Metrics for Beckmann Sample, normalization factor

analyze44.0ms (1.8%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.3%	87.7%	0%	0%	0%	0
0%	0%	12.3%	87.7%	0%	0%	0%	1
50%	6.2%	6.2%	87.7%	0%	0%	0%	2
50%	6.2%	6.2%	87.7%	0%	0%	0%	3
75%	9.2%	3.1%	87.7%	0%	0%	0%	4
75%	9.2%	3.1%	87.7%	0%	0%	0%	5
87.5%	10.8%	1.5%	87.7%	0%	0%	0%	6
87.5%	10.8%	1.5%	87.7%	0%	0%	0%	7
93.8%	11.5%	0.8%	87.7%	0%	0%	0%	8
93.8%	11.5%	0.8%	87.7%	0%	0%	0%	9
96.9%	11.9%	0.4%	87.7%	0%	0%	0%	10
96.9%	11.9%	0.4%	87.7%	0%	0%	0%	11
98.4%	12.1%	0.2%	87.7%	0%	0%	0%	12

Compiler

Compiled 42 to 32 computations (23.8% saved)

sample2.2s (87.1%)

Results

2.2s	8256×	body	256	valid
10.0ms	58×	body	256	invalid

Bogosity

preprocess278.0ms (11.1%)

Algorithm

1×	egg-herbie

Rules

1470×	`distribute-lft-neg-in`
1276×	`distribute-rgt-neg-in`
1122×	`associate-r`
1040×	`associate-*r/`
820×	`associate-/l*`

Problems

248×	No Errors
7×	`(*.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta))`
1×	`(-.f32 (-.f32 1 cosTheta) cosTheta)`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	687
1	142	596
2	390	596
3	1325	564
4	6237	564

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 (neg.f32 cosTheta)) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (exp.f32 (*.f32 (neg.f32 (neg.f32 cosTheta)) (neg.f32 cosTheta))))))
(/.f32 1 (+.f32 (+.f32 1 (neg.f32 c)) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(neg.f32 (/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 (neg.f32 cosTheta)) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (exp.f32 (*.f32 (neg.f32 (neg.f32 cosTheta)) (neg.f32 cosTheta)))))))
(neg.f32 (/.f32 1 (+.f32 (+.f32 1 (neg.f32 c)) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))))
(/.f32 1 (+.f32 (+.f32 1 cosTheta) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 c) c)) c)) (exp.f32 (*.f32 (neg.f32 c) c)))))

Outputs
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(/.f32 1 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 cosTheta -2))) cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (+.f32 1 c)))
(/.f32 1 (+.f32 1 (fma.f32 (/.f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) c)))
(/.f32 1 (+.f32 c (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) 1)))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(/.f32 1 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 cosTheta -2))) cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (+.f32 1 c)))
(/.f32 1 (+.f32 1 (fma.f32 (/.f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) c)))
(/.f32 1 (+.f32 c (fma.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (*.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) 1)))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 (neg.f32 cosTheta)) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (exp.f32 (*.f32 (neg.f32 (neg.f32 cosTheta)) (neg.f32 cosTheta))))))
(/.f32 1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (+.f32 (+.f32 1 cosTheta) cosTheta)) (neg.f32 cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(/.f32 1 (fma.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 2 cosTheta))) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 1 c)))
(/.f32 1 (+.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 1 (fma.f32 (/.f32 -1 (sqrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta 2 1)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))) c)))
(/.f32 1 (+.f32 (+.f32 1 (neg.f32 c)) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta)))))
(/.f32 1 (+.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))) (-.f32 1 c)))
(/.f32 1 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 cosTheta -2))) cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (-.f32 1 c)))
(/.f32 1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 1 c)))
(/.f32 1 (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta))) cosTheta)) (-.f32 1 c)))
(neg.f32 (/.f32 1 (+.f32 (+.f32 1 c) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 (neg.f32 cosTheta)) (neg.f32 cosTheta))) (neg.f32 cosTheta))) (exp.f32 (*.f32 (neg.f32 (neg.f32 cosTheta)) (neg.f32 cosTheta)))))))
(/.f32 -1 (+.f32 (+.f32 1 c) (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (+.f32 (+.f32 1 cosTheta) cosTheta)) (neg.f32 cosTheta)) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(/.f32 -1 (fma.f32 (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 2 cosTheta))) (neg.f32 cosTheta)) (sqrt.f32 (PI.f32))) (+.f32 1 c)))
(/.f32 -1 (+.f32 1 (+.f32 c (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) (neg.f32 cosTheta))) (pow.f32 (exp.f32 cosTheta) cosTheta)))))
(/.f32 -1 (+.f32 1 (fma.f32 (/.f32 -1 (sqrt.f32 (PI.f32))) (/.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta 2 1)) cosTheta) (exp.f32 (*.f32 cosTheta cosTheta))) c)))
(neg.f32 (/.f32 1 (+.f32 (+.f32 1 (neg.f32 c)) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta)) (exp.f32 (*.f32 (neg.f32 cosTheta) cosTheta))))))
(/.f32 -1 (+.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (.f32 (/.f32 (sqrt.f32 (-.f32 (-.f32 1 cosTheta) cosTheta)) cosTheta) (exp.f32 (neg.f32 (*.f32 cosTheta cosTheta))))) (-.f32 1 c)))
(/.f32 -1 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (+.f32 1 (*.f32 cosTheta -2))) cosTheta) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 (neg.f32 cosTheta)) cosTheta) (-.f32 1 c)))
(/.f32 -1 (+.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta 2))) (.f32 (sqrt.f32 (PI.f32)) cosTheta)) (pow.f32 (exp.f32 cosTheta) cosTheta)) (-.f32 1 c)))
(/.f32 -1 (+.f32 (/.f32 (sqrt.f32 (fma.f32 cosTheta -2 1)) (.f32 (.f32 (sqrt.f32 (PI.f32)) (exp.f32 (*.f32 cosTheta cosTheta))) cosTheta)) (-.f32 1 c)))
(/.f32 1 (+.f32 (+.f32 1 cosTheta) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 c) c)) c)) (exp.f32 (*.f32 (neg.f32 c) c)))))
(/.f32 1 (+.f32 (+.f32 1 cosTheta) (.f32 (.f32 (/.f32 1 (sqrt.f32 (PI.f32))) (/.f32 (sqrt.f32 (-.f32 (-.f32 1 c) c)) c)) (pow.f32 (exp.f32 (neg.f32 c)) c))))
(/.f32 1 (fma.f32 (/.f32 (/.f32 (sqrt.f32 (-.f32 1 (*.f32 2 c))) c) (sqrt.f32 (PI.f32))) (pow.f32 (exp.f32 c) (neg.f32 c)) (+.f32 1 cosTheta)))
(/.f32 1 (fma.f32 (/.f32 (sqrt.f32 (+.f32 1 (.f32 c -2))) (.f32 (sqrt.f32 (PI.f32)) c)) (pow.f32 (exp.f32 c) (neg.f32 c)) (+.f32 1 cosTheta)))
(/.f32 1 (+.f32 (+.f32 1 cosTheta) (/.f32 (sqrt.f32 (fma.f32 c -2 1)) (.f32 (pow.f32 (exp.f32 c) c) (.f32 c (sqrt.f32 (PI.f32)))))))

Compiler

Compiled 129 to 70 computations (45.7% saved)

Beckmann Sample, normalization factor

analyze44.0ms (1.8%)

sample2.2s (87.1%)

preprocess278.0ms (11.1%)

end0.0ms (0%)

Profiling