Metrics for Beckmann Distribution sample, tan2theta, alphax == alphay

analyze57.0ms (0.8%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.2%	99.8%	0%	0%	0%	0
0%	0%	0.2%	99.8%	0%	0%	0%	1
0%	0%	0.2%	99.8%	0%	0%	0%	2
50%	0.1%	0.1%	99.8%	0%	0%	0%	3
50%	0.1%	0.1%	99.8%	0%	0%	0%	4
75%	0.1%	0%	99.8%	0%	0%	0%	5
75%	0.1%	0%	99.8%	0%	0%	0%	6
87.5%	0.1%	0%	99.8%	0%	0%	0%	7
87.5%	0.1%	0%	99.8%	0%	0%	0%	8
93.8%	0.2%	0%	99.8%	0%	0%	0%	9
93.8%	0.2%	0%	99.8%	0%	0%	0%	10
96.9%	0.2%	0%	99.8%	0%	0%	0%	11
96.9%	0.2%	0%	99.8%	0%	0%	0%	12

Compiler

Compiled 26 to 19 computations (26.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

Operation ival-<=, time spent: 5.0ms, 27.0% of total-time

Operation ival-mult, time spent: 4.0ms, 22.0% of total-time

Operation ival-log, time spent: 4.0ms, 22.0% of total-time

Operation ival-neg, time spent: 2.0ms, 11.0% of total-time

Operation ival-sub, time spent: 1.0ms, 5.0% of total-time

Operation const, time spent: 1.0ms, 5.0% of total-time

Operation ival-and, time spent: 1.0ms, 5.0% of total-time

sample2.8s (41.6%)

Results

2.7s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

Operation ival-<=, time spent: 548.0ms, 41.0% of total-time

Operation ival-log, time spent: 261.0ms, 20.0% of total-time

Operation ival-sub, time spent: 217.0ms, 16.0% of total-time

Operation ival-mult, time spent: 161.0ms, 12.0% of total-time

Operation ival-neg, time spent: 64.0ms, 5.0% of total-time

Operation const, time spent: 44.0ms, 3.0% of total-time

Operation ival-and, time spent: 43.0ms, 3.0% of total-time

Bogosity

preprocess1.4s (21.3%)

Algorithm

1×	egg-herbie

Rules

944×	`distribute-rgt-in`
939×	`distribute-lft-in`
839×	`fma-define`
458×	`associate-+r+`
338×	`sub-neg`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))`
-	-	`(*.f32 (neg.f32 alpha) alpha)`
-	-	`alpha`
-	-	`(neg.f32 alpha)`
-	-	`(log.f32 (-.f32 1 u0))`
-	-	`(-.f32 1 u0)`
-	-	`1`
-	-	`u0`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	268
1	77	222
2	195	222
3	461	222
4	853	222
5	1184	222
6	1261	222
7	1462	222
8	2842	222
9	4130	222
10	4945	222
11	5477	222
12	5789	222
13	5931	222
14	5981	222
15	5999	222
16	5999	222
17	6036	222
18	6060	222
19	6060	222
20	6060	222

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
(.f32 (.f32 (neg.f32 (neg.f32 alpha)) (neg.f32 alpha)) (log.f32 (-.f32 1 u0)))
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 (neg.f32 u0))))
(neg.f32 (.f32 (.f32 (neg.f32 (neg.f32 alpha)) (neg.f32 alpha)) (log.f32 (-.f32 1 u0))))
(neg.f32 (.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 (neg.f32 u0)))))
(.f32 (.f32 (neg.f32 u0) u0) (log.f32 (-.f32 1 alpha)))

Outputs
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
(.f32 alpha (.f32 (neg.f32 alpha) (log.f32 (-.f32 1 u0))))
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
(.f32 alpha (.f32 alpha (neg.f32 (log1p.f32 (neg.f32 u0)))))
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
(.f32 alpha (.f32 (neg.f32 alpha) (log.f32 (-.f32 1 u0))))
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
(.f32 alpha (.f32 alpha (neg.f32 (log1p.f32 (neg.f32 u0)))))
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 (.f32 (neg.f32 (neg.f32 alpha)) (neg.f32 alpha)) (log.f32 (-.f32 1 u0)))
(.f32 alpha (.f32 (neg.f32 alpha) (log.f32 (-.f32 1 u0))))
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
(.f32 alpha (.f32 alpha (neg.f32 (log1p.f32 (neg.f32 u0)))))
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 (neg.f32 u0))))
(.f32 (.f32 alpha (neg.f32 alpha)) (log.f32 (-.f32 1 (neg.f32 u0))))
(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 u0))
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 u0))
(neg.f32 (.f32 (.f32 (neg.f32 (neg.f32 alpha)) (neg.f32 alpha)) (log.f32 (-.f32 1 u0))))
(.f32 (.f32 alpha (neg.f32 alpha)) (neg.f32 (log.f32 (-.f32 1 u0))))
(.f32 (log1p.f32 (neg.f32 u0)) (.f32 alpha alpha))
(neg.f32 (.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 (neg.f32 u0)))))
(.f32 (.f32 alpha (neg.f32 alpha)) (neg.f32 (log.f32 (-.f32 1 (neg.f32 u0)))))
(.f32 alpha (.f32 alpha (log1p.f32 u0)))
(.f32 (.f32 (neg.f32 u0) u0) (log.f32 (-.f32 1 alpha)))
(.f32 (neg.f32 u0) (.f32 u0 (log.f32 (-.f32 1 alpha))))
(.f32 (neg.f32 u0) (.f32 u0 (log1p.f32 (neg.f32 alpha))))
(.f32 u0 (.f32 (neg.f32 u0) (log1p.f32 (neg.f32 alpha))))

Symmetry

(abs alpha)

Compiler

Compiled 67 to 38 computations (43.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 447.0ms

Operation ival-sub, time spent: 181.0ms, 40.0% of total-time

Operation ival-log, time spent: 154.0ms, 34.0% of total-time

Operation ival-mult, time spent: 64.0ms, 14.0% of total-time

Operation ival-neg, time spent: 27.0ms, 6.0% of total-time

Operation const, time spent: 20.0ms, 4.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 35 to 18 computations (48.6% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	56.2%	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
▶	99.2%	(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
▶	99.0%	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 31 to 22 computations (29% saved)

localize1.3s (19%)

Compiler: Compiled 73 to 22 computations (69.9% saved)
Precisions: Click to see histograms. Total time spent on operations: 609.0ms
Operation ival-log, time spent: 147.0ms, 24.0% of total-time
Operation ival-sub, time spent: 132.0ms, 22.0% of total-time
Operation composed, time spent: 116.0ms, 19.0% of total-time
Operation ival-mult, time spent: 89.0ms, 15.0% of total-time
Operation ival-add, time spent: 58.0ms, 10.0% of total-time
Operation ival-neg, time spent: 54.0ms, 9.0% of total-time
Operation const, time spent: 13.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune4.0ms (0.1%)

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

99.7%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	56.2%	(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))
✓	99.2%	(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
✓	99.0%	(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Compiler

Compiled 58 to 37 computations (36.2% saved)

regimes22.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))

Outputs
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))

Calls

6 calls:

5.0ms	u0
3.0ms	(*.f32 (neg.f32 alpha) alpha)
3.0ms	(log.f32 (-.f32 1 u0))
3.0ms	alpha
3.0ms	(-.f32 1 u0)

Results

Accuracy	Segments	Branch
99.2%	1	`alpha`
99.2%	1	`u0`
99.2%	1	`(.f32 (.f32 (neg.f32 alpha) alpha) (log.f32 (-.f32 1 u0)))`
99.2%	1	`(*.f32 (neg.f32 alpha) alpha)`
99.2%	1	`(log.f32 (-.f32 1 u0))`
99.2%	1	`(-.f32 1 u0)`

Compiler

Compiled 34 to 25 computations (26.5% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Outputs
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Calls

2 calls:

2.0ms	u0
2.0ms	alpha

Results

Accuracy	Segments	Branch
99.0%	1	`alpha`
99.0%	1	`u0`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative`
8×	`neg-sub0`
8×	`neg-mul-1`
7×	`sub-neg`
7×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	68
1	33	68
2	54	68
3	73	68
4	79	68
5	81	68

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))

Outputs
(.f32 (neg.f32 (.f32 alpha alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 (.f32 alpha (neg.f32 alpha)) (log1p.f32 (neg.f32 u0)))
(.f32 alpha (.f32 (neg.f32 alpha) (log1p.f32 (neg.f32 u0))))
(.f32 alpha (.f32 (log1p.f32 (neg.f32 u0)) (neg.f32 alpha)))
(neg.f32 (.f32 (.f32 alpha (log1p.f32 (neg.f32 u0))) alpha))
(.f32 alpha (.f32 alpha (neg.f32 (log1p.f32 (neg.f32 u0)))))

Compiler

Compiled 20 to 14 computations (30% saved)

soundness1.1s (16%)

Rules

944×	`distribute-rgt-in`
944×	`distribute-rgt-in`
939×	`distribute-lft-in`
939×	`distribute-lft-in`
839×	`fma-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	268
1	77	222
2	195	222
3	461	222
4	853	222
5	1184	222
6	1261	222
7	1462	222
8	2842	222
9	4130	222
10	4945	222
11	5477	222
12	5789	222
13	5931	222
14	5981	222
15	5999	222
16	5999	222
17	6036	222
18	6060	222
19	6060	222
20	6060	222
0	27	268
1	77	222
2	195	222
3	461	222
4	853	222
5	1184	222
6	1261	222
7	1462	222
8	2842	222
9	4130	222
10	4945	222
11	5477	222
12	5789	222
13	5931	222
14	5981	222
15	5999	222
16	5999	222
17	6036	222
18	6060	222
19	6060	222
20	6060	222

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 121 to 72 computations (40.5% saved)

end0.0ms (0%)

preprocess48.0ms (0.7%)

Remove: (abs alpha)
Compiler: Compiled 118 to 78 computations (33.9% saved)

analyze57.0ms (0.8%)

sample2.8s (41.6%)

preprocess1.4s (21.3%)

eval1.0ms (0%)

prune2.0ms (0%)

localize1.3s (19%)

eval0.0ms (0%)

prune4.0ms (0.1%)

regimes22.0ms (0.3%)

regimes5.0ms (0.1%)

simplify4.0ms (0.1%)

soundness1.1s (16%)

end0.0ms (0%)

preprocess48.0ms (0.7%)

Profiling