Metrics for Disney BSSRDF, sample scattering profile, lower

analyze53.0ms (0.7%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	1.5%	98.5%	0%	0%	0%	0
0%	0%	1.5%	98.5%	0%	0%	0%	1
0%	0%	1.5%	98.5%	0%	0%	0%	2
50%	0.8%	0.8%	98.5%	0%	0%	0%	3
50%	0.8%	0.8%	98.5%	0%	0%	0%	4
75%	1.2%	0.4%	98.5%	0%	0%	0%	5
75%	1.2%	0.4%	98.5%	0%	0%	0%	6
87.5%	1.4%	0.2%	98.5%	0%	0%	0%	7
87.5%	1.4%	0.2%	98.5%	0%	0%	0%	8
93.8%	1.4%	0.1%	98.5%	0%	0%	0%	9
93.8%	1.4%	0.1%	98.5%	0%	0%	0%	10
96.9%	1.5%	0%	98.5%	0%	0%	0%	11
96.9%	1.5%	0%	98.5%	0%	0%	0%	12

Compiler

Compiled 27 to 21 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

Operation ival-mult, time spent: 5.0ms, 31.0% of total-time

Operation ival-log, time spent: 3.0ms, 19.0% of total-time

Operation ival-<=, time spent: 3.0ms, 19.0% of total-time

Operation ival-div, time spent: 1.0ms, 6.0% of total-time

Operation ival-sub, time spent: 1.0ms, 6.0% of total-time

Operation const, time spent: 1.0ms, 6.0% of total-time

Operation ival-and, time spent: 1.0ms, 6.0% of total-time

sample2.5s (33.7%)

Results

2.3s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

Operation ival-<=, time spent: 562.0ms, 46.0% of total-time

Operation ival-log, time spent: 202.0ms, 16.0% of total-time

Operation ival-mult, time spent: 157.0ms, 13.0% of total-time

Operation ival-sub, time spent: 149.0ms, 12.0% of total-time

Operation ival-div, time spent: 78.0ms, 6.0% of total-time

Operation const, time spent: 42.0ms, 3.0% of total-time

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

Bogosity

preprocess1.9s (26.8%)

Algorithm

1×	egg-herbie

Rules

2433×	`fma-def`
1451×	`fma-neg`
530×	`unsub-neg`
452×	`distribute-lft-in`
393×	`distribute-rgt-in`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(/.f32 1 (-.f32 1 (*.f32 4 u)))`
-	-	`(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))`
-	-	`s`
-	-	`u`
-	-	`4`
-	-	`(*.f32 4 u)`
-	-	`(log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u))))`
-	-	`1`
-	-	`(-.f32 1 (*.f32 4 u))`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	247
1	84	181
2	156	181
3	337	181
4	543	181
5	756	181
6	833	181
7	965	181
8	1749	181
9	3001	181
10	3811	181
11	4109	181
12	4197	181
13	4232	181
14	4244	181
15	4769	181
16	6275	181
17	6377	181
18	6443	181
19	6487	181
20	6487	181
21	6575	181
22	6728	181
23	6728	181

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 (neg.f32 s) (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 (neg.f32 u))))))
(neg.f32 (.f32 (neg.f32 s) (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u))))))
(neg.f32 (.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 (neg.f32 u)))))))
(.f32 u (log.f32 (/.f32 1 (-.f32 1 (.f32 4 s)))))

Outputs
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
(.f32 (neg.f32 s) (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))
(.f32 (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))) (neg.f32 s))
(.f32 s (log1p.f32 (.f32 u -4)))
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 (neg.f32 u))))))
(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 (neg.f32 u))))))
(.f32 s (neg.f32 (log1p.f32 (.f32 4 u))))
(neg.f32 (.f32 (neg.f32 s) (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u))))))
(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
(neg.f32 (.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 (neg.f32 u)))))))
(.f32 s (neg.f32 (neg.f32 (log.f32 (+.f32 1 (.f32 -4 (neg.f32 u)))))))
(.f32 s (log1p.f32 (.f32 4 u)))
(.f32 u (log.f32 (/.f32 1 (-.f32 1 (.f32 4 s)))))
(.f32 u (neg.f32 (log.f32 (+.f32 1 (.f32 -4 s)))))
(.f32 u (neg.f32 (log1p.f32 (.f32 s -4))))
(.f32 (neg.f32 u) (log1p.f32 (.f32 s -4)))

Symmetry

(negabs s)

Compiler

Compiled 92 to 74 computations (19.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 954.0ms

Operation ival-log, time spent: 355.0ms, 37.0% of total-time

Operation ival-sub, time spent: 279.0ms, 29.0% of total-time

Operation ival-mult, time spent: 166.0ms, 17.0% of total-time

Operation ival-div, time spent: 117.0ms, 12.0% of total-time

Operation const, time spent: 37.0ms, 4.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 25 to 19 computations (24% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
▶	62.0%	(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
▶	59.7%	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize2.3s (32%)

Compiler: Compiled 93 to 69 computations (25.8% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.6s
Operation ival-log, time spent: 542.0ms, 35.0% of total-time
Operation ival-mult, time spent: 516.0ms, 33.0% of total-time
Operation ival-log1p, time spent: 135.0ms, 9.0% of total-time
Operation ival-sub, time spent: 125.0ms, 8.0% of total-time
Operation ival-add, time spent: 121.0ms, 8.0% of total-time
Operation ival-div, time spent: 54.0ms, 3.0% of total-time
Operation const, time spent: 39.0ms, 2.0% of total-time
Operation ival-neg, time spent: 30.0ms, 2.0% of total-time

eval0.0ms (0%)

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

prune2.0ms (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

99.3%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
✓	62.0%	(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
✓	59.7%	(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Compiler

Compiled 60 to 48 computations (20% saved)

regimes25.0ms (0.3%)

Accuracy

Total -12.8b remaining (-5358.9%)

Threshold costs -12.8b (-5358.9%)

Counts

3 → 1

Calls

Call 1

Inputs
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
(.f32 s (neg.f32 (log.f32 (+.f32 1 (.f32 -4 u)))))
(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))

Outputs
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))

Calls

7 calls:

5.0ms	(/.f32 1 (-.f32 1 (*.f32 4 u)))
4.0ms	(*.f32 4 u)
3.0ms	s
3.0ms	u
3.0ms	(-.f32 1 (*.f32 4 u))

Results

Accuracy	Segments	Branch
99.3%	1	`s`
99.3%	1	`u`
99.3%	1	`(.f32 s (log.f32 (/.f32 1 (-.f32 1 (.f32 4 u)))))`
99.3%	1	`(log.f32 (/.f32 1 (-.f32 1 (*.f32 4 u))))`
99.3%	1	`(/.f32 1 (-.f32 1 (*.f32 4 u)))`
99.3%	1	`(-.f32 1 (*.f32 4 u))`
99.3%	1	`(*.f32 4 u)`

Compiler

Compiled 49 to 41 computations (16.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative`
3×	`sub-neg`
3×	`neg-mul-1`
3×	`+-commutative`
3×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	27
1	21	27
2	29	27
3	36	27
4	39	27
5	40	27

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))

Outputs
(.f32 (neg.f32 s) (log1p.f32 (.f32 u -4)))
(.f32 s (neg.f32 (log1p.f32 (.f32 u -4))))

Compiler

Compiled 9 to 7 computations (22.2% saved)

soundness437.0ms (6%)

Rules

2433×	`fma-def`
1451×	`fma-neg`
530×	`unsub-neg`
452×	`distribute-lft-in`
393×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	30	247
1	84	181
2	156	181
3	337	181
4	543	181
5	756	181
6	833	181
7	965	181
8	1749	181
9	3001	181
10	3811	181
11	4109	181
12	4197	181
13	4232	181
14	4244	181
15	4769	181
16	6275	181
17	6377	181
18	6443	181
19	6487	181
20	6487	181
21	6575	181
22	6728	181
23	6728	181

Stop Event

1×	node limit

Compiler

Compiled 72 to 52 computations (27.8% saved)

end0.0ms (0%)

preprocess21.0ms (0.3%)

Remove: (negabs s)
Compiler: Compiled 78 to 62 computations (20.5% saved)

analyze53.0ms (0.7%)

sample2.5s (33.7%)

preprocess1.9s (26.8%)

eval1.0ms (0%)

prune2.0ms (0%)

localize2.3s (32%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes25.0ms (0.3%)

simplify5.0ms (0.1%)

soundness437.0ms (6%)

end0.0ms (0%)

preprocess21.0ms (0.3%)

Profiling