Metrics for HairBSDF, sample

analyze72.0ms (0.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.9%	99.1%	0%	0%	0%	0
0%	0%	0.9%	99.1%	0%	0%	0%	1
0%	0%	0.9%	99.1%	0%	0%	0%	2
50%	0.4%	0.4%	99.1%	0%	0%	0%	3
50%	0.4%	0.4%	99.1%	0%	0%	0%	4
75%	0.6%	0.2%	99.1%	0%	0%	0%	5
75%	0.6%	0.2%	99.1%	0%	0%	0%	6
87.5%	0.7%	0.1%	99.1%	0%	0%	0%	7
87.5%	0.7%	0.1%	99.1%	0%	0%	0%	8
93.7%	0.8%	0.1%	99.1%	0%	0%	0%	9
93.7%	0.8%	0.1%	99.1%	0%	0%	0%	10
96.9%	0.8%	0%	99.1%	0%	0%	0%	11
96.9%	0.8%	0%	99.1%	0%	0%	0%	12

Compiler

Compiled 32 to 24 computations (25% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

Operation ival-log, time spent: 4.0ms, 21.0% of total-time

Operation ival-<=, time spent: 4.0ms, 21.0% of total-time

Operation ival-mult, time spent: 3.0ms, 15.0% of total-time

Operation ival-add, time spent: 2.0ms, 10.0% of total-time

Operation ival-exp, time spent: 2.0ms, 10.0% of total-time

Operation ival-sub, time spent: 2.0ms, 10.0% of total-time

Operation ival-div, 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

sample2.6s (26%)

Results

2.4s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

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

Operation ival-add, time spent: 308.0ms, 23.0% of total-time

Operation ival-log, time spent: 234.0ms, 18.0% of total-time

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

Operation ival-<=, time spent: 178.0ms, 13.0% of total-time

Operation ival-mult, time spent: 139.0ms, 10.0% of total-time

Operation ival-div, time spent: 96.0ms, 7.0% of total-time

Operation ival-exp, time spent: 72.0ms, 5.0% of total-time

Operation const, time spent: 48.0ms, 4.0% of total-time

Operation ival-and, time spent: 34.0ms, 3.0% of total-time

Bogosity

preprocess4.5s (44.5%)

Algorithm

1×	egg-herbie

Rules

1953×	`fma-def`
678×	`unsub-neg`
502×	`fma-neg`
301×	`distribute-rgt-in`
300×	`distribute-lft-in`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(+.f32 u (*.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v))))`
-	-	`(-.f32 1 u)`
-	-	`(exp.f32 (/.f32 -2 v))`
-	-	`v`
-	-	`(log.f32 (+.f32 u (*.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))`
-	-	`(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))`
-	-	`u`
-	-	`(*.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))`
-	-	`(.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v))))))`
-	-	`(/.f32 -2 v)`
-	-	`1`
-	-	`-2`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	43	439
1	84	363
2	191	359
3	481	359
4	1246	359
5	2666	359
6	3658	359
7	3899	359
8	4086	359
9	4401	359
10	4587	359
11	5755	359
12	6681	359
13	7336	359
14	7577	359
15	7758	359
16	7814	359
17	7814	359

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
(+.f32 1 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (-.f32 1 (neg.f32 u)) (exp.f32 (/.f32 -2 v)))))))
(+.f32 1 (.f32 (neg.f32 v) (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 (neg.f32 v))))))))
(neg.f32 (+.f32 1 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (-.f32 1 (neg.f32 u)) (exp.f32 (/.f32 -2 v))))))))
(neg.f32 (+.f32 1 (.f32 (neg.f32 v) (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 (neg.f32 v)))))))))
(+.f32 1 (.f32 u (log.f32 (+.f32 v (.f32 (-.f32 1 v) (exp.f32 (/.f32 -2 u)))))))

Outputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
(+.f32 1 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (-.f32 1 (neg.f32 u)) (exp.f32 (/.f32 -2 v)))))))
(+.f32 1 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 (neg.f32 u)))))))
(fma.f32 v (log.f32 (-.f32 (*.f32 (exp.f32 (/.f32 -2 v)) (+.f32 1 u)) u)) 1)
(+.f32 1 (.f32 (neg.f32 v) (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 (neg.f32 v))))))))
(-.f32 1 (*.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 2 v)) u))))
(neg.f32 (+.f32 1 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (-.f32 1 (neg.f32 u)) (exp.f32 (/.f32 -2 v))))))))
(+.f32 -1 (neg.f32 (.f32 v (log.f32 (+.f32 (neg.f32 u) (.f32 (exp.f32 (/.f32 -2 v)) (-.f32 1 (neg.f32 u))))))))
(-.f32 -1 (.f32 v (log.f32 (-.f32 (.f32 (exp.f32 (/.f32 -2 v)) (+.f32 1 u)) u))))
(neg.f32 (fma.f32 v (log.f32 (-.f32 (*.f32 (exp.f32 (/.f32 -2 v)) (+.f32 1 u)) u)) 1))
(fma.f32 (log.f32 (-.f32 (*.f32 (exp.f32 (/.f32 -2 v)) (+.f32 1 u)) u)) (neg.f32 v) -1)
(neg.f32 (+.f32 1 (.f32 (neg.f32 v) (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 (neg.f32 v)))))))))
(+.f32 -1 (neg.f32 (.f32 (neg.f32 v) (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 (neg.f32 v)))))))))
(+.f32 -1 (*.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 2 v)) u))))
(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 2 v)) u)) -1)
(+.f32 1 (.f32 u (log.f32 (+.f32 v (.f32 (-.f32 1 v) (exp.f32 (/.f32 -2 u)))))))
(fma.f32 u (log.f32 (fma.f32 (-.f32 1 v) (exp.f32 (/.f32 -2 u)) v)) 1)

Compiler

Compiled 165 to 119 computations (27.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.2s

Operation ival-exp, time spent: 1.2s, 38.0% of total-time

Operation ival-log, time spent: 635.0ms, 20.0% of total-time

Operation ival-sub, time spent: 482.0ms, 15.0% of total-time

Operation ival-add, time spent: 352.0ms, 11.0% of total-time

Operation ival-div, time spent: 249.0ms, 8.0% of total-time

Operation ival-mult, time spent: 222.0ms, 7.0% of total-time

Operation const, time spent: 49.0ms, 2.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.7%	(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
▶	99.7%	(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Compiler

Compiled 32 to 24 computations (25% saved)

localize2.8s (28.3%)

Compiler: Compiled 120 to 84 computations (30% saved)
Precisions: Click to see histograms. Total time spent on operations: 2.1s
Operation ival-exp, time spent: 846.0ms, 39.0% of total-time
Operation ival-log, time spent: 430.0ms, 20.0% of total-time
Operation ival-sub, time spent: 299.0ms, 14.0% of total-time
Operation ival-div, time spent: 200.0ms, 9.0% of total-time
Operation ival-add, time spent: 149.0ms, 7.0% of total-time
Operation ival-mult, time spent: 97.0ms, 5.0% of total-time
Operation ival-fma, time spent: 84.0ms, 4.0% of total-time
Operation const, time spent: 41.0ms, 2.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	0	0
Total	2	2

Accuracy

99.8%

Counts

2 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.7%	(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)
✓	99.7%	(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Compiler

Compiled 62 to 46 computations (25.8% saved)

regimes14.0ms (0.1%)

Accuracy

Total -0.0b remaining (-18.7%)

Threshold costs -0b (-18.7%)

Counts

2 → 1

Calls

Call 1

Inputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
(fma.f32 v (log.f32 (fma.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)) u)) 1)

Outputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Calls

4 calls:

5.0ms	u
3.0ms	(.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v))))))
3.0ms	(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))
3.0ms	v

Results

Accuracy	Segments	Branch
99.7%	1	`u`
99.7%	1	`v`
99.7%	1	`(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))`
99.7%	1	`(.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v))))))`

Compiler

Compiled 38 to 28 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative`
3×	`1-exp`
3×	`*-commutative`
2×	`sub-neg`
1×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	57
1	29	57
2	33	57
3	35	57
4	36	57

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Outputs
(+.f32 1 (.f32 v (log.f32 (+.f32 u (.f32 (-.f32 1 u) (exp.f32 (/.f32 -2 v)))))))

Compiler

Compiled 17 to 13 computations (23.5% saved)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess28.0ms (0.3%)

Compiler: Compiled 68 to 52 computations (23.5% saved)

HairBSDF, sample_f, cosTheta

analyze72.0ms (0.7%)

sample2.6s (26%)

preprocess4.5s (44.5%)

eval0.0ms (0%)

prune1.0ms (0%)

localize2.8s (28.3%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes14.0ms (0.1%)

simplify3.0ms (0%)

soundness0.0ms (0%)

end0.0ms (0%)

preprocess28.0ms (0.3%)

Profiling