Metrics for Beckmann Distribution sample, tan2theta, alphax != alphay, u1 <= 0.5

analyze750.0ms (7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
0%	0%	0%	100%	0%	0%	0%	3
0%	0%	0%	100%	0%	0%	0%	4
25%	0%	0%	100%	0%	0%	0%	5
37.5%	0%	0%	100%	0%	0%	0%	6
37.5%	0%	0%	100%	0%	0%	0%	7
37.5%	0%	0%	100%	0%	0%	0%	8
56.3%	0%	0%	100%	0%	0%	0%	9
65.6%	0%	0%	100%	0%	0%	0%	10
70.3%	0%	0%	100%	0%	0%	0%	11
70.3%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 57 to 41 computations (28.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 215.0ms

Operation ival-<=, time spent: 63.0ms, 29.0% of total-time

Operation ival-sub, time spent: 37.0ms, 17.0% of total-time

Operation ival-log, time spent: 32.0ms, 15.0% of total-time

Operation ival-div, time spent: 26.0ms, 12.0% of total-time

Operation ival-mult, time spent: 22.0ms, 10.0% of total-time

Operation ival-and, time spent: 11.0ms, 5.0% of total-time

Operation ival-add, time spent: 9.0ms, 4.0% of total-time

Operation ival-neg, time spent: 7.0ms, 3.0% of total-time

Operation const, time spent: 7.0ms, 3.0% of total-time

sample4.4s (41.6%)

Results

4.1s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.7s

Operation ival-<=, time spent: 443.0ms, 26.0% of total-time

Operation ival-div, time spent: 289.0ms, 17.0% of total-time

Operation ival-log, time spent: 262.0ms, 15.0% of total-time

Operation ival-sub, time spent: 194.0ms, 11.0% of total-time

Operation ival-add, time spent: 148.0ms, 9.0% of total-time

Operation ival-mult, time spent: 137.0ms, 8.0% of total-time

Operation ival-and, time spent: 109.0ms, 6.0% of total-time

Operation const, time spent: 79.0ms, 5.0% of total-time

Operation ival-neg, time spent: 53.0ms, 3.0% of total-time

Bogosity

preprocess2.5s (23.8%)

Algorithm

1×	egg-herbie

Rules

1638×	`fma-neg`
629×	`times-frac`
486×	`div-sub`
423×	`sub-neg`
333×	`associate-/r*`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))`
-	-	`(/.f32 sin2phi (*.f32 alphay alphay))`
-	-	`alphay`
-	-	`cos2phi`
-	-	`u0`
-	-	`alphax`
-	-	`(neg.f32 (log.f32 (-.f32 1 u0)))`
-	-	`(/.f32 cos2phi (*.f32 alphax alphax))`
-	-	`sin2phi`
-	-	`(log.f32 (-.f32 1 u0))`
-	-	`(-.f32 1 u0)`
-	-	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`
-	-	`1`
-	-	`(*.f32 alphax alphax)`
-	-	`(*.f32 alphay alphay)`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	1620
1	254	1504
2	527	1504
3	1371	1504
4	4090	1504
5	5656	1504
6	6396	1504
7	6612	1504
8	6997	1504
9	7710	1504

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 (neg.f32 alphax) (neg.f32 alphax))) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 (neg.f32 alphay) (neg.f32 alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (neg.f32 sin2phi) (.f32 alphay alphay))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 (neg.f32 alphax) (neg.f32 alphax))) (/.f32 sin2phi (.f32 alphay alphay)))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 (neg.f32 alphay) (neg.f32 alphay))))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (neg.f32 sin2phi) (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphax alphax))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 alphax))) (+.f32 (/.f32 cos2phi (.f32 u0 u0)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 alphax (.f32 cos2phi cos2phi)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 sin2phi sin2phi)) (/.f32 alphax (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 alphay))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 u0 u0))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 alphay (.f32 alphax alphax)) (/.f32 sin2phi (.f32 cos2phi cos2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 alphay (.f32 sin2phi sin2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 cos2phi))) (+.f32 (/.f32 u0 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 sin2phi))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 u0 (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphay alphay))))

Outputs
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 (neg.f32 alphax) (neg.f32 alphax))) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 (neg.f32 alphay) (neg.f32 alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log1p.f32 u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (log1p.f32 u0) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (neg.f32 sin2phi) (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 (neg.f32 sin2phi) alphay) alphay)))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 (neg.f32 alphax) (neg.f32 alphax))) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (log1p.f32 (neg.f32 u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 (neg.f32 alphay) (neg.f32 alphay))))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (log1p.f32 (neg.f32 u0)) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (log1p.f32 u0) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 (/.f32 (neg.f32 sin2phi) alphay) alphay)))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 alphax alphax))))
(neg.f32 (/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 (neg.f32 sin2phi) (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 (neg.f32 cos2phi) (.f32 alphax alphax))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphax alphax))))
(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphax alphax)))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 cos2phi (.f32 alphay (neg.f32 alphay))) (/.f32 sin2phi (.f32 alphax alphax))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 alphax))) (+.f32 (/.f32 cos2phi (.f32 u0 u0)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 alphax))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 u0 u0))))
(/.f32 (log1p.f32 (neg.f32 alphax)) (neg.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 u0 u0)))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 alphax))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 cos2phi (.f32 u0 u0))))
(/.f32 (log1p.f32 (neg.f32 alphax)) (-.f32 (/.f32 sin2phi (.f32 alphay (neg.f32 alphay))) (/.f32 cos2phi (.f32 u0 u0))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 alphax (.f32 cos2phi cos2phi)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 alphax (.f32 cos2phi cos2phi))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 alphax (.f32 cos2phi cos2phi))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 sin2phi (.f32 alphay (neg.f32 alphay))) (/.f32 alphax (.f32 cos2phi cos2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 sin2phi sin2phi)) (/.f32 alphax (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 sin2phi sin2phi)) (/.f32 alphax (.f32 alphay alphay)))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 sin2phi sin2phi)) (/.f32 alphax (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 alphax (.f32 alphay (neg.f32 alphay))) (/.f32 cos2phi (.f32 sin2phi sin2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 alphay))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 u0 u0))))
(/.f32 (log1p.f32 (neg.f32 alphay)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 u0 u0)))))
(/.f32 (log1p.f32 (neg.f32 alphay)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 u0 u0))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 alphay (.f32 alphax alphax)) (/.f32 sin2phi (.f32 cos2phi cos2phi))))
(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 alphay (.f32 alphax alphax)) (/.f32 sin2phi (.f32 cos2phi cos2phi)))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 alphay (.f32 alphax alphax)) (/.f32 sin2phi (.f32 cos2phi cos2phi))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (neg.f32 alphay) (.f32 alphax alphax)) (/.f32 sin2phi (.f32 cos2phi cos2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 alphay (.f32 sin2phi sin2phi))))
(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 alphay (.f32 sin2phi sin2phi)))))
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 alphay (.f32 sin2phi sin2phi))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 alphay (*.f32 sin2phi sin2phi))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 cos2phi))) (+.f32 (/.f32 u0 (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 cos2phi))) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 u0 (.f32 alphax alphax))))
(/.f32 (log1p.f32 (neg.f32 cos2phi)) (neg.f32 (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 u0 (.f32 alphax alphax)))))
(neg.f32 (/.f32 (log1p.f32 (neg.f32 cos2phi)) (+.f32 (/.f32 sin2phi (.f32 alphay alphay)) (/.f32 u0 (.f32 alphax alphax)))))
(/.f32 (log1p.f32 (neg.f32 cos2phi)) (-.f32 (/.f32 (/.f32 u0 alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 sin2phi))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 u0 (.f32 alphay alphay))))
(/.f32 (log1p.f32 (neg.f32 sin2phi)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 u0 (.f32 alphay alphay)))))
(/.f32 (log1p.f32 (neg.f32 sin2phi)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 (/.f32 u0 alphay) alphay)))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 sin2phi (.f32 alphax alphax)) (/.f32 cos2phi (.f32 alphay alphay))))
(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphax alphax))))
(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 cos2phi (.f32 alphay alphay)) (/.f32 sin2phi (.f32 alphax alphax)))))
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 cos2phi (.f32 alphay (neg.f32 alphay))) (/.f32 sin2phi (.f32 alphax alphax))))

Symmetry

(abs alphax)

(abs alphay)

Compiler

Compiled 158 to 67 computations (57.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 818.0ms

Operation ival-sub, time spent: 256.0ms, 31.0% of total-time

Operation ival-log, time spent: 248.0ms, 30.0% of total-time

Operation ival-div, time spent: 101.0ms, 12.0% of total-time

Operation ival-add, time spent: 77.0ms, 9.0% of total-time

Operation ival-mult, time spent: 56.0ms, 7.0% of total-time

Operation ival-neg, time spent: 54.0ms, 7.0% of total-time

Operation const, time spent: 25.0ms, 3.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 37 to 19 computations (48.6% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.5%	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
▶	61.0%	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
▶	98.4%	(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Status

Accuracy

Program

▶

98.5%

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

▶

61.0%

(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

▶

98.4%

(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 64 to 43 computations (32.8% saved)

localize2.2s (20.4%)

Compiler: Compiled 182 to 35 computations (80.8% saved)
Precisions: Click to see histograms. Total time spent on operations: 696.0ms
Operation ival-log, time spent: 175.0ms, 25.0% of total-time
Operation ival-sub, time spent: 152.0ms, 22.0% of total-time
Operation ival-div, time spent: 116.0ms, 17.0% of total-time
Operation composed, time spent: 90.0ms, 13.0% of total-time
Operation ival-add, time spent: 64.0ms, 9.0% of total-time
Operation ival-neg, time spent: 56.0ms, 8.0% of total-time
Operation ival-mult, time spent: 28.0ms, 4.0% of total-time
Operation const, time spent: 15.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 5 to 5 computations (0% saved)

prune3.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	3	3
Done	0	0
Total	3	3

Accuracy

98.6%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.5%	(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
✓	61.0%	(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))
✓	98.4%	(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Status

Accuracy

Program

✓

98.5%

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

✓

61.0%

(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

✓

98.4%

(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 118 to 67 computations (43.2% saved)

regimes51.0ms (0.5%)

Counts

3 → 1

Calls

Call 1

Inputs

(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Outputs
(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))

Calls

14 calls:

5.0ms	cos2phi
5.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
4.0ms	(-.f32 1 u0)
3.0ms	(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))
3.0ms	(/.f32 cos2phi (*.f32 alphax alphax))

Results

Accuracy	Segments	Branch
98.5%	1	`alphax`
98.5%	1	`alphay`
98.5%	1	`u0`
98.5%	1	`cos2phi`
98.5%	1	`sin2phi`
98.5%	1	`(/.f32 (neg.f32 (log.f32 (-.f32 1 u0))) (+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay))))`
98.5%	1	`(neg.f32 (log.f32 (-.f32 1 u0)))`
98.5%	1	`(log.f32 (-.f32 1 u0))`
98.5%	1	`(-.f32 1 u0)`
98.5%	1	`(+.f32 (/.f32 cos2phi (.f32 alphax alphax)) (/.f32 sin2phi (.f32 alphay alphay)))`
98.5%	1	`(/.f32 cos2phi (*.f32 alphax alphax))`
98.5%	1	`(*.f32 alphax alphax)`
98.5%	1	`(/.f32 sin2phi (*.f32 alphay alphay))`
98.5%	1	`(*.f32 alphay alphay)`

Compiler

Compiled 131 to 100 computations (23.7% saved)

regimes20.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Outputs
(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Calls

7 calls:

4.0ms	alphax
4.0ms	(*.f32 alphay alphay)
3.0ms	alphay
3.0ms	(/.f32 sin2phi (*.f32 alphay alphay))
3.0ms	sin2phi

Results

Accuracy	Segments	Branch
98.4%	1	`alphax`
98.4%	1	`alphay`
98.4%	1	`u0`
98.4%	1	`cos2phi`
98.4%	1	`sin2phi`
98.4%	1	`(/.f32 sin2phi (*.f32 alphay alphay))`
98.4%	1	`(*.f32 alphay alphay)`

Compiler

Compiled 48 to 38 computations (20.8% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

19×	`+-commutative`
17×	`sub-neg`
16×	`*-commutative`
16×	`neg-sub0`
16×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	140
1	43	140
2	66	140
3	99	140
4	126	140
5	143	140
6	149	140
7	150	140

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Outputs

(/.f32 (neg.f32 (log1p.f32 (neg.f32 u0))) (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

(/.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 (+.f32 (/.f32 cos2phi (*.f32 alphax alphax)) (/.f32 sin2phi (*.f32 alphay alphay)))))

(/.f32 (log1p.f32 (neg.f32 u0)) (-.f32 (/.f32 (/.f32 cos2phi alphax) (neg.f32 alphax)) (/.f32 sin2phi (*.f32 alphay alphay))))

Compiler

Compiled 42 to 28 computations (33.3% saved)

soundness635.0ms (6%)

Rules

1638×	`fma-neg`
1638×	`fma-neg`
629×	`times-frac`
629×	`times-frac`
486×	`div-sub`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	99	1620
1	254	1504
2	527	1504
3	1371	1504
4	4090	1504
5	5656	1504
6	6396	1504
7	6612	1504
8	6997	1504
9	7710	1504
0	99	1620
1	254	1504
2	527	1504
3	1371	1504
4	4090	1504
5	5656	1504
6	6396	1504
7	6612	1504
8	6997	1504
9	7710	1504

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 394 to 133 computations (66.2% saved)

end0.0ms (0%)

preprocess36.0ms (0.3%)

Remove

(abs alphay)

(abs alphax)

Compiler

Compiled 370 to 236 computations (36.2% saved)

analyze750.0ms (7%)

sample4.4s (41.6%)

preprocess2.5s (23.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize2.2s (20.4%)

eval0.0ms (0%)

prune3.0ms (0%)

regimes51.0ms (0.5%)

regimes20.0ms (0.2%)

simplify7.0ms (0.1%)

soundness635.0ms (6%)

end0.0ms (0%)

preprocess36.0ms (0.3%)

Profiling