 binary64)))))
(+ (pow x 2) (pow z 2))
(fma.f64 x x (*.f64 z z))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(pow y 2)
(*.f64 y y)
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(* (pow y 2) (+ 1 (+ (/ (pow x 2) (pow y 2)) (/ (pow z 2) (pow y 2)))))
(.f64 (.f64 y y) (fma.f64 z (/.f64 z (.f64 y y)) (fma.f64 x (/.f64 x (.f64 y y)) #s(literal 1 binary64))))
(+ (pow x 2) (pow y 2))
(fma.f64 x x (*.f64 y y))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(+ (pow x 2) (+ (pow y 2) (pow z 2)))
(fma.f64 z z (fma.f64 x x (*.f64 y y)))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))
(pow z 2)
(*.f64 z z)
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))
(* (pow z 2) (+ 1 (+ (/ (pow x 2) (pow z 2)) (/ (pow y 2) (pow z 2)))))
(.f64 (.f64 z z) (fma.f64 y (/.f64 y (.f64 z z)) (fma.f64 x (/.f64 x (.f64 z z)) #s(literal 1 binary64))))

eval153.0ms (2.1%)

Memory: 17.9MiB live, 329.4MiB allocated
Compiler: Compiled 25 374 to 2 229 computations (91.2% saved)

prune95.0ms (1.3%)

Memory

5.9MiB live, 285.7MiB allocated

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	1 002	3	1 005
Fresh	0	0	0
Picked	2	3	5
Done	0	0	0
Total	1 004	6	1 010

Accuracy

99.9%

Counts

1 010 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.1%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
▶	98.4%	(*.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))))
✓	99.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	40.5%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
▶	40.2%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	40.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))

Compiler

Compiled 60 to 43 computations (28.3% saved)

simplify6.0ms (0.1%)

Memory

16.6MiB live, 16.6MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
✓	cost-diff	0	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))
✓	cost-diff	0	(sqrt.f64 z)
✓	cost-diff	0	(/.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
✓	cost-diff	14592	(*.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))))
✓	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)))

Rules

64×	`-lowering-.f32`
64×	`-lowering-.f64`
26×	`associate-r`
22×	`*-commutative`
18×	`associate-l`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	60
1	20	60
2	27	52
3	32	44
4	51	42
5	72	42
6	76	42
7	78	42
0	78	42

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(sqrt (* (* z z) 1/3))
(* (* z z) 1/3)
(* z z)
z
1/3
(* (/ (sqrt z) (pow 3 1/4)) (/ (sqrt z) (pow 3 1/4)))
(/ (sqrt z) (pow 3 1/4))
(sqrt z)
z
(pow 3 1/4)
3
1/4
(/ z (sqrt 3))
z
(sqrt 3)
3

Outputs
(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)
(*.f64 z z)
z
1/3
#s(literal 1/3 binary64)
(* (/ (sqrt z) (pow 3 1/4)) (/ (sqrt z) (pow 3 1/4)))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ (sqrt z) (pow 3 1/4))
(/.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(sqrt z)
(sqrt.f64 z)
z
(pow 3 1/4)
(pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))
3
#s(literal 3 binary64)
1/4
#s(literal 1/4 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)

localize52.0ms (0.7%)

Memory

-22.8MiB live, 135.5MiB allocated

Localize:

Found 9 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.5%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))
✓	accuracy	100.0%	(sqrt.f64 z)
✓	accuracy	99.3%	(/.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
✓	accuracy	99.3%	(*.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))))
✓	accuracy	100.0%	(*.f64 z z)
✓	accuracy	99.4%	(.f64 (.f64 z z) #s(literal 1/3 binary64))
✓	accuracy	41.0%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))

Samples

34.0ms

256×

valid

Compiler

Compiled 53 to 17 computations (67.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 23.0ms

ival-mult: 5.0ms (21.4% of total)

ival-sqrt: 5.0ms (21.4% of total)

ival-pow: 5.0ms (21.4% of total)

ival-div: 4.0ms (17.1% of total)

const: 4.0ms (17.1% of total)

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

exact: 0.0ms (0% of total)

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

series40.0ms (0.5%)

Memory

22.8MiB live, 99.9MiB allocated

Counts

9 → 84

Calls

Call 1

Inputs
#<alt (sqrt (* (* z z) 1/3))>
#<alt (* (* z z) 1/3)>
#<alt (* z z)>
#<alt (* (/ (sqrt z) (pow 3 1/4)) (/ (sqrt z) (pow 3 1/4)))>
#<alt (/ (sqrt z) (pow 3 1/4))>
#<alt (sqrt z)>
#<alt (pow 3 1/4)>
#<alt (/ z (sqrt 3))>
#<alt (sqrt 3)>

Outputs
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* z (sqrt 1/3))>
#<alt (* -1 (* z (sqrt 1/3)))>
#<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 (* 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 (* (pow (sqrt -1) 2) (sqrt 1/3))))>
#<alt (* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))>
#<alt (* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))>
#<alt (* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* (pow 1/3 1/4) (sqrt z))>
#<alt (* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))>
#<alt (* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (sqrt z)>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt z) (pow (sqrt -1) 2)))>
#<alt (/ z (sqrt 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))>

Calls

21 calls:

Time	Variable		Point	Expression
35.0ms	z	@	0	(/ (sqrt z) (pow 3 1/4))
1.0ms	z	@	-inf	(* (/ (sqrt z) (pow 3 1/4)) (/ (sqrt z) (pow 3 1/4)))
1.0ms	z	@	inf	(/ z (sqrt 3))
1.0ms	z	@	-inf	(/ (sqrt z) (pow 3 1/4))
0.0ms	z	@	0	(/ z (sqrt 3))

rewrite92.0ms (1.3%)

Memory

-10.9MiB live, 165.4MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

1 062×	`-lowering-.f32`
1 062×	`-lowering-.f64`
714×	`/-lowering-/.f32`
714×	`/-lowering-/.f64`
280×	`frac-times`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	43
1	55	33
2	266	33
0	1829	33

Stop Event

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

Counts

9 → 381

Calls

Call 1

Inputs
(sqrt (* (* z z) 1/3))
(* (* z z) 1/3)
(* z z)
(* (/ (sqrt z) (pow 3 1/4)) (/ (sqrt z) (pow 3 1/4)))
(/ (sqrt z) (pow 3 1/4))
(sqrt z)
(pow 3 1/4)
(/ z (sqrt 3))
(sqrt 3)

Outputs
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 z (*.f64 z #s(literal 1/3 binary64))))))
(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
(pow.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))) (.f64 z (*.f64 z #s(literal 1/3 binary64)))) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 (log.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))) #s(literal 1/2 binary64))
(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
(.f64 (sqrt.f64 z) (sqrt.f64 (.f64 z #s(literal 1/3 binary64))))
(.f64 (sqrt.f64 (.f64 z #s(literal 1/3 binary64))) (sqrt.f64 z))
(*.f64 (sqrt.f64 #s(literal 1/3 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 (.f64 z (.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64)) (pow.f64 (.f64 z (*.f64 z #s(literal 1/3 binary64))) #s(literal 1/4 binary64)))
(.f64 z (.f64 z #s(literal 1/3 binary64)))
(.f64 (.f64 z z) #s(literal 1/3 binary64))
(.f64 #s(literal 1/3 binary64) (.f64 z z))
(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (*.f64 z #s(literal 1/3 binary64))))
(.f64 (.f64 z #s(literal 1/3 binary64)) z)
(.f64 (.f64 (*.f64 z #s(literal 1/3 binary64)) (sqrt.f64 z)) (sqrt.f64 z))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 z)))
(fabs.f64 (*.f64 z z))
(sqrt.f64 (.f64 (.f64 z 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 (.f64 z z) (*.f64 z z)) #s(literal 1/2 binary64))
(pow.f64 (exp.f64 (log.f64 z)) #s(literal 2 binary64))
(*.f64 z z)
(.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) z))
(*.f64 (exp.f64 (log.f64 z)) (exp.f64 (log.f64 z)))
(.f64 (.f64 z (sqrt.f64 z)) (sqrt.f64 z))
(exp.f64 (.f64 #s(literal 2 binary64) (log.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))
(-.f64 #s(literal 0 binary64) (/.f64 z (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))) (/.f64 z (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(sqrt.f64 (/.f64 (*.f64 z z) #s(literal 3 binary64)))
(neg.f64 (/.f64 z (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))))
(neg.f64 (.f64 (.f64 (sqrt.f64 z) (neg.f64 (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)))))
(neg.f64 (.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (*.f64 (sqrt.f64 z) (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))))
(neg.f64 (*.f64 #s(literal 1 binary64) (/.f64 z (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))))
(neg.f64 (/.f64 (*.f64 (sqrt.f64 z) (neg.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 z))))
(neg.f64 (/.f64 (*.f64 z (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/.f64 (sqrt.f64 z) (/.f64 (sqrt.f64 #s(literal 3 binary64)) (sqrt.f64 z)))
(/.f64 (sqrt.f64 z) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(/.f64 (sqrt.f64 z) (neg.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 (*.f64 (sqrt.f64 z) (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 z)))
(/.f64 (-.f64 #s(literal 0 binary64) z) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (/.f64 (sqrt.f64 #s(literal 3 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
(/.f64 #s(literal 1 binary64) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)))))
(/.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) z))
(/.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 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)))
(/.f64 #s(literal -1 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)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 #s(literal -1 binary64) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (sqrt.f64 z))))
(/.f64 (-.f64 #s(literal 0 binary64) (*.f64 z (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(/.f64 (/.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (sqrt.f64 z)))
(/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) (.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(/.f64 (*.f64 (sqrt.f64 z) (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))))
(/.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))
(/.f64 (sqrt.f64 (/.f64 z #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 z)))
(/.f64 (.f64 (sqrt.f64 z) (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal -1 binary64)) (.f64 (-.f64 #s(literal 0 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 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))) (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))) (*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(/.f64 (.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)))
(/.f64 (.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) (-.f64 #s(literal 0 binary64) (sqrt.f64 z))) (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(/.f64 (.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) #s(literal 1 binary64)) (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (sqrt.f64 z))))
(/.f64 (.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) #s(literal -1 binary64)) (*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))))
(/.f64 (*.f64 z (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) z) #s(literal 1 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) z) #s(literal -1 binary64)) (sqrt.f64 #s(literal 3 binary64)))
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
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(.f64 (.f64 (sqrt.f64 z) (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))) (/.f64 (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (/.f64 #s(literal 1 binary64) (sqrt.f64 z))))
(*.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)) (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (sqrt.f64 z))))
(*.f64 (sqrt.f64 (/.f64 z #s(literal 3 binary64))) (sqrt.f64 z))
(*.f64 (sqrt.f64 (/.f64 z #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 z))))
(.f64 (exp.f64 (log.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))) (exp.f64 (log.f64 (*.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/8 binary64)))) (/.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))))
(*.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(*.f64 (/.f64 z (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (/.f64 (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (sqrt.f64 z))))
(.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))))
(*.f64 (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (/.f64 (sqrt.f64 z) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (sqrt.f64 z))))
(.f64 (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) #s(literal -1 binary64)) (*.f64 (sqrt.f64 z) (neg.f64 (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))))
(.f64 (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))) (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))))
(*.f64 (/.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 z)) #s(literal -1 binary64)) (sqrt.f64 (/.f64 z #s(literal 3 binary64))))
(.f64 (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (*.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))))
(*.f64 (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)) (pow.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z) #s(literal -1/2 binary64)))
(.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) z)) (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (.f64 (*.f64 z (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) #s(literal 1 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64)))
(.f64 (/.f64 (.f64 (sqrt.f64 z) (pow.f64 #s(literal 3 binary64) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 z)))
(exp.f64 (*.f64 (log.f64 #s(literal 3 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 #s(literal 9 binary64)) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/4 binary64) (log.f64 #s(literal 3 binary64))) #s(literal 2 binary64)))
(-.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))
(sqrt.f64 #s(literal 3 binary64))
(neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))
(/.f64 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(/.f64 (-.f64 #s(literal 0 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))))
(pow.f64 #s(literal 3 binary64) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) #s(literal 4 binary64))
(pow.f64 #s(literal 9 binary64) #s(literal 1/4 binary64))
(pow.f64 #s(literal 81 binary64) #s(literal 1/8 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 (sqrt.f64 #s(literal 3 binary64)) #s(literal 1 binary64))
(*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))))
(*.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)) #s(literal 1 binary64)))
(*.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))
(.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/16 binary64)) (.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/16 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))
(*.f64 (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)) (/.f64 (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)) #s(literal 1 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 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 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) #s(literal -1 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/4 binary64))) (-.f64 #s(literal 0 binary64) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))) (pow.f64 #s(literal 3 binary64) #s(literal 1/8 binary64)))
(.f64 (.f64 (pow.f64 #s(literal 3 binary64) #s(literal 3/8 binary64)) (pow.f64 #s(literal 3 binary64) #s(literal 1/16 binary64))) (pow.f64 #s(literal 3 binary64) #s(literal 1/16 binary64)))

simplify500.0ms (6.9%)

Memory

-9.0MiB live, 149.5MiB allocated

Algorithm

1×	egg-herbie

Rules

1 184×	`-lowering-.f32`
1 184×	`-lowering-.f64`
1 184×	`accelerator-lowering-fma.f32`
1 184×	`accelerator-lowering-fma.f64`
1 062×	`associate-r`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	340
1	52	340
2	158	340
3	303	340
4	874	340
5	1394	340
6	1875	340
7	2186	340
8	2718	340
9	2824	340
10	2882	340
11	2912	340
12	2972	340
13	3512	340
14	3512	340
15	3514	340
16	3514	340
17	3786	340
18	4190	340
19	4302	340
20	4330	340
21	4334	340
22	4334	340
23	4353	340
24	4353	340
25	4603	340
0	4603	340

Stop Event

1×	iter limit
1×	saturated

Counts

84 → 84

Calls

Call 1

Inputs
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* z (sqrt 1/3))
(* -1 (* z (sqrt 1/3)))
(* -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))
(* 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 (* (pow (sqrt -1) 2) (sqrt 1/3))))
(* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))
(* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))
(* -1 (* z (* (pow (sqrt -1) 2) (sqrt 1/3))))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* (pow 1/3 1/4) (sqrt z))
(* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))
(* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))
(* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))
(* -1 (* (pow 1/3 1/4) (* (sqrt z) (pow (sqrt -1) 2))))
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(sqrt z)
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(* -1 (* (sqrt z) (pow (sqrt -1) 2)))
(/ z (sqrt 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))

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

eval437.0ms (6%)

Memory: -15.7MiB live, 138.9MiB allocated
Compiler: Compiled 7 515 to 767 computations (89.8% saved)

prune77.0ms (1.1%)

Memory

29.0MiB live, 111.0MiB allocated

Pruning

7 alts after pruning (2 fresh and 5 done)

	Pruned	Kept	Total
New	579	2	581
Fresh	0	0	0
Picked	1	2	3
Done	0	3	3
Total	580	7	587

Accuracy

99.9%

Counts

587 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.9%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	99.1%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	99.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	40.5%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	40.2%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	40.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
▶	90.3%	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Compiler

Compiled 66 to 53 computations (19.7% saved)

simplify17.0ms (0.2%)

Memory

-25.5MiB live, 13.8MiB allocated

Algorithm

1×	egg-herbie

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 #s(literal 3 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	cost-diff	0	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	cost-diff	1408	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	cost-diff	0	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
✓	cost-diff	0	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
✓	cost-diff	320	(*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64))
✓	cost-diff	12800	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Rules

48×	`-lowering-.f32`
48×	`-lowering-.f64`
32×	`/-lowering-/.f32`
32×	`/-lowering-/.f64`
16×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	23	43
2	38	39
3	52	38
4	75	38
5	95	38
6	109	38
7	112	38
0	112	38

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize51.0ms (0.7%)

Memory

-4.1MiB live, 115.8MiB allocated

Localize:

Found 8 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	99.5%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64))))
✓	accuracy	98.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))
✓	accuracy	100.0%	(sqrt.f64 #s(literal 3 binary64))
✓	accuracy	100.0%	(log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z))
✓	accuracy	99.3%	(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
✓	accuracy	90.7%	(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 #s(literal 3 binary64)) z)) #s(literal -1 binary64)))

Samples

29.0ms

256×

valid

Compiler

Compiled 54 to 16 computations (70.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-div: 7.0ms (40.2% of total)

ival-log: 3.0ms (17.2% of total)

ival-exp: 3.0ms (17.2% of total)

ival-mult: 2.0ms (11.5% of total)

ival-sqrt: 2.0ms (11.5% of total)

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

exact: 0.0ms (0% of total)

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

series40.0ms (0.5%)

Memory

11.3MiB live, 87.4MiB allocated

Counts

8 → 60

Calls

Call 1

Inputs
#<alt (exp (* (log (/ (sqrt 3) z)) -1))>
#<alt (* (log (/ (sqrt 3) z)) -1)>
#<alt (log (/ (sqrt 3) z))>
#<alt (/ (sqrt 3) z)>
#<alt (/ 1 (/ 1 (sqrt 3)))>
#<alt (/ z (/ 1 (/ 1 (sqrt 3))))>
#<alt (/ 1 (sqrt 3))>
#<alt (sqrt 3)>

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

Calls

15 calls:

Time	Variable		Point	Expression
16.0ms	z	@	-inf	(* (log (/ (sqrt 3) z)) -1)
14.0ms	z	@	0	(* (log (/ (sqrt 3) z)) -1)
9.0ms	z	@	inf	(* (log (/ (sqrt 3) z)) -1)
0.0ms	z	@	0	(exp (* (log (/ (sqrt 3) z)) -1))
0.0ms	z	@	inf	(exp (* (log (/ (sqrt 3) z)) -1))

rewrite83.0ms (1.1%)

Memory

-0.3MiB live, 155.2MiB allocated

Algorithm

1×	batch-egg-rewrite

Rules

486×	`-lowering-.f32`
486×	`-lowering-.f64`
302×	`/-lowering-/.f32`
302×	`/-lowering-/.f64`
244×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	36
1	55	30
2	229	29
0	1025	29

Stop Event

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

Counts

8 → 301

Calls

Call 1

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

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

simplify24.0ms (0.3%)

Memory

15.0MiB live, 53.9MiB allocated

Algorithm

1×	egg-herbie

Rules

164×	`accelerator-lowering-fma.f32`
164×	`accelerator-lowering-fma.f64`
100×	`-lowering-.f32`
100×	`-lowering-.f64`
78×	`sub-neg`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	340
1	48	324
2	67	316
3	87	316
4	141	316
5	231	316
6	278	316
7	315	316
8	325	316
9	328	316
0	328	316

Stop Event

1×	iter limit
1×	saturated

Counts

60 → 60

Calls

Call 1

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

Outputs
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (* -1 (log z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (sqrt 3)) (log (/ 1 z))))
(-.f64 (log.f64 z) (log.f64 (sqrt.f64 #s(literal 3 binary64))))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(* -1 (+ (log (* -1 (sqrt 3))) (log (/ -1 z))))
(-.f64 (-.f64 #s(literal 0 binary64) (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64))))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(+ (log (sqrt 3)) (* -1 (log z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (* -1 (log z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (* -1 (log z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (* -1 (log z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (log (/ 1 z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (log (/ 1 z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (log (/ 1 z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (sqrt 3)) (log (/ 1 z)))
(-.f64 (log.f64 (sqrt.f64 #s(literal 3 binary64))) (log.f64 z))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(+ (log (* -1 (sqrt 3))) (log (/ -1 z)))
(+.f64 (log.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal 3 binary64)))) (log.f64 (/.f64 #s(literal -1 binary64) z)))
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ (sqrt 3) z)
(/.f64 (sqrt.f64 #s(literal 3 binary64)) z)
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
(/ z (sqrt 3))
(/.f64 z (sqrt.f64 #s(literal 3 binary64)))

eval47.0ms (0.6%)

Memory: -1.8MiB live, 119.1MiB allocated
Compiler: Compiled 4 516 to 928 computations (79.5% saved)

prune81.0ms (1.1%)

Memory

-17.4MiB live, 105.3MiB allocated

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	391	1	392
Fresh	0	0	0
Picked	1	1	2
Done	0	5	5
Total	392	7	399

Accuracy

99.9%

Counts

399 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	97.9%	(/.f64 z (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (sqrt.f64 #s(literal 3 binary64)))))
✓	99.1%	(/.f64 z (sqrt.f64 #s(literal 3 binary64)))
✓	99.0%	(*.f64 z (sqrt.f64 #s(literal 1/3 binary64)))
✓	40.5%	(sqrt.f64 (.f64 (fma.f64 y y (.f64 z z)) #s(literal 1/3 binary64)))
✓	40.2%	(sqrt.f64 (.f64 (.f64 z z) #s(literal 1/3 binary64)))
✓	40.6%	(sqrt.f64 (.f64 z (.f64 z #s(literal 1/3 binary64))))
	90.3%	(exp.f64 (log.f64 (/.f64 z (sqrt.f64 #s(literal 3 binary64)))))

Compiler

Compiled 164 to 96 computations (41.5% saved)

regimes53.0ms (0.7%)

Memory

20.3MiB live, 98.9MiB allocated

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

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

Calls

10 calls:

18.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	z
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
99.1%	1	`x`
99.1%	1	`y`
99.1%	1	`z`
99.1%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.1%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.1%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.1%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.1%	1	`(*.f64 x x)`
99.1%	1	`(*.f64 y y)`
99.1%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

regimes21.0ms (0.3%)

Memory

-1.0MiB live, 43.8MiB allocated

Accuracy

Total -37.7b remaining (-5631.5%)

Threshold costs -37.7b (-5631.5%)

Counts

3 → 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)))

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

Calls

10 calls:

5.0ms	(*.f64 x x)
2.0ms	z
2.0ms	x
2.0ms	y
2.0ms	(+.f64 (.f64 x x) (.f64 y y))

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`y`
99.0%	1	`z`
99.0%	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64)))`
99.0%	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) #s(literal 3 binary64))`
99.0%	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
99.0%	1	`(+.f64 (.f64 x x) (.f64 y y))`
99.0%	1	`(*.f64 x x)`
99.0%	1	`(*.f64 y y)`
99.0%	1	`(*.f64 z z)`

Compiler

Compiled 87 to 56 computations (35.6% saved)

simplify8.0ms (0.1%)

Memory

-18.9MiB live, 20.7MiB allocated

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	8	8

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness243.0ms (3.3%)

Memory

-3.7MiB live, 233.9MiB allocated

Rules

13 366×	`accelerator-lowering-fma.f32`
13 366×	`accelerator-lowering-fma.f64`
5 460×	`-lowering-.f32`
5 460×	`-lowering-.f64`
4 584×	`accelerator-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	95
1	92	95
2	597	95
3	7151	95
0	9077	83
0	230	2442
1	673	2442
2	2272	2406
3	5706	2289
0	8198	1992

Stop Event

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

Compiler

Compiled 32 to 27 computations (15.6% saved)

preprocess82.0ms (1.1%)

Memory: 15.7MiB live, 253.5MiB allocated
Compiler: Compiled 182 to 134 computations (26.4% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Iter	Nodes	Cost
0	22	340
1	48	324
2	67	316
3	87	316
4	141	316
5	231	316
6	278	316
7	315	316
8	325	316
9	328	316
0	328	316

Iter	Nodes	Cost
0	22	340
1	48	324
2	67	316
3	87	316
4	141	316
5	231	316
6	278	316
7	315	316
8	325	316
9	328	316
0	328	316

analyze1.0ms (0%)

sample1.1s (14.9%)

preprocess47.0ms (0.6%)

explain257.0ms (3.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify5.0ms (0.1%)

localize60.0ms (0.8%)

series12.0ms (0.2%)

rewrite853.0ms (11.8%)

simplify782.0ms (10.8%)

eval202.0ms (2.8%)

prune66.0ms (0.9%)

simplify17.0ms (0.2%)

localize83.0ms (1.1%)

series21.0ms (0.3%)

rewrite1.0s (14%)

simplify552.0ms (7.6%)

eval153.0ms (2.1%)

prune95.0ms (1.3%)

simplify6.0ms (0.1%)

localize52.0ms (0.7%)

series40.0ms (0.5%)

rewrite92.0ms (1.3%)

simplify500.0ms (6.9%)

eval437.0ms (6%)

prune77.0ms (1.1%)

simplify17.0ms (0.2%)

localize51.0ms (0.7%)

series40.0ms (0.5%)

rewrite83.0ms (1.1%)

simplify24.0ms (0.3%)

eval47.0ms (0.6%)

prune81.0ms (1.1%)

regimes53.0ms (0.7%)

regimes21.0ms (0.3%)

simplify8.0ms (0.1%)

soundness243.0ms (3.3%)

preprocess82.0ms (1.1%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	22	340
1	48	324
2	67	316
3	87	316
4	141	316
5	231	316
6	278	316
7	315	316
8	325	316
9	328	316
0	328	316