Details

analyze94.0ms (4.9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
26.7%	25%	68.7%	0.1%	0%	6.2%	0%	5
27.6%	25%	65.6%	0.1%	0%	9.4%	0%	6
49%	37.5%	39%	0.1%	0%	23.4%	0%	7
50.5%	37.5%	36.7%	0.1%	0%	25.8%	0%	8
67.9%	43.7%	20.7%	0.1%	0%	35.5%	0%	9
69.3%	43.7%	19.3%	0.1%	0%	36.9%	0%	10
81.5%	46.8%	10.6%	0.1%	0%	42.4%	0%	11
82.5%	46.8%	9.9%	0.1%	0%	43.2%	0%	12

Compiler

Compiled 19 to 17 computations (10.5% saved)

sample1.7s (86.5%)

Results

1.4s	8256×	body	256	valid
231.0ms	1113×	body	256	invalid

Bogosity

preprocess21.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

32×	`fma-def`
32×	`+-commutative`
28×	`associate-+l-`
24×	`*-commutative`
20×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	102
1	42	90
2	62	82
3	81	82
4	95	82
5	114	82
6	142	82
7	192	82
8	194	82
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 h) g)) 3))))

Outputs
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (+.f64 (/.f64 2 (/.f64 3 (PI.f64))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(.f64 2 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 h) g)) 3))))
(*.f64 2 (cos.f64 (+.f64 (/.f64 2 (/.f64 3 (PI.f64))) (/.f64 (acos.f64 (neg.f64 (/.f64 h g))) 3))))
(.f64 2 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (neg.f64 (/.f64 h g))) 3))))
(*.f64 2 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (neg.f64 (/.f64 h g))) 3))))
(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (neg.f64 (/.f64 h g))) 3))))
(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 h) g)) 3))))

Compiler

Compiled 20 to 18 computations (10% saved)

simplify14.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def`
14×	`*-commutative`
14×	`associate-+l-`
14×	`+-commutative`
8×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	29	45
2	43	41
3	54	41
4	61	41
5	71	41
6	85	41
7	109	41

Stop Event

1×

saturated

Counts

1 → 5

Calls

Call 1

Inputs
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Outputs
(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (+.f64 (/.f64 2 (/.f64 3 (PI.f64))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(.f64 2 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (fma.f64 2/3 (PI.f64) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

eval1.0ms (0.1%)

Compiler: Compiled 74 to 48 computations (35.1% saved)

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	2	6

Error

98.5%

Counts

6 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	98.5%	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
▶	98.5%	(.f64 2 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 31 to 27 computations (12.9% saved)

localize22.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	98.5%	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	98.5%	(+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	98.5%	(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
✓	98.4%	(*.f64 2/3 (PI.f64))

Compiler

Compiled 66 to 32 computations (51.5% saved)

series8.0ms (0.4%)

Counts

4 → 72

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	h	@	-inf	(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0ms	g	@	0	(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0ms	g	@	-inf	(+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0ms	g	@	inf	(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0ms	g	@	-inf	(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

rewrite99.0ms (5.1%)

Algorithm

1×	batch-egg-rewrite

Rules

1800×	`associate-*r/`
1260×	`associate-*l/`
374×	`add-sqr-sqrt`
356×	`pow1`
356×	`*-un-lft-identity`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	96
1	356	84
2	4758	84

Stop Event

1×	node limit

Calls

Call 1

Inputs
(*.f64 2/3 (PI.f64))
(cos.f64 (+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
(+.f64 (*.f64 2/3 (PI.f64)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

Outputs
((((x -.f64 (exp.f64 (log1p.f64 (.f64 2/3 (PI.f64)))) 1))) (((x pow.f64 (.f64 2/3 (PI.f64)) 1))) (((x pow.f64 (sqrt.f64 (.f64 2/3 (PI.f64))) 2))) (((x pow.f64 (cbrt.f64 (.f64 2/3 (PI.f64))) 3))) (((x pow.f64 (.f64 8/27 (pow.f64 (PI.f64) 3)) 1/3))) (((x sqrt.f64 (.f64 4/9 (pow.f64 (PI.f64) 2))))) (((x log.f64 (pow.f64 (exp.f64 2/3) (PI.f64))))) (((x log.f64 (+.f64 1 (expm1.f64 (.f64 2/3 (PI.f64))))))) (((x cbrt.f64 (.f64 8/27 (pow.f64 (PI.f64) 3))))) (((x expm1.f64 (log1p.f64 (.f64 2/3 (PI.f64)))))) (((x exp.f64 (log.f64 (.f64 2/3 (PI.f64)))))) (((x exp.f64 (.f64 (log.f64 (.f64 2/3 (PI.f64))) 1)))) (((x log1p.f64 (expm1.f64 (*.f64 2/3 (PI.f64)))))))
((((x +.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))) (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x +.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))) (+.f64 (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))))) (((x +.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (neg.f64 (sin.f64 (.f64 2/3 (PI.f64)))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x +.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (neg.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x +.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (+.f64 (.f64 (neg.f64 (sin.f64 (.f64 2/3 (PI.f64)))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))))) (((x +.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (+.f64 (neg.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))))) (((x +.f64 (.f64 (neg.f64 (sin.f64 (.f64 2/3 (PI.f64)))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x +.f64 (neg.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x +.f64 (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x -.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x -.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (-.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))))) (((x -.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))))) 1))) (((x -.f64 (exp.f64 (log1p.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))))) (-.f64 1 (fma.f64 (neg.f64 (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (sin.f64 (.f64 2/3 (PI.f64))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))))) (((x .f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))) 1))) (((x .f64 1 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (((x .f64 (sqrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (sqrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x .f64 (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))) 2)))) (((x .f64 (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3)))) 2) (cbrt.f64 (cos.f64 (fma.f64 2/3 (PI.f64) (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x /.f64 (-.f64 (.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))) (+.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x /.f64 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) 3) (pow.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) 3)) (+.f64 (.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (+.f64 (.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))))))) (((x /.f64 (.f64 1 (-.f64 (.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))) (.f64 (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3)))))) (+.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) (.f64 (sin.f64 (.f64 2/3 (PI.f64))) (sin.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))))))) (((x /.f64 (.f64 1 (-.f64 (pow.f64 (.f64 (cos.f64 (.f64 2/3 (PI.f64))) (cos.f64 (.f64 (acos.f64 (/.f64 g h)) 1/3))) 3) (pow.f64 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Details

analyze94.0ms (4.9%)

sample1.7s (86.5%)

preprocess21.0ms (1.1%)

simplify14.0ms (0.8%)

eval1.0ms (0.1%)

prune2.0ms (0.1%)

localize22.0ms (1.1%)

series8.0ms (0.4%)

rewrite99.0ms (5.1%)

end0.0ms (0%)

Profiling