Details

analyze318.0ms (4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
42.1%	57.7%	0.1%	10
49.1%	50.7%	0.1%	11
57.3%	42.5%	0.1%	12

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample1.7s (21.4%)

Results

1.7s

8256×

body

256

valid

preprocess34.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

9×	`fma-def_binary64`
6×	`+-commutative_binary64`
4×	`associate-+l+_binary64`
1×	`swap-x-z`
1×	`swap-x-y`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	76
1	35	68
2	40	68
0	3	3
1	3	3

Stop Event

1×	unsound
1×	saturated

Calls

Call 1

Inputs
0
1
2

Outputs
0
1
0
2
0

Call 2

Inputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 y y) (.f64 x x)) (*.f64 z z)) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 z z) (.f64 y y)) (*.f64 x x)) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 z z)) (*.f64 y y)) 3))

Outputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(sqrt.f64 (/.f64 (+.f64 (.f64 x x) (fma.f64 z z (.f64 y y))) 3))
(sqrt.f64 (/.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 y y) (.f64 x x)) (*.f64 z z)) 3))
(sqrt.f64 (/.f64 (+.f64 (.f64 x x) (fma.f64 z z (.f64 y y))) 3))
(sqrt.f64 (/.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 z z) (.f64 y y)) (*.f64 x x)) 3))
(sqrt.f64 (/.f64 (+.f64 (.f64 x x) (fma.f64 z z (.f64 y y))) 3))
(sqrt.f64 (/.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 z z)) (*.f64 y y)) 3))
(sqrt.f64 (/.f64 (+.f64 (.f64 x x) (fma.f64 z z (.f64 y y))) 3))
(sqrt.f64 (/.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) 3))

Symmetry

(sort x y z)

Compiler

Compiled 20 to 14 computations (30% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

9×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	17	17
2	28	17
3	34	17

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Outputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(sqrt.f64 (/.f64 (+.f64 (fma.f64 x x (.f64 y y)) (.f64 z z)) 3))
(sqrt.f64 (/.f64 (fma.f64 x x (fma.f64 y y (*.f64 z z))) 3))
(sqrt.f64 (/.f64 (fma.f64 y y (fma.f64 z z (*.f64 x x))) 3))

eval1.0ms (0%)

Compiler: Compiled 29 to 16 computations (44.8% saved)

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

40.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	40.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Compiler

Compiled 17 to 11 computations (35.3% saved)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
✓	0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
✓	37.2b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Compiler

Compiled 61 to 14 computations (77% saved)

series23.0ms (0.3%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	x	@	0	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
2.0ms	x	@	0	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
1.0ms	x	@	inf	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
1.0ms	y	@	0	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
1.0ms	z	@	0	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite92.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`log-prod_binary64`
496×	`fma-def_binary64`
330×	`pow2_binary64`
241×	`fma-neg_binary64`
224×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	50
1	268	35
2	3677	35

Stop Event

1×	node limit

Counts

3 → 161

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (exp.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))) 2)) (log.f64 (cbrt.f64 (exp.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (exp.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) (cbrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (hypot.f64 y z)) (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 2)) (sqrt.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 1 1/2) (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 3 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 3) (hypot.f64 x (hypot.f64 y z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))) (sqrt.f64 -3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (hypot.f64 x (hypot.f64 y z))) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 3 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) (hypot.f64 x (hypot.f64 y z))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)))) 2)) (log.f64 (cbrt.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))) (log.f64 (sqrt.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) (pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) (.f64 (cbrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 2) (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)) 2) (.f64 (cbrt.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) (.f64 (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (hypot.f64 x (hypot.f64 y z)) (.f64 (hypot.f64 x (hypot.f64 y z)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (neg.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1/3 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))) 3) (sqrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))) (cbrt.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 3 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (/.f64 3 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) -3))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (exp.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 1/3)) 1))))))
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Outputs

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((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 y) y) (pow.f64 (exp.f64 z) z)) (pow.f64 (exp.f64 x) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (exp.f64 (pow.f64 (hypot.f64 y z) 2)) (+.f64 1 (expm1.f64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (*.f64 (*.f64 (pow.f64 (exp.f64 y) y) (pow.f64 (exp.f64 z) z)) (+.f64 1 (expm1.f64 (*.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 2 (log.f64 (hypot.f64 x (hypot.f64 y z)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (*.f64 2 (log.f64 (hypot.f64 x (hypot.f64 y z)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 x x (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x x) 1 (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 y y (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y y) 1 (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (hypot.f64 x y) 2) 1 (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 z z (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z z) 1 (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 x x) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 y y) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (hypot.f64 x y) 2) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (*.f64 z z) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (pow.f64 (hypot.f64 y z) 2) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 (pow.f64 z 4)) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) z) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 z 4)) (pow.f64 (cbrt.f64 z) 2) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (cbrt.f64 (pow.f64 y 4)) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 y) 2) (*.f64 (cbrt.f64 y) y) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 y 4)) (pow.f64 (cbrt.f64 y) 2) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) 2) (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) 2) 2) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (pow.f64 (cbrt.f64 (hypot.f64 x y)) 2) 2) (pow.f64 (cbrt.f64 (hypot.f64 x y)) 2) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 (pow.f64 x 4)) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) x) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (pow.f64 x 4)) (pow.f64 (cbrt.f64 x) 2) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) x) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 x y) (hypot.f64 x y) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) z) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) y) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (+.f64 (pow.f64 x 6) (pow.f64 y 6)) (/.f64 1 (+.f64 (pow.f64 x 4) (-.f64 (pow.f64 y 4) (pow.f64 (*.f64 x y) 2)))) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (-.f64 (pow.f64 x 4) (pow.f64 y 4)) (/.f64 1 (-.f64 (*.f64 x x) (*.f64 y y))) (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (sqrt.f64 z)) (sqrt.f64 z) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (sqrt.f64 x)) (sqrt.f64 x) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (sqrt.f64 y)) (sqrt.f64 y) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 y z) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 y z) 2)) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (hypot.f64 y z) (hypot.f64 y z) (*.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 z (pow.f64 (cbrt.f64 z) 2)) (cbrt.f64 z) (pow.f64 (hypot.f64 x y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 y (pow.f64 (cbrt.f64 y) 2)) (cbrt.f64 y) (fma.f64 x x (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (*.f64 x (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) (*.f64 (pow.f64 (hypot.f64 y z) 2) 1))))))

simplify112.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
756×	`associate-r_binary64`
724×	`associate-l_binary64`
468×	`times-frac_binary64`
393×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2870
1	584	2433
2	1880	2413

Stop Event

1×	node limit

Counts

269 → 261

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (sqrt.f64 1/3))
(+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (sqrt.f64 1/3)) (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (.f64 (sqrt.f64 1/3) (pow.f64 x 2)))))
(+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (sqrt.f64 1/3)) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (.f64 (sqrt.f64 1/3) (pow.f64 x 2)))) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3))) (*.f64 (sqrt.f64 1/3) (pow.f64 x 4))))))
(+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 5))) (.f64 (sqrt.f64 1/3) (pow.f64 x 6)))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (sqrt.f64 1/3)) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (.f64 (sqrt.f64 1/3) (pow.f64 x 2)))) (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3))) (.f64 (sqrt.f64 1/3) (pow.f64 x 4)))))))
(*.f64 (sqrt.f64 1/3) x)
(+.f64 (.f64 (sqrt.f64 1/3) x) (.f64 1/2 (/.f64 (*.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x)))
(+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 (sqrt.f64 1/3) x) (.f64 1/2 (/.f64 (*.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x))))
(+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3) (sqrt.f64 1/3)) (pow.f64 x 5))) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 (sqrt.f64 1/3) x) (.f64 1/2 (/.f64 (*.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x)))))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3) (sqrt.f64 1/3)) (pow.f64 x 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (sqrt.f64 1/3))
(+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 2) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))))) (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (sqrt.f64 1/3)))
(+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 2) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))))) (+.f64 (.f64 -1/8 (.f64 (.f64 (pow.f64 y 4) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3))))) (*.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (sqrt.f64 1/3))))
(+.f64 (.f64 1/2 (.f64 (.f64 (pow.f64 y 2) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))))) (+.f64 (.f64 -1/8 (.f64 (.f64 (pow.f64 y 4) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3))))) (+.f64 (.f64 1/16 (.f64 (.f64 (pow.f64 y 6) (sqrt.f64 1/3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 5))))) (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (sqrt.f64 1/3)))))
(*.f64 y (sqrt.f64 1/3))
(+.f64 (.f64 y (sqrt.f64 1/3)) (.f64 1/2 (/.f64 (*.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)))
(+.f64 (.f64 y (sqrt.f64 1/3)) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 y 3)))))
(+.f64 (.f64 y (sqrt.f64 1/3)) (+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3) (sqrt.f64 1/3)) (pow.f64 y 5))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 y 3))))))
(.f64 -1 (.f64 y (sqrt.f64 1/3)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)) (.f64 -1 (.f64 y (sqrt.f64 1/3))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)) (+.f64 (.f64 -1 (.f64 y (sqrt.f64 1/3))) (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 y 3)))))
(+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3) (sqrt.f64 1/3)) (pow.f64 y 5))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (sqrt.f64 1/3)) y)) (+.f64 (.f64 -1 (.f64 y (sqrt.f64 1/3))) (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 y 3))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (sqrt.f64 1/3))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (.f64 (pow.f64 z 2) (sqrt.f64 1/3)))) (.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (sqrt.f64 1/3)))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3))) (.f64 (pow.f64 z 4) (sqrt.f64 1/3)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (.f64 (pow.f64 z 2) (sqrt.f64 1/3)))) (*.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (sqrt.f64 1/3))))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3))) (.f64 (pow.f64 z 4) (sqrt.f64 1/3)))) (+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (.f64 (pow.f64 z 2) (sqrt.f64 1/3)))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 5))) (.f64 (pow.f64 z 6) (sqrt.f64 1/3)))) (.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (sqrt.f64 1/3)))))
(*.f64 z (sqrt.f64 1/3))
(+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z)) (*.f64 z (sqrt.f64 1/3)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 z 3)))))
(+.f64 (.f64 1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (+.f64 (.f64 1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3) (sqrt.f64 1/3)) (pow.f64 z 5))) (.f64 -1/8 (/.f64 (*.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 z 3))))))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z)))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 z 3))) (+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z))))
(+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 2) (sqrt.f64 1/3)) (pow.f64 z 3))) (+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3) (sqrt.f64 1/3)) (pow.f64 z 5))) (.f64 -1/2 (/.f64 (.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (sqrt.f64 1/3)) z)))))
(*.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))))
(+.f64 (.f64 1/3 (pow.f64 x 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))))
(*.f64 1/3 (pow.f64 x 2))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(*.f64 1/3 (pow.f64 x 2))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 y 2))) (.f64 1/3 (pow.f64 x 2)))
(*.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(*.f64 1/3 (pow.f64 y 2))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(*.f64 1/3 (pow.f64 y 2))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(+.f64 (.f64 1/3 (pow.f64 y 2)) (.f64 1/3 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))
(*.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(*.f64 1/3 (pow.f64 z 2))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(*.f64 1/3 (pow.f64 z 2))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (.f64 1/3 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (.f64 1/3 (pow.f64 z 2)))
(+.f64 (pow.f64 z 2) (pow.f64 y 2))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 x 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (pow.f64 x 2))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 y 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 y 2) (pow.f64 x 2))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 z 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(pow.f64 z 2)
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))
(+.f64 (pow.f64 z 2) (+.f64 (pow.f64 y 2) (pow.f64 x 2)))

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

eval185.0ms (2.3%)

Compiler: Compiled 5241 to 3301 computations (37% saved)

prune63.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	253	8	261
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	253	9	262

Error

Counts

262 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.4b	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
▶	51.5b	(sqrt.f64 (/.f64 (*.f64 z z) 3))
▶	31.0b	(*.f64 z (sqrt.f64 1/3))
✓	40.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
▶	51.5b	(sqrt.f64 (.f64 z (.f64 z 1/3)))
	31.5b	(*.f64 x (neg.f64 (sqrt.f64 1/3)))
	30.4b	(*.f64 (hypot.f64 z y) (sqrt.f64 1/3))
	50.4b	(sqrt.f64 (/.f64 (*.f64 x x) 3))
▶	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

Compiler

Compiled 159 to 123 computations (22.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

Compiler

Compiled 17 to 10 computations (41.2% saved)

series5.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	z	@	0	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
1.0ms	z	@	inf	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
1.0ms	x	@	0	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
1.0ms	x	@	inf	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
1.0ms	x	@	-inf	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`pow1_binary64`
552×	`add-log-exp_binary64`
552×	`log1p-expm1-u_binary64`
552×	`expm1-log1p-u_binary64`
540×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	140	9
2	1540	9

Stop Event

1×	node limit

Counts

1 → 11

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (.f64 1/3 (pow.f64 (hypot.f64 z x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (hypot.f64 z x)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/3 (pow.f64 (hypot.f64 z x) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (hypot.f64 z x)) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/3) (hypot.f64 z x))))))))

simplify132.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

777×	`associate-/r/_binary64`
650×	`associate-/l/_binary64`
504×	`unswap-sqr_binary64`
367×	`times-frac_binary64`
293×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	757
1	231	754
2	755	754
3	3568	700
4	6889	700

Stop Event

1×	node limit

Counts

35 → 42

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/3) x)
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (*.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (*.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 (sqrt.f64 1/3) x) (.f64 1/16 (/.f64 (*.f64 (pow.f64 z 6) (sqrt.f64 1/3)) (pow.f64 x 5))))))
(*.f64 z (sqrt.f64 1/3))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (*.f64 z (sqrt.f64 1/3)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3)))))
(+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 6)) (pow.f64 z 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3))))))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)))
(+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3))) (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z))))
(+.f64 (.f64 -1 (.f64 z (sqrt.f64 1/3))) (+.f64 (.f64 1/8 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (.f64 -1/16 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 6)) (pow.f64 z 5))))))
(*.f64 z (sqrt.f64 1/3))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (*.f64 z (sqrt.f64 1/3)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3)))))
(+.f64 (.f64 1/16 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 6)) (pow.f64 z 5))) (+.f64 (.f64 1/2 (/.f64 (.f64 (sqrt.f64 1/3) (pow.f64 x 2)) z)) (+.f64 (.f64 z (sqrt.f64 1/3)) (.f64 -1/8 (/.f64 (*.f64 (sqrt.f64 1/3) (pow.f64 x 4)) (pow.f64 z 3))))))
(*.f64 (sqrt.f64 1/3) x)
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (*.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (*.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 -1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (+.f64 (.f64 (sqrt.f64 1/3) x) (.f64 1/16 (/.f64 (*.f64 (pow.f64 z 6) (sqrt.f64 1/3)) (pow.f64 x 5))))))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (.f64 -1 (.f64 (sqrt.f64 1/3) x))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (+.f64 (.f64 -1/16 (/.f64 (.f64 (pow.f64 z 6) (sqrt.f64 1/3)) (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 (.f64 (pow.f64 z 4) (sqrt.f64 1/3)) (pow.f64 x 3))) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))))

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

localize10.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 z (sqrt.f64 1/3))

Compiler

Compiled 11 to 9 computations (18.2% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(*.f64 z (sqrt.f64 1/3))
1.0ms	z	@	inf	(*.f64 z (sqrt.f64 1/3))
1.0ms	z	@	-inf	(*.f64 z (sqrt.f64 1/3))

rewrite62.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`pow1_binary64`
404×	`add-sqr-sqrt_binary64`
395×	`*-un-lft-identity_binary64`
387×	`add-log-exp_binary64`
387×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	100	6
2	1077	6

Stop Event

1×	node limit

Counts

1 → 15

Calls

Call 1

Inputs
(*.f64 z (sqrt.f64 1/3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (sqrt.f64 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 1/3 (*.f64 z z)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/3 (*.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (sqrt.f64 1/3))))))))

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

15 → 15

Calls

Call 1

Inputs

Outputs

localize33.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 z (.f64 z 1/3))
✓	0.3b	(*.f64 z 1/3)
✓	31.4b	(sqrt.f64 (.f64 z (.f64 z 1/3)))

Compiler

Compiled 19 to 13 computations (31.6% saved)

series6.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(.f64 z (.f64 z 1/3))
1.0ms	z	@	-inf	(*.f64 z 1/3)
1.0ms	z	@	inf	(*.f64 z 1/3)
1.0ms	z	@	0	(*.f64 z 1/3)
1.0ms	z	@	inf	(.f64 z (.f64 z 1/3))

rewrite80.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

528×	`pow1_binary64`
510×	`add-sqr-sqrt_binary64`
490×	`add-log-exp_binary64`
490×	`log1p-expm1-u_binary64`
490×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	122	17
2	1375	17

Stop Event

1×	node limit

Counts

3 → 47

Calls

Call 1

Inputs
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(*.f64 z 1/3)
(.f64 z (.f64 z 1/3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (sqrt.f64 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (sqrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) (cbrt.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) (cbrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) (sqrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (sqrt.f64 (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z 1/3)) (sqrt.f64 z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 2)) (sqrt.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (*.f64 z z) 1/2) (sqrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 2) 1/2) (pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (*.f64 z 1/3)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (sqrt.f64 1/3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z 1/3) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 z 1/3) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z 1/3) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z 1/3)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (*.f64 z 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (*.f64 z 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (*.f64 z 1/3))))))))

simplify123.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
398×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
313×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	212
1	23	212
2	44	212
3	84	212
4	203	212
5	618	212
6	967	212
7	1614	212
8	2017	212
9	2884	212
10	3721	212
11	4581	212
12	5715	212

Stop Event

1×	node limit

Counts

83 → 53

Calls

Call 1

Inputs
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 z)
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))

Outputs
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 z)
(*.f64 z 1/3)
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))

localize16.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (*.f64 z z) 3)
✓	31.4b	(sqrt.f64 (/.f64 (*.f64 z z) 3))

Compiler

Compiled 19 to 10 computations (47.4% saved)

series6.0ms (0.1%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
4.0ms	z	@	inf	(sqrt.f64 (/.f64 (*.f64 z z) 3))
1.0ms	z	@	0	(sqrt.f64 (/.f64 (*.f64 z z) 3))
0.0ms	z	@	-inf	(sqrt.f64 (/.f64 (*.f64 z z) 3))
0.0ms	z	@	0	(/.f64 (*.f64 z z) 3)
0.0ms	z	@	-inf	(/.f64 (*.f64 z z) 3)

rewrite131.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

577×	`pow1_binary64`
544×	`add-log-exp_binary64`
544×	`log1p-expm1-u_binary64`
544×	`expm1-log1p-u_binary64`
532×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	131	13
2	1577	13

Stop Event

1×	node limit

Counts

2 → 59

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(/.f64 (*.f64 z z) 3)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (sqrt.f64 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (sqrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (pow.f64 1/3 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (/.f64 1 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) (cbrt.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) (cbrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) (sqrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (cbrt.f64 (*.f64 (pow.f64 z 4) 1/9))) (sqrt.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 1 1/2) (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (*.f64 (pow.f64 z 4) 1/9)) 1/2) (pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 z (sqrt.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (/.f64 3 (*.f64 z z))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 3) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 z) (sqrt.f64 (/.f64 3 z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (neg.f64 (*.f64 z z))) (sqrt.f64 -3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 z) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (*.f64 z 1/3)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (sqrt.f64 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (sqrt.f64 1/3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 z (*.f64 z 1/3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (/.f64 1 (/.f64 3 z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (*.f64 z 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z z) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (*.f64 z 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 z (sqrt.f64 1/3)) (*.f64 z (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 z (*.f64 z 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 z 4)) (*.f64 (pow.f64 (cbrt.f64 z) 2) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) (cbrt.f64 (*.f64 (pow.f64 z 4) 1/9)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) (*.f64 (cbrt.f64 (*.f64 z (sqrt.f64 1/3))) (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (pow.f64 z 4) 1/9)) (cbrt.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) (*.f64 (sqrt.f64 (*.f64 z (sqrt.f64 1/3))) (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (*.f64 z z)) -1/3)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1/3 (*.f64 z z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 z (sqrt.f64 1/3)) (sqrt.f64 (*.f64 z (sqrt.f64 1/3)))) (sqrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 z 3) z)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (*.f64 z (sqrt.f64 1/3)) (cbrt.f64 (*.f64 z (*.f64 z 1/3)))) (cbrt.f64 (*.f64 z (sqrt.f64 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (*.f64 z 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 z (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (pow.f64 z 4) 1/9) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 z (*.f64 z 1/3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 3 (*.f64 z z)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (*.f64 z z) -3))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (pow.f64 z 4) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (cbrt.f64 (pow.f64 (exp.f64 z) z)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 z (*.f64 z 1/3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 z (*.f64 z 1/3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 z (*.f64 z 1/3))))))))

simplify110.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

964×	`fma-def_binary64`
414×	`distribute-rgt-neg-out_binary64`
365×	`fma-neg_binary64`
337×	`distribute-rgt-neg-in_binary64`
321×	`fabs-mul_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	164
1	21	164
2	44	164
3	86	164
4	204	164
5	634	164
6	988	164
7	1635	164
8	2038	164
9	2907	164
10	3744	164
11	4607	164
12	5737	164

Stop Event

1×	node limit

Counts

83 → 62

Calls

Call 1

Inputs
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))
(*.f64 1/3 (pow.f64 z 2))

Outputs
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 z (sqrt.f64 1/3))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(.f64 -1 (.f64 z (sqrt.f64 1/3)))
(neg.f64 (*.f64 z (sqrt.f64 1/3)))
(*.f64 z (neg.f64 (sqrt.f64 1/3)))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))
(*.f64 1/3 (pow.f64 z 2))
(.f64 1/3 (.f64 z z))
(.f64 z (.f64 z 1/3))

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 y z)
✓	0.4b	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))

Compiler

Compiled 25 to 11 computations (56% saved)

series28.0ms (0.3%)

Counts

2 → 60

Calls

15 calls:

Time	Variable		Point	Expression
7.0ms	z	@	0	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
4.0ms	y	@	inf	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
3.0ms	z	@	inf	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
2.0ms	x	@	0	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
2.0ms	y	@	0	(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))

rewrite85.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`pow1_binary64`
809×	`add-log-exp_binary64`
809×	`log1p-expm1-u_binary64`
809×	`expm1-log1p-u_binary64`
791×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	186	16
2	2212	16

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

Inputs
(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))
(hypot.f64 y z)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 x (hypot.f64 y z)) (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 3)) (cbrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) 2) (*.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))) (sqrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) (*.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 x (hypot.f64 y z))) (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 3 -1/2) (hypot.f64 x (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) 2) 1) (/.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) 1) (/.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 x (hypot.f64 y z)) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) 2) (cbrt.f64 3)) (cbrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) (cbrt.f64 3)) (/.f64 (sqrt.f64 (hypot.f64 x (hypot.f64 y z))) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 3 1/4)) (/.f64 (hypot.f64 x (hypot.f64 y z)) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) 2) (pow.f64 3 1/4)) (/.f64 (cbrt.f64 (hypot.f64 x (hypot.f64 y z))) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) (hypot.f64 x (hypot.f64 y z))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (hypot.f64 x (hypot.f64 y z)) 3) (*.f64 3 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 y z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 y z) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 y z))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 y z)) (pow.f64 (cbrt.f64 (hypot.f64 y z)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 y z)) 2) (cbrt.f64 (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 y z)) (sqrt.f64 (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 y z) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 y z) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 y z) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 y z)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 y z)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 y z) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 y z) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 y z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 y z)))))))

simplify310.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

855×	`associate-/l*_binary64`
656×	`associate-l_binary64`
639×	`associate-/r*_binary64`
377×	`distribute-rgt-in_binary64`
354×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	2558
1	774	2147
2	2891	2105

Stop Event

1×	node limit

Counts

108 → 147

Calls

Call 1

Inputs
(*.f64 (/.f64 1 (sqrt.f64 3)) (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (/.f64 (pow.f64 x 2) (sqrt.f64 3)))) (*.f64 (/.f64 1 (sqrt.f64 3)) (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (/.f64 (pow.f64 x 2) (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3))) (/.f64 (pow.f64 x 4) (sqrt.f64 3)))) (*.f64 (/.f64 1 (sqrt.f64 3)) (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2))))))
(+.f64 (.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))) (/.f64 (pow.f64 x 2) (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3))) (/.f64 (pow.f64 x 4) (sqrt.f64 3)))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 5))) (/.f64 (pow.f64 x 6) (sqrt.f64 3)))) (*.f64 (/.f64 1 (sqrt.f64 3)) (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)))))))
(/.f64 x (sqrt.f64 3))
(+.f64 (/.f64 x (sqrt.f64 3)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))))
(+.f64 (/.f64 x (sqrt.f64 3)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (.f64 (sqrt.f64 3) (pow.f64 x 3))))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3) (.f64 (sqrt.f64 3) (pow.f64 x 5)))) (+.f64 (/.f64 x (sqrt.f64 3)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))) (.f64 -1/8 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (.f64 (sqrt.f64 3) (pow.f64 x 3)))))))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))) (*.f64 -1 (/.f64 x (sqrt.f64 3))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1 (/.f64 x (sqrt.f64 3))) (.f64 1/8 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (*.f64 (sqrt.f64 3) (pow.f64 x 3))))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 3) (.f64 (sqrt.f64 3) (pow.f64 x 5)))) (+.f64 (.f64 -1 (/.f64 x (sqrt.f64 3))) (.f64 1/8 (/.f64 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 y 2)) 2) (*.f64 (sqrt.f64 3) (pow.f64 x 3)))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3)))
(+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (.f64 1/2 (*.f64 (/.f64 (pow.f64 y 2) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 y 4) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3))))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (.f64 1/2 (*.f64 (/.f64 (pow.f64 y 2) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2))))))))
(+.f64 (.f64 -1/8 (.f64 (/.f64 (pow.f64 y 4) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 3))))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (+.f64 (.f64 1/2 (.f64 (/.f64 (pow.f64 y 2) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 z 2) (pow.f64 x 2)))))) (.f64 1/16 (*.f64 (/.f64 (pow.f64 y 6) (sqrt.f64 3)) (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) 5))))))))
(/.f64 y (sqrt.f64 3))
(+.f64 (/.f64 y (sqrt.f64 3)) (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (.f64 y (sqrt.f64 3)))))
(+.f64 (/.f64 y (sqrt.f64 3)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (.f64 y (sqrt.f64 3)))) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2)) (*.f64 (pow.f64 y 3) (sqrt.f64 3))))))
(+.f64 (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 1/8 (pow.f64 z 6)) (.f64 -1/8 (pow.f64 z 6))) (.f64 1/2 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2))))) (.f64 (pow.f64 y 5) (sqrt.f64 3)))) (+.f64 (/.f64 y (sqrt.f64 3)) (+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (.f64 y (sqrt.f64 3)))) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 y 3) (sqrt.f64 3)))))))
(*.f64 -1 (/.f64 y (sqrt.f64 3)))
(+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (*.f64 y (sqrt.f64 3)))))
(+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (.f64 y (sqrt.f64 3))))))
(+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2)) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (.f64 y (sqrt.f64 3)))) (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 1/8 (pow.f64 z 6)) (.f64 -1/8 (pow.f64 z 6))) (.f64 1/2 (.f64 (+.f64 (pow.f64 z 2) (pow.f64 x 2)) (-.f64 (+.f64 (.f64 -1/4 (pow.f64 z 4)) (.f64 1/4 (pow.f64 z 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 z 2) (pow.f64 x 2))) 2))))) (*.f64 (pow.f64 y 5) (sqrt.f64 3)))))))
(*.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3)))
(+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (/.f64 (pow.f64 z 2) (sqrt.f64 3)))))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3))) (/.f64 (pow.f64 z 4) (sqrt.f64 3)))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (/.f64 (pow.f64 z 2) (sqrt.f64 3))))))
(+.f64 (.f64 -1/8 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 3))) (/.f64 (pow.f64 z 4) (sqrt.f64 3)))) (+.f64 (.f64 1/16 (.f64 (sqrt.f64 (/.f64 1 (pow.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) 5))) (/.f64 (pow.f64 z 6) (sqrt.f64 3)))) (+.f64 (.f64 (sqrt.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) (/.f64 1 (sqrt.f64 3))) (.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (+.f64 (pow.f64 y 2) (pow.f64 x 2)))) (/.f64 (pow.f64 z 2) (sqrt.f64 3)))))))
(/.f64 z (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (*.f64 (sqrt.f64 3) (pow.f64 z 3))))))
(+.f64 (.f64 1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 1/8 (pow.f64 y 6)) (.f64 -1/8 (pow.f64 y 6))) (.f64 1/2 (.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (+.f64 (pow.f64 y 2) (pow.f64 x 2))))) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (.f64 (sqrt.f64 3) (pow.f64 z 3)))))))
(*.f64 -1 (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (*.f64 -1 (/.f64 z (sqrt.f64 3))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (.f64 -1 (/.f64 z (sqrt.f64 3)))))
(+.f64 (.f64 -1/2 (/.f64 (+.f64 (pow.f64 y 2) (pow.f64 x 2)) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (+.f64 (.f64 -1 (/.f64 z (sqrt.f64 3))) (.f64 -1/2 (/.f64 (-.f64 (+.f64 (.f64 1/8 (pow.f64 y 6)) (.f64 -1/8 (pow.f64 y 6))) (.f64 1/2 (.f64 (-.f64 (+.f64 (.f64 1/4 (pow.f64 y 4)) (.f64 -1/4 (pow.f64 y 4))) (pow.f64 (.f64 1/2 (+.f64 (pow.f64 y 2) (pow.f64 x 2))) 2)) (+.f64 (pow.f64 y 2) (pow.f64 x 2))))) (*.f64 (sqrt.f64 3) (pow.f64 z 5)))))))
z
(+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (.f64 1/2 (/.f64 (pow.f64 y 2) z))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))))
y
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 z 2) y)) y)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 y (.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 y (*.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))
(*.f64 -1 y)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (.f64 -1 y))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 -1 y) (*.f64 1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 -1 y) (.f64 1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))
y
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 z 2) y)) y)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 y (.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 y (*.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))
z
(+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (.f64 1/2 (/.f64 (pow.f64 y 2) z))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))))
(*.f64 -1 z)
(+.f64 (.f64 -1 z) (.f64 -1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1 z) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) z)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3)))))
(+.f64 (.f64 -1 z) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) z)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))))))

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

eval125.0ms (1.6%)

Compiler: Compiled 5695 to 4033 computations (29.2% saved)

prune61.0ms (0.8%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	312	7	319
Fresh	3	0	3
Picked	1	0	1
Done	2	3	5
Total	318	10	328

Error

Counts

328 → 10

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.0b	(*.f64 z (sqrt.f64 1/3))
✓	40.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
	31.7b	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
▶	31.5b	(*.f64 (sqrt.f64 1/3) (neg.f64 x))
▶	31.2b	(*.f64 z (/.f64 1 (sqrt.f64 3)))
▶	0.4b	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
▶	31.0b	(/.f64 z (sqrt.f64 3))
	30.4b	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
▶	31.5b	(/.f64 (neg.f64 x) (sqrt.f64 3))

Compiler

Compiled 163 to 130 computations (20.2% saved)

localize9.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (hypot.f64 z x) (sqrt.f64 3))

Compiler

Compiled 17 to 10 computations (41.2% saved)

series4.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	z	@	0	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
1.0ms	x	@	0	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
1.0ms	z	@	inf	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
1.0ms	z	@	-inf	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
1.0ms	x	@	inf	(/.f64 (hypot.f64 z x) (sqrt.f64 3))

rewrite60.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`pow1_binary64`
644×	`add-log-exp_binary64`
644×	`log1p-expm1-u_binary64`
644×	`expm1-log1p-u_binary64`
630×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	9
2	1751	9

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

Inputs
(/.f64 (hypot.f64 z x) (sqrt.f64 3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (hypot.f64 z x) (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 z x) (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (hypot.f64 z x) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z x) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z x) 2) 3)) (cbrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 z x)) 2) (*.f64 (cbrt.f64 (hypot.f64 z x)) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))) (sqrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 z x)) (*.f64 (sqrt.f64 (hypot.f64 z x)) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 z x)) (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 3 -1/2) (hypot.f64 z x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z x)) 2) 1) (/.f64 (cbrt.f64 (hypot.f64 z x)) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 z x)) 1) (/.f64 (sqrt.f64 (hypot.f64 z x)) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z x) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z x)) 2) (cbrt.f64 3)) (cbrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 z x)) (cbrt.f64 3)) (/.f64 (sqrt.f64 (hypot.f64 z x)) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 3 1/4)) (/.f64 (hypot.f64 z x) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z x)) 2) (pow.f64 3 1/4)) (/.f64 (cbrt.f64 (hypot.f64 z x)) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) (hypot.f64 z x)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (hypot.f64 z x) (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (hypot.f64 z x) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z x) 3) (*.f64 3 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (hypot.f64 z x) (sqrt.f64 3))))))))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-neg_binary64`
662×	`associate-/l/_binary64`
590×	`times-frac_binary64`
540×	`unswap-sqr_binary64`
528×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	758
1	252	754
2	790	754
3	3899	734
4	6937	734

Stop Event

1×	node limit

Counts

55 → 63

Calls

Call 1

Inputs
(/.f64 x (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (/.f64 x (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (/.f64 x (sqrt.f64 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (+.f64 (/.f64 x (sqrt.f64 3)) (.f64 1/16 (/.f64 (pow.f64 z 6) (.f64 (sqrt.f64 3) (pow.f64 x 5)))))))
(/.f64 z (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 -1/8 (/.f64 (pow.f64 x 4) (.f64 (sqrt.f64 3) (pow.f64 z 3))))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 -1/8 (/.f64 (pow.f64 x 4) (.f64 (sqrt.f64 3) (pow.f64 z 3)))))))
(*.f64 -1 (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (*.f64 -1 (/.f64 z (sqrt.f64 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (*.f64 -1 (/.f64 z (sqrt.f64 3)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 x 4) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 x 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (*.f64 -1 (/.f64 z (sqrt.f64 3))))))
(/.f64 z (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (.f64 (pow.f64 z 3) (sqrt.f64 3)))) (/.f64 z (sqrt.f64 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (.f64 (pow.f64 z 3) (sqrt.f64 3)))) (/.f64 z (sqrt.f64 3)))))
(/.f64 x (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (/.f64 x (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (/.f64 x (sqrt.f64 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (+.f64 (/.f64 x (sqrt.f64 3)) (.f64 1/16 (/.f64 (pow.f64 z 6) (.f64 (sqrt.f64 3) (pow.f64 x 5)))))))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (*.f64 -1 (/.f64 x (sqrt.f64 3))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (*.f64 -1 (/.f64 x (sqrt.f64 3)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 z 4) (.f64 (sqrt.f64 3) (pow.f64 x 3)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) (.f64 (sqrt.f64 3) x))) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 z 6) (.f64 (sqrt.f64 3) (pow.f64 x 5)))) (*.f64 -1 (/.f64 x (sqrt.f64 3))))))

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

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 z (sqrt.f64 3))

Compiler

Compiled 11 to 9 computations (18.2% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	z	@	inf	(/.f64 z (sqrt.f64 3))
1.0ms	z	@	0	(/.f64 z (sqrt.f64 3))
1.0ms	z	@	-inf	(/.f64 z (sqrt.f64 3))

rewrite51.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

510×	`pow1_binary64`
494×	`add-sqr-sqrt_binary64`
478×	`add-log-exp_binary64`
478×	`log1p-expm1-u_binary64`
478×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	106	6
2	1285	6

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 z (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 z (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 z (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 z (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 z (sqrt.f64 3))) (cbrt.f64 (/.f64 (*.f64 z z) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 z z) 3)) (cbrt.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 z) 2) (*.f64 (cbrt.f64 z) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 z (sqrt.f64 3))) (sqrt.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 z) (*.f64 (sqrt.f64 z) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 z) (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 3 -1/2) z)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 z) 2) 1) (/.f64 (cbrt.f64 z) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 z) 1) (/.f64 (sqrt.f64 z) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 z (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 z) 2) (cbrt.f64 3)) (cbrt.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 z) (cbrt.f64 3)) (/.f64 (sqrt.f64 z) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 3 1/4)) (/.f64 z (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 z) 2) (pow.f64 3 1/4)) (/.f64 (cbrt.f64 z) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 z (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 z (sqrt.f64 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 z (sqrt.f64 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 z (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) z) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 z (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 z z) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 z (sqrt.f64 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 z (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 z (sqrt.f64 3))))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (sqrt.f64 1/3) (neg.f64 x))

Compiler

Compiled 14 to 10 computations (28.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(*.f64 (sqrt.f64 1/3) (neg.f64 x))
1.0ms	x	@	inf	(*.f64 (sqrt.f64 1/3) (neg.f64 x))
0.0ms	x	@	-inf	(*.f64 (sqrt.f64 1/3) (neg.f64 x))

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

450×	`pow1_binary64`
438×	`add-sqr-sqrt_binary64`
428×	`*-un-lft-identity_binary64`
419×	`add-log-exp_binary64`
418×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	125	6
2	1475	6

Stop Event

1×	node limit

Counts

1 → 13

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/3) (neg.f64 x))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (*.f64 (sqrt.f64 1/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/3) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/3) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (*.f64 (sqrt.f64 1/3) x))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 1/3 (*.f64 x x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 (sqrt.f64 1/3)) x))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/3) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/3) x)))))))

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

38×	`fma-def_binary64`
9×	`sub-neg_binary64`
6×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	12	96
2	25	96
3	29	96
4	33	96
5	51	96
6	73	96
7	84	96
8	96	96
9	121	96

Stop Event

1×

saturated

Counts

25 → 15

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))

Outputs
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (neg.f64 x) (sqrt.f64 3))

Compiler

Compiled 14 to 10 computations (28.6% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 (neg.f64 x) (sqrt.f64 3))
1.0ms	x	@	inf	(/.f64 (neg.f64 x) (sqrt.f64 3))
0.0ms	x	@	-inf	(/.f64 (neg.f64 x) (sqrt.f64 3))

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

526×	`pow1_binary64`
493×	`add-log-exp_binary64`
492×	`log1p-expm1-u_binary64`
492×	`expm1-log1p-u_binary64`
483×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	131	6
2	1750	6

Stop Event

1×	node limit

Counts

1 → 35

Calls

Call 1

Inputs
(/.f64 (neg.f64 x) (sqrt.f64 3))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (/.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 x (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 0 (sqrt.f64 3)) (/.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 x (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 x (sqrt.f64 3))) (cbrt.f64 (/.f64 (*.f64 x x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (*.f64 x x) 3)) (cbrt.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 x) 2) (*.f64 (cbrt.f64 x) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 x (sqrt.f64 3))) (sqrt.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 x) (*.f64 (sqrt.f64 x) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 3 -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) 1) (/.f64 (cbrt.f64 x) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) 1) (/.f64 (sqrt.f64 x) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 x (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (cbrt.f64 3)) (cbrt.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 x) (cbrt.f64 3)) (/.f64 (sqrt.f64 x) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (cbrt.f64 3)) (/.f64 x (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 3 1/4)) (/.f64 x (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 x) 2) (pow.f64 3 1/4)) (/.f64 (cbrt.f64 x) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 -1 (pow.f64 3 1/4)) (/.f64 x (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 x (sqrt.f64 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 x (sqrt.f64 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 x (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) x) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 x (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (*.f64 x x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 x (sqrt.f64 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (sqrt.f64 3))))))))

simplify387.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	11	96
2	18	96
3	24	96
4	30	96
5	38	96
6	46	96
7	56	96
8	64	96
9	78	96

Stop Event

1×

saturated

Counts

47 → 36

Calls

Call 1

Inputs
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))

Outputs
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 z (/.f64 1 (sqrt.f64 3)))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

Compiler

Compiled 18 to 16 computations (11.1% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	z	@	0	(*.f64 z (/.f64 1 (sqrt.f64 3)))
0.0ms	z	@	-inf	(*.f64 z (/.f64 1 (sqrt.f64 3)))
0.0ms	z	@	inf	(*.f64 z (/.f64 1 (sqrt.f64 3)))

rewrite55.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

583×	`pow1_binary64`
544×	`add-log-exp_binary64`
544×	`log1p-expm1-u_binary64`
544×	`expm1-log1p-u_binary64`
533×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	142	9
2	1595	9

Stop Event

1×	node limit

Counts

2 → 42

Calls

Call 1

Inputs
(/.f64 1 (sqrt.f64 3))
(*.f64 z (/.f64 1 (sqrt.f64 3)))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (sqrt.f64 1/3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (sqrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (sqrt.f64 1/3)) (cbrt.f64 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 1/3) (cbrt.f64 (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (sqrt.f64 1/3)) (sqrt.f64 (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 -1 (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 3) -1) (pow.f64 (cbrt.f64 (sqrt.f64 3)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (pow.f64 3 1/4) -1) (pow.f64 (pow.f64 3 1/4) -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 3 -1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 3) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 1/3) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) 1/3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (sqrt.f64 1/3)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (sqrt.f64 1/3)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (sqrt.f64 1/3) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (sqrt.f64 1/3)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (*.f64 (sqrt.f64 1/3) z)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (sqrt.f64 3) z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 z (sqrt.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (pow.f64 (cbrt.f64 z) 2) (/.f64 (sqrt.f64 3) (cbrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 z) (/.f64 (sqrt.f64 3) (sqrt.f64 z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 z) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 z (pow.f64 3 1/4)) (pow.f64 3 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 z 1) (sqrt.f64 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 z (cbrt.f64 3)) (cbrt.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 -1 z) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 z -1) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (sqrt.f64 1/3) z) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) z) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (*.f64 (sqrt.f64 1/3) z)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (*.f64 (sqrt.f64 1/3) z)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (*.f64 z z) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (sqrt.f64 1/3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (*.f64 (sqrt.f64 1/3) z) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (*.f64 (sqrt.f64 1/3) z)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (*.f64 (sqrt.f64 1/3) z)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (*.f64 (sqrt.f64 1/3) z)))))))

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	72

Stop Event

1×

saturated

Counts

54 → 42

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))

Outputs
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))
(/.f64 z (sqrt.f64 3))

eval50.0ms (0.6%)

Compiler: Compiled 2043 to 1536 computations (24.8% saved)

prune32.0ms (0.4%)

Pruning

11 alts after pruning (3 fresh and 8 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	2	2
Picked	0	1	1
Done	0	7	7
Total	185	11	196

Error

Counts

196 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.0b	(*.f64 z (sqrt.f64 1/3))
✓	40.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
▶	31.7b	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
▶	31.7b	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
✓	31.5b	(*.f64 (sqrt.f64 1/3) (neg.f64 x))
✓	31.2b	(*.f64 z (/.f64 1 (sqrt.f64 3)))
✓	0.4b	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
✓	31.0b	(/.f64 z (sqrt.f64 3))
▶	30.4b	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
✓	31.5b	(/.f64 (neg.f64 x) (sqrt.f64 3))

Compiler

Compiled 108 to 86 computations (20.4% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
✓	1.0b	(/.f64 1 (neg.f64 (sqrt.f64 3)))

Compiler

Compiled 23 to 21 computations (8.7% saved)

series1.0ms (0%)

Counts

2 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
0.0ms	x	@	-inf	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
0.0ms	x	@	inf	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))

rewrite118.0ms (1.5%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

76×	`add-sqr-sqrt_binary64`
76×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
71×	`pow1_binary64`
71×	`*-un-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	16
1	163	16
2	1946	16
0	6	8
1	121	8
2	1362	8
0	6	8
0	8	8
1	163	8
2	1946	8
0	8	8

Stop Event

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

Counts

2 → 18

Calls

Call 1

Inputs
(/.f64 1 (neg.f64 (sqrt.f64 3)))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cbrt.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))) (cbrt.f64 (/.f64 1 (neg.f64 (sqrt.f64 3))))) (cbrt.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))) (sqrt.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (neg.f64 (sqrt.f64 3)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (neg.f64 (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (/.f64 1 (neg.f64 (sqrt.f64 3))) (/.f64 1 (neg.f64 (sqrt.f64 3)))) (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 1 (neg.f64 (sqrt.f64 3)))))))))

((#(struct:change #<rule egg-rr> (2) ((x /.f64 x (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 x 1) (neg.f64 (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (neg.f64 (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 x (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (*.f64 (*.f64 (/.f64 x (neg.f64 (sqrt.f64 3))) (/.f64 x (neg.f64 (sqrt.f64 3)))) (/.f64 x (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 x (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 x (neg.f64 (sqrt.f64 3)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 x (neg.f64 (sqrt.f64 3)))))))))

simplify21.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

14×	`fma-def_binary64`
8×	`sub-neg_binary64`
4×	`+-commutative_binary64`
4×	`fma-neg_binary64`
3×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	96
1	11	96
2	18	96
3	24	96
4	30	96
5	38	96
6	46	96
7	56	96
8	64	96
9	78	96

Stop Event

1×

saturated

Counts

30 → 20

Calls

Call 1

Inputs
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))

Outputs
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 -1 (/.f64 x (sqrt.f64 3)))
(neg.f64 (/.f64 x (sqrt.f64 3)))
(/.f64 (neg.f64 x) (sqrt.f64 3))

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 -1/2 (.f64 (/.f64 z x) z))
✓	0.0b	(-.f64 (.f64 -1/2 (.f64 (/.f64 z x) z)) x)
✓	0.1b	(*.f64 (/.f64 z x) z)
✓	0.3b	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))

Compiler

Compiled 45 to 20 computations (55.6% saved)

series19.0ms (0.2%)

Counts

4 → 96

Calls

24 calls:

Time	Variable		Point	Expression
2.0ms	x	@	0	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
2.0ms	z	@	inf	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
2.0ms	z	@	0	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
1.0ms	x	@	inf	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
1.0ms	x	@	-inf	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))

rewrite177.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`prod-diff_binary64`
598×	`log-prod_binary64`
305×	`pow2_binary64`
283×	`fma-def_binary64`
226×	`pow-unpow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	48
1	241	48
2	3164	48

Stop Event

1×	node limit

Counts

4 → 199

Calls

Call 1

Inputs
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
(*.f64 (/.f64 z x) z)
(-.f64 (.f64 -1/2 (.f64 (/.f64 z x) z)) x)
(.f64 -1/2 (.f64 (/.f64 z x) z))

Outputs
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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 z (/.f64 z x)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (/.f64 z x))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (/.f64 z x)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 z (/.f64 z x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 z (/.f64 x z))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 x (.f64 z z)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 z z) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (.f64 z z)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (neg.f64 z) z) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 z (neg.f64 z)) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 z z) 1) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 z z) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 (.f64 z z) (sqrt.f64 x)) (sqrt.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 z (/.f64 z x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 z (/.f64 z x)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 z (/.f64 z x)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 z (/.f64 z x))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 z (sqrt.f64 x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 z 3) (pow.f64 (/.f64 z x) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (/.f64 z x) 3) (pow.f64 z 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (.f64 z z)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 z (/.f64 z x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (/.f64 z x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 z (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (.f64 z (/.f64 z x)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 z 3) (pow.f64 (/.f64 z x) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (/.f64 z x) 3) (pow.f64 z 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 z (/.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 z (/.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 z (/.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (*.f64 z (/.f64 z x))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) (neg.f64 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) (.f64 (neg.f64 x) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/2 (.f64 z (/.f64 z x)) (neg.f64 x)) (fma.f64 (neg.f64 x) 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/2 (.f64 z (/.f64 z x)) (neg.f64 x)) (fma.f64 (neg.f64 (cbrt.f64 x)) (pow.f64 (cbrt.f64 x) 2) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/2 (.f64 z (/.f64 z x)) (neg.f64 x)) (+.f64 (neg.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/2 (.f64 z (/.f64 z x)) (neg.f64 x)) (fma.f64 -1 x x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 -1/2 (.f64 z (/.f64 z x)) (neg.f64 x)) (fma.f64 (neg.f64 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (neg.f64 x) (.f64 -1/2 (.f64 z (/.f64 z x))))))) (#(struct:change #<rule 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((#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 -1/2 (.f64 z (/.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (pow.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (.f64 -1/2 (/.f64 z x)))) 2)) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 z) (.f64 -1/2 (/.f64 z x))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (.f64 -1/2 (/.f64 z x))))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 z) (.f64 -1/2 (/.f64 z x))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (.f64 -1/2 (.f64 z (/.f64 z x))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (.f64 z z) -1/2) x)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 -1/2 (.f64 z z)) x)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (.f64 -1/2 (.f64 z (/.f64 z x)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (/.f64 z (sqrt.f64 x)) (sqrt.f64 -1/2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (.f64 (pow.f64 (.f64 z (/.f64 z x)) 3) -1/8) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (pow.f64 (exp.f64 z) (.f64 -1/2 (/.f64 z x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (.f64 -1/2 (.f64 z (/.f64 z x))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (.f64 (pow.f64 (.f64 z (/.f64 z x)) 3) -1/8))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (.f64 -1/2 (.f64 z (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (.f64 -1/2 (.f64 z (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (.f64 -1/2 (.f64 z (/.f64 z x)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (.f64 (log.f64 (.f64 -1/2 (*.f64 z (/.f64 z x)))) 1))))))

simplify222.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

647×	`fma-neg_binary64`
567×	`distribute-rgt-neg-in_binary64`
566×	`distribute-neg-frac_binary64`
530×	`distribute-lft-neg-in_binary64`
433×	`associate-/l/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	1164
1	44	1164
2	93	1164
3	193	1074
4	582	1074
5	2429	1074
6	6007	1074
7	7990	1074

Stop Event

1×	node limit

Counts

295 → 213

Calls

Call 1

Inputs
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(/.f64 (pow.f64 z 2) x)
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))

Outputs
(.f64 -1 (.f64 (sqrt.f64 1/3) x))
(neg.f64 (*.f64 (sqrt.f64 1/3) x))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x))
(.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))))
(.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3)))
(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (*.f64 z z)))
(.f64 (sqrt.f64 1/3) (/.f64 (.f64 z z) (/.f64 x -1/2)))
(.f64 (sqrt.f64 1/3) (.f64 -1/2 (/.f64 (*.f64 z z) x)))
(.f64 z (/.f64 (.f64 -1/2 z) (/.f64 x (sqrt.f64 1/3))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x))
(.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))))
(.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3)))
(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (*.f64 z z)))
(.f64 (sqrt.f64 1/3) (/.f64 (.f64 z z) (/.f64 x -1/2)))
(.f64 (sqrt.f64 1/3) (.f64 -1/2 (/.f64 (*.f64 z z) x)))
(.f64 z (/.f64 (.f64 -1/2 z) (/.f64 x (sqrt.f64 1/3))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
(-.f64 (.f64 -1/2 (.f64 (/.f64 z (/.f64 x z)) (sqrt.f64 1/3))) (*.f64 (sqrt.f64 1/3) x))
(-.f64 (.f64 -1/2 (.f64 (/.f64 (sqrt.f64 1/3) x) (.f64 z z))) (.f64 (sqrt.f64 1/3) x))
(.f64 (sqrt.f64 1/3) (-.f64 (/.f64 (.f64 z z) (/.f64 x -1/2)) x))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (/.f64 (*.f64 z z) x)) x))
(.f64 (neg.f64 (sqrt.f64 1/3)) (fma.f64 (.f64 z z) (/.f64 1/2 x) x))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 z 2) (sqrt.f64 1/3)) x)) (.f64 -1 (.f64 (sqrt.f64 1/3) x)))
(fma.f64 -1/2 (/.f64 (.f64 z z) (/.f64 x (sqrt.f64 1/3))) (neg.f64 (.f64 (sqrt.f64 1/3) x)))
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(-.f64 (/.f64 (.f64 -1/2 (.f64 z z)) x) x)
(-.f64 (.f64 -1/2 (/.f64 (.f64 z z) x)) x)
(-.f64 (/.f64 (*.f64 z z) (/.f64 x -1/2)) x)
(-.f64 (*.f64 -1/2 (/.f64 z (/.f64 x z))) x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (*.f64 z z) x) (neg.f64 x))
(-.f64 (/.f64 (.f64 -1/2 (.f64 z z)) x) x)
(-.f64 (.f64 -1/2 (/.f64 (.f64 z z) x)) x)
(-.f64 (/.f64 (*.f64 z z) (/.f64 x -1/2)) x)
(-.f64 (*.f64 -1/2 (/.f64 z (/.f64 x z))) x)
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (*.f64 z z) x) (neg.f64 x))
(-.f64 (/.f64 (.f64 -1/2 (.f64 z z)) x) x)
(-.f64 (.f64 -1/2 (/.f64 (.f64 z z) x)) x)
(-.f64 (/.f64 (*.f64 z z) (/.f64 x -1/2)) x)
(-.f64 (*.f64 -1/2 (/.f64 z (/.f64 x z))) x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (*.f64 z z) x) (neg.f64 x))
(-.f64 (/.f64 (.f64 -1/2 (.f64 z z)) x) x)
(-.f64 (.f64 -1/2 (/.f64 (.f64 z z) x)) x)
(-.f64 (/.f64 (*.f64 z z) (/.f64 x -1/2)) x)
(-.f64 (*.f64 -1/2 (/.f64 z (/.f64 x z))) x)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) x)) (.f64 -1 x))
(fma.f64 -1/2 (/.f64 (*.f64 z z) x) (neg.f64 x))
(-.f64 (/.f64 (.f64 -1/2 (.f64 z z)) x) x)
(-.f64 (.f64 -1/2 (/.f64 (.f64 z z) x)) x)
(-.f64 (/.f64 (*.f64 z z) (/.f64 x -1/2)) x)
(-.f64 (*.f64 -1/2 (/.f64 z (/.f64 x z))) x)
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))
(*.f64 -1/2 (/.f64 (pow.f64 z 2) x))
(.f64 -1/2 (/.f64 (.f64 z z) x))
(/.f64 (.f64 -1/2 (.f64 z z)) x)
(/.f64 (*.f64 z z) (/.f64 x -1/2))
(*.f64 -1/2 (/.f64 z (/.f64 x z)))

localize15.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 z y)
✓	0.4b	(/.f64 (hypot.f64 z y) (sqrt.f64 3))

Compiler

Compiled 17 to 10 computations (41.2% saved)

series10.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	y	@	-inf	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
1.0ms	z	@	0	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
1.0ms	z	@	inf	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
1.0ms	z	@	-inf	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
1.0ms	y	@	0	(/.f64 (hypot.f64 z y) (sqrt.f64 3))

rewrite102.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

694×	`pow1_binary64`
644×	`add-log-exp_binary64`
644×	`log1p-expm1-u_binary64`
644×	`expm1-log1p-u_binary64`
630×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	146	13
2	1751	13

Stop Event

1×	node limit

Counts

2 → 48

Calls

Call 1

Inputs
(/.f64 (hypot.f64 z y) (sqrt.f64 3))
(hypot.f64 z y)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (/.f64 (hypot.f64 z y) (sqrt.f64 3))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 z y) (pow.f64 3 -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (hypot.f64 z y) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))) (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z y) 2) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z y) 2) 3)) (cbrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2) (*.f64 (cbrt.f64 (hypot.f64 z y)) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))) (sqrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 z y)) (*.f64 (sqrt.f64 (hypot.f64 z y)) (pow.f64 3 -1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (hypot.f64 z y)) (/.f64 1 (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 3 -1/2) (hypot.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2) 1) (/.f64 (cbrt.f64 (hypot.f64 z y)) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 z y)) 1) (/.f64 (sqrt.f64 (hypot.f64 z y)) (sqrt.f64 3)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (cbrt.f64 3)) (/.f64 (hypot.f64 z y) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2) (cbrt.f64 3)) (cbrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (hypot.f64 z y)) (cbrt.f64 3)) (/.f64 (sqrt.f64 (hypot.f64 z y)) (cbrt.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 3 1/4)) (/.f64 (hypot.f64 z y) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2) (pow.f64 3 1/4)) (/.f64 (cbrt.f64 (hypot.f64 z y)) (pow.f64 3 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 3) (hypot.f64 z y)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (hypot.f64 z y) (neg.f64 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (/.f64 (pow.f64 (hypot.f64 z y) 2) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (/.f64 (pow.f64 (hypot.f64 z y) 3) (*.f64 3 (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (hypot.f64 z y) (sqrt.f64 3))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f64 (+.f64 1 (hypot.f64 z y)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (hypot.f64 z y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (hypot.f64 z y))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (hypot.f64 z y)) (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (cbrt.f64 (hypot.f64 z y)) 2) (cbrt.f64 (hypot.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (hypot.f64 z y)) (sqrt.f64 (hypot.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (hypot.f64 z y) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 z y) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (hypot.f64 z y) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (hypot.f64 z y)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (hypot.f64 z y)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (hypot.f64 z y) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (hypot.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (hypot.f64 z y) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (hypot.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (hypot.f64 z y)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (hypot.f64 z y)))))))

simplify149.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

694×	`fma-neg_binary64`
692×	`times-frac_binary64`
600×	`unswap-sqr_binary64`
443×	`fma-def_binary64`
434×	`associate-/l*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	1250
1	335	1208
2	1051	1208
3	4955	1188
4	6947	1188

Stop Event

1×	node limit

Counts

96 → 110

Calls

Call 1

Inputs
(/.f64 y (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (.f64 (pow.f64 y 5) (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3)))))
(/.f64 z (sqrt.f64 3))
(+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (.f64 (sqrt.f64 3) (pow.f64 z 3)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))))))
(*.f64 -1 (/.f64 z (sqrt.f64 3)))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))) (*.f64 -1 (/.f64 z (sqrt.f64 3))))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 -1 (/.f64 z (sqrt.f64 3))) (.f64 1/8 (/.f64 (pow.f64 y 4) (*.f64 (sqrt.f64 3) (pow.f64 z 3))))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))) (+.f64 (.f64 -1 (/.f64 z (sqrt.f64 3))) (.f64 1/8 (/.f64 (pow.f64 y 4) (*.f64 (sqrt.f64 3) (pow.f64 z 3)))))))
(/.f64 z (sqrt.f64 3))
(+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (.f64 (pow.f64 z 3) (sqrt.f64 3)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z)))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (.f64 (sqrt.f64 3) (pow.f64 z 5)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (.f64 (pow.f64 z 3) (sqrt.f64 3)))) (+.f64 (/.f64 z (sqrt.f64 3)) (.f64 1/2 (/.f64 (pow.f64 y 2) (.f64 (sqrt.f64 3) z))))))
(/.f64 y (sqrt.f64 3))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3)))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) (.f64 y (sqrt.f64 3)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (.f64 (pow.f64 y 5) (sqrt.f64 3)))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (/.f64 y (sqrt.f64 3)))))
(*.f64 -1 (/.f64 y (sqrt.f64 3)))
(+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (.f64 -1/2 (/.f64 (pow.f64 z 2) (*.f64 y (sqrt.f64 3)))))
(+.f64 (.f64 1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (.f64 -1/2 (/.f64 (pow.f64 z 2) (*.f64 y (sqrt.f64 3))))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 z 6) (.f64 (pow.f64 y 5) (sqrt.f64 3)))) (+.f64 (.f64 1/8 (/.f64 (pow.f64 z 4) (.f64 (pow.f64 y 3) (sqrt.f64 3)))) (+.f64 (.f64 -1 (/.f64 y (sqrt.f64 3))) (.f64 -1/2 (/.f64 (pow.f64 z 2) (*.f64 y (sqrt.f64 3)))))))
y
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 z 2) y)) y)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 y (.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 y (*.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))
z
(+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (.f64 1/2 (/.f64 (pow.f64 y 2) z))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))))
(*.f64 -1 z)
(+.f64 (.f64 -1 z) (.f64 -1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1 z) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) z)) (*.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3)))))
(+.f64 (.f64 -1 z) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 y 2) z)) (+.f64 (.f64 -1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (.f64 1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))))))
z
(+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (.f64 1/2 (/.f64 (pow.f64 y 2) z))))
(+.f64 (.f64 1/16 (/.f64 (pow.f64 y 6) (pow.f64 z 5))) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 y 4) (pow.f64 z 3))) (+.f64 z (*.f64 1/2 (/.f64 (pow.f64 y 2) z)))))
y
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 z 2) y)) y)
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 y (.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 y (*.f64 -1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))
(*.f64 -1 y)
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (.f64 -1 y))
(+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 -1 y) (*.f64 1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3)))))
(+.f64 (.f64 -1/16 (/.f64 (pow.f64 z 6) (pow.f64 y 5))) (+.f64 (.f64 -1/2 (/.f64 (pow.f64 z 2) y)) (+.f64 (.f64 -1 y) (.f64 1/8 (/.f64 (pow.f64 z 4) (pow.f64 y 3))))))

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

eval305.0ms (3.8%)

Compiler: Compiled 6042 to 3547 computations (41.3% saved)

prune122.0ms (1.5%)

Pruning

11 alts after pruning (0 fresh and 11 done)

	Pruned	Kept	Total
New	343	0	343
Fresh	0	0	0
Picked	0	1	1
Done	0	10	10
Total	343	11	354

Error

Counts

354 → 11

Alt Table

Click to see full alt table

Status	Error	Program
✓	31.0b	(*.f64 z (sqrt.f64 1/3))
✓	40.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
✓	0.4b	(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
✓	31.7b	(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
✓	31.7b	(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
✓	31.5b	(*.f64 (sqrt.f64 1/3) (neg.f64 x))
✓	31.2b	(*.f64 z (/.f64 1 (sqrt.f64 3)))
✓	0.4b	(/.f64 (hypot.f64 z x) (sqrt.f64 3))
✓	31.0b	(/.f64 z (sqrt.f64 3))
✓	30.4b	(/.f64 (hypot.f64 z y) (sqrt.f64 3))
✓	31.5b	(/.f64 (neg.f64 x) (sqrt.f64 3))

Compiler

Compiled 108 to 86 computations (20.4% saved)

regimes164.0ms (2.1%)

Counts

17 → 1

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(/.f64 (hypot.f64 z x) (sqrt.f64 3))
(/.f64 (hypot.f64 z y) (sqrt.f64 3))
(*.f64 (hypot.f64 z y) (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
(/.f64 (hypot.f64 x (hypot.f64 y z)) (sqrt.f64 3))

Outputs
(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))

Calls

13 calls:

21.0ms	x
17.0ms	z
16.0ms	(+.f64 (.f64 x x) (.f64 y y))
16.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
15.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`y`
0.4b	1	`z`
0.4b	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))`
0.4b	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)`
0.4b	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0.4b	1	`(+.f64 (.f64 x x) (.f64 y y))`
0.4b	1	`(+.f64 (.f64 x x) (.f64 y y))`
0.4b	1	`(*.f64 x x)`
0.4b	1	`(*.f64 x x)`
0.4b	1	`(*.f64 y y)`
0.4b	1	`(*.f64 z z)`
0.4b	1	`(*.f64 z z)`

Compiler

Compiled 224 to 146 computations (34.8% saved)

regimes206.0ms (2.6%)

Counts

15 → 1

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(/.f64 (hypot.f64 z x) (sqrt.f64 3))
(/.f64 (hypot.f64 z y) (sqrt.f64 3))
(*.f64 (hypot.f64 z y) (sqrt.f64 1/3))

Outputs
(/.f64 (hypot.f64 z x) (sqrt.f64 3))

Calls

13 calls:

18.0ms	(*.f64 x x)
18.0ms	z
17.0ms	y
17.0ms	x
17.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)

Results

Error	Segments	Branch
0.4b	1	`x`
0.4b	1	`y`
0.4b	1	`z`
0.4b	1	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))`
0.4b	1	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)`
0.4b	1	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
0.4b	1	`(+.f64 (.f64 x x) (.f64 y y))`
0.4b	1	`(+.f64 (.f64 x x) (.f64 y y))`
0.4b	1	`(*.f64 x x)`
0.4b	1	`(*.f64 x x)`
0.4b	1	`(*.f64 y y)`
0.4b	1	`(*.f64 z z)`
0.4b	1	`(*.f64 z z)`

Compiler

Compiled 210 to 138 computations (34.3% saved)

regimes343.0ms (4.3%)

Counts

12 → 5

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Outputs
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
(*.f64 z (sqrt.f64 1/3))

Calls

13 calls:

42.0ms	(+.f64 (.f64 x x) (.f64 y y))
40.0ms	y
35.0ms	z
34.0ms	(+.f64 (.f64 x x) (.f64 y y))
27.0ms	x

Results

Error	Segments	Branch
8.6b	3	`x`
15.3b	4	`y`
8.3b	5	`z`
19.6b	2	`(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))`
19.6b	2	`(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)`
19.6b	2	`(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))`
13.9b	6	`(+.f64 (.f64 x x) (.f64 y y))`
13.9b	6	`(+.f64 (.f64 x x) (.f64 y y))`
9.3b	5	`(*.f64 x x)`
9.3b	5	`(*.f64 x x)`
24.5b	4	`(*.f64 y y)`
10.1b	6	`(*.f64 z z)`
10.1b	6	`(*.f64 z z)`

Compiler

Compiled 192 to 127 computations (33.9% saved)

bsearch94.0ms (1.2%)

Algorithm

4×	binary-search

Steps

Time	Left	Right
23.0ms	1.7016962358190419e+139	5.633754605598011e+139
24.0ms	7.84609961846016e-48	2.689197315799583e-39
23.0ms	1.3620628828259381e-73	4.3959539711013473e-69
24.0ms	1.689795153928526e-131	9.268002001859243e-130

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes152.0ms (1.9%)

Counts

11 → 4

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))

Outputs
(.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (*.f64 (/.f64 z x) z)) x))
(/.f64 z (sqrt.f64 3))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 z (sqrt.f64 1/3))

Calls

7 calls:

32.0ms	y
27.0ms	(*.f64 x x)
25.0ms	x
24.0ms	(*.f64 x x)
19.0ms	z

Results

Error	Segments	Branch
8.9b	4	`x`
15.4b	4	`y`
12.1b	2	`z`
9.8b	6	`(*.f64 x x)`
9.8b	6	`(*.f64 x x)`
12.6b	2	`(*.f64 z z)`
12.6b	2	`(*.f64 z z)`

Compiler

Compiled 105 to 76 computations (27.6% saved)

bsearch70.0ms (0.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
23.0ms	-1.324235702978373e-39	-2.1986649126275866e-40
23.0ms	-9.584113791128849e-5	-1.5936717305920108e-6
23.0ms	-123540533935966.03	-10479944771.514187

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes195.0ms (2.5%)

Counts

10 → 4

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 x (/.f64 1 (neg.f64 (sqrt.f64 3))))

Outputs
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 z (sqrt.f64 3))
(sqrt.f64 (/.f64 (*.f64 x x) 3))
(*.f64 z (sqrt.f64 1/3))

Calls

7 calls:

54.0ms	y
44.0ms	x
30.0ms	z
23.0ms	(*.f64 x x)
22.0ms	(*.f64 x x)

Results

Error	Segments	Branch
9.1b	4	`x`
15.4b	4	`y`
12.1b	2	`z`
10.0b	6	`(*.f64 x x)`
10.0b	6	`(*.f64 x x)`
12.6b	2	`(*.f64 z z)`
12.6b	2	`(*.f64 z z)`

Compiler

Compiled 93 to 68 computations (26.9% saved)

bsearch122.0ms (1.5%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
41.0ms	-1.324235702978373e-39	-2.1986649126275866e-40
41.0ms	-9.584113791128849e-5	-1.5936717305920108e-6
40.0ms	-123540533935966.03	-10479944771.514187

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes149.0ms (1.9%)

Counts

8 → 4

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 (neg.f64 x) (sqrt.f64 3))
(*.f64 x (neg.f64 (sqrt.f64 1/3)))
(*.f64 z (/.f64 1 (sqrt.f64 3)))
(sqrt.f64 (/.f64 (*.f64 z z) 3))
(sqrt.f64 (.f64 z (.f64 z 1/3)))

Outputs
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(/.f64 z (sqrt.f64 3))
(*.f64 (sqrt.f64 1/3) (neg.f64 x))
(*.f64 z (sqrt.f64 1/3))

Calls

5 calls:

49.0ms	y
35.0ms	x
30.0ms	z
15.0ms	(*.f64 z z)
15.0ms	(*.f64 z z)

Results

Error	Segments	Branch
9.1b	4	`x`
15.4b	4	`y`
12.1b	2	`z`
12.6b	2	`(*.f64 z z)`
12.6b	2	`(*.f64 z z)`

Compiler

Compiled 68 to 50 computations (26.5% saved)

bsearch73.0ms (0.9%)

Algorithm

3×	binary-search

Steps

Time	Left	Right
23.0ms	-1.324235702978373e-39	-2.1986649126275866e-40
24.0ms	-9.584113791128849e-5	-1.5936717305920108e-6
26.0ms	-123540533935966.03	-10479944771.514187

Compiler

Compiled 23 to 16 computations (30.4% saved)

regimes12.0ms (0.2%)

Accuracy

Total -0.2b remaining (-0.6%)

Threshold costs -0.2b (-0.6%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 z (sqrt.f64 3))
(*.f64 z (sqrt.f64 1/3))

Outputs
(*.f64 z (sqrt.f64 1/3))

Calls

3 calls:

5.0ms	z
3.0ms	y
3.0ms	x

Results

Error	Segments	Branch
31.0b	1	`x`
31.0b	1	`y`
31.0b	1	`z`

Compiler

Compiled 23 to 18 computations (21.7% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
7×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	268
1	74	268
2	85	268
3	93	268
4	97	268
5	98	268

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
(/.f64 (hypot.f64 z x) (sqrt.f64 3))
(if (<=.f64 z 6752147932297427/399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 z 4335267334916093/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (if (<=.f64 z 6455396339686185/822752278660603021077484591278675252491367932816789931674304512) (/.f64 (neg.f64 x) (sqrt.f64 3)) (if (<=.f64 z 17016962358190418522196055021585507936456020243399854177651179394420077889955865062663702674262692188191083342787974929141816904740977508352) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (.f64 z (sqrt.f64 1/3))))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (.f64 (/.f64 z x) z)) x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 z (sqrt.f64 1/3)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 z (sqrt.f64 1/3)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (*.f64 z (sqrt.f64 1/3)))))
(*.f64 z (sqrt.f64 1/3))
(/.f64 z (sqrt.f64 3))

Outputs
(*.f64 (sqrt.f64 1/3) (hypot.f64 z x))
(/.f64 (hypot.f64 z x) (sqrt.f64 3))
(if (<=.f64 z 6752147932297427/399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 z 4335267334916093/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (if (<=.f64 z 6455396339686185/822752278660603021077484591278675252491367932816789931674304512) (/.f64 (neg.f64 x) (sqrt.f64 3)) (if (<=.f64 z 17016962358190418522196055021585507936456020243399854177651179394420077889955865062663702674262692188191083342787974929141816904740977508352) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (.f64 z (sqrt.f64 1/3))))))
(if (<=.f64 z 6752147932297427/399583814440447005616844445413525287135820562261116307309972090832047582568929999375399181192126972308457847183540047730617340886948900519205142528) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 z 4335267334916093/31828687130226345097944463881396533766429193651030253916189694521162207808802136034115584) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (if (<=.f64 z 6455396339686185/822752278660603021077484591278675252491367932816789931674304512) (/.f64 (neg.f64 x) (sqrt.f64 3)) (if (<=.f64 z 17016962358190418522196055021585507936456020243399854177651179394420077889955865062663702674262692188191083342787974929141816904740977508352) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 3)) (.f64 (sqrt.f64 1/3) z)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (.f64 (/.f64 z x) z)) x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 z (sqrt.f64 1/3)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (-.f64 (.f64 -1/2 (.f64 z (/.f64 z x))) x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 (sqrt.f64 1/3) z))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 z (sqrt.f64 1/3)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (sqrt.f64 (/.f64 (.f64 x x) 3)) (*.f64 (sqrt.f64 1/3) z))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (*.f64 z (sqrt.f64 1/3)))))
(if (<=.f64 x -3953297085950913/32) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (if (<=.f64 x -7071827771130563/73786976294838206464) (/.f64 z (sqrt.f64 3)) (if (<=.f64 x -8117541239479049/6129982163463555433433388108601236734474956488734408704) (.f64 (sqrt.f64 1/3) (neg.f64 x)) (*.f64 (sqrt.f64 1/3) z))))
(*.f64 z (sqrt.f64 1/3))
(*.f64 (sqrt.f64 1/3) z)
(/.f64 z (sqrt.f64 3))

Compiler

Compiled 201 to 143 computations (28.9% saved)

soundness62.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
756×	`associate-r_binary64`
724×	`associate-l_binary64`
468×	`times-frac_binary64`
393×	`associate-/l*_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	193	2870
1	584	2433
2	1880	2413

Stop Event

1×	node limit

Compiler

Compiled 65 to 52 computations (20% saved)

end128.0ms (1.6%)

Compiler: Compiled 198 to 131 computations (33.8% saved)