Metrics for Disney BSSRDF, sample scattering profile, upper

analyze67.0ms (0.5%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.1%	99.9%	0%	0%	0%	0
0%	0%	0.1%	99.9%	0%	0%	0%	1
0%	0%	0.1%	99.9%	0%	0%	0%	2
50%	0.1%	0.1%	99.9%	0%	0%	0%	3
50%	0.1%	0.1%	99.9%	0%	0%	0%	4
75%	0.1%	0%	99.9%	0%	0%	0%	5
75%	0.1%	0%	99.9%	0%	0%	0%	6
87.5%	0.1%	0%	99.9%	0%	0%	0%	7
87.5%	0.1%	0%	99.9%	0%	0%	0%	8
93.8%	0.1%	0%	99.9%	0%	0%	0%	9
93.8%	0.1%	0%	99.9%	0%	0%	0%	10
96.9%	0.1%	0%	99.9%	0%	0%	0%	11
96.9%	0.1%	0%	99.9%	0%	0%	0%	12

Compiler

Compiled 31 to 25 computations (19.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 27.0ms

Operation ival-sub, time spent: 9.0ms, 34.0% of total-time

Operation ival-<=, time spent: 6.0ms, 22.0% of total-time

Operation ival-mult, time spent: 4.0ms, 15.0% of total-time

Operation ival-log, time spent: 3.0ms, 11.0% of total-time

Operation ival-div, time spent: 3.0ms, 11.0% of total-time

Operation const, time spent: 1.0ms, 4.0% of total-time

Operation ival-and, time spent: 1.0ms, 4.0% of total-time

sample2.7s (19.1%)

Results

2.4s	8255×	0	valid
0.0ms	1×	0	valid

Precisions

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

Operation ival-sub, time spent: 306.0ms, 26.0% of total-time

Operation ival-div, time spent: 234.0ms, 20.0% of total-time

Operation ival-log, time spent: 189.0ms, 16.0% of total-time

Operation ival-<=, time spent: 159.0ms, 14.0% of total-time

Operation ival-mult, time spent: 150.0ms, 13.0% of total-time

Operation const, time spent: 75.0ms, 6.0% of total-time

Operation ival-and, time spent: 44.0ms, 4.0% of total-time

Bogosity

preprocess3.3s (23.5%)

Algorithm

1×	egg-herbie

Rules

3500×	`fma-neg`
903×	`fma-define`
480×	`unsub-neg`
455×	`sub-neg`
351×	`distribute-neg-in`

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`(-.f32 u 1/4)`
-	-	`1/4`
-	-	`s`
-	-	`u`
-	-	`(/.f32 (-.f32 u 1/4) 3/4)`
-	-	`(-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))`
-	-	`3`
-	-	`(*.f32 3 s)`
-	-	`3/4`
-	-	`1`
-	-	`(/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))`
-	-	`(log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))))`
-	-	`(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	331
1	105	261
2	258	245
3	633	229
4	1162	217
5	1955	217
6	2676	217
7	3662	217
8	5168	217
9	6476	217
10	7069	217
11	7480	217
12	7644	217
13	7747	217
14	7762	217
15	7763	217
16	7763	217
17	7813	217
18	7825	217
19	7825	217
20	7977	217
21	7977	217

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 (.f32 3 (neg.f32 s)) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 (neg.f32 u) 1/4) 3/4)))))
(neg.f32 (.f32 (.f32 3 (neg.f32 s)) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))))))
(neg.f32 (.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 (neg.f32 u) 1/4) 3/4))))))
(.f32 (.f32 3 u) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 s 1/4) 3/4)))))

Outputs
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))
(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))
(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
(.f32 (.f32 3 (neg.f32 s)) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 3 (.f32 (neg.f32 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3))))))
(.f32 (neg.f32 (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4))) (.f32 s -3))
(.f32 3 (.f32 s (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))
(.f32 3 (.f32 s (log1p.f32 (fma.f32 u -4/3 1/3))))
(.f32 3 (.f32 s (log.f32 (fma.f32 u -4/3 4/3))))
(.f32 (.f32 3 s) (log.f32 (fma.f32 u -4/3 4/3)))
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 (neg.f32 u) 1/4) 3/4)))))
(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 (neg.f32 u) 3/4) 1/3)))))
(.f32 (.f32 3 s) (neg.f32 (log1p.f32 (/.f32 (fma.f32 -1 u -1/4) -3/4))))
(.f32 s (.f32 -3 (log1p.f32 (/.f32 (-.f32 -1/4 u) -3/4))))
(.f32 s (.f32 (log.f32 (+.f32 (*.f32 u 4/3) 4/3)) -3))
(.f32 s (.f32 (log.f32 (fma.f32 u 4/3 4/3)) -3))
(neg.f32 (.f32 (.f32 3 (neg.f32 s)) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))))))
(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))
(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
(neg.f32 (.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 (neg.f32 u) 1/4) 3/4))))))
(.f32 (.f32 3 (neg.f32 s)) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 (neg.f32 u) 3/4) 1/3)))))
(.f32 s (.f32 3 (log1p.f32 (/.f32 (fma.f32 -1 u -1/4) -3/4))))
(.f32 3 (.f32 s (log1p.f32 (/.f32 (-.f32 -1/4 u) -3/4))))
(.f32 3 (.f32 s (log.f32 (+.f32 (*.f32 u 4/3) 4/3))))
(.f32 3 (.f32 s (log.f32 (fma.f32 u 4/3 4/3))))
(.f32 (.f32 3 u) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 s 1/4) 3/4)))))
(.f32 (.f32 3 u) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 s 3/4) 1/3)))))
(.f32 (.f32 3 u) (neg.f32 (log1p.f32 (/.f32 (+.f32 s -1/4) -3/4))))
(.f32 u (.f32 -3 (log1p.f32 (-.f32 (/.f32 s -3/4) -1/3))))
(.f32 u (.f32 (log1p.f32 (-.f32 1/3 (*.f32 s 4/3))) -3))
(.f32 u (.f32 (log1p.f32 (fma.f32 s -4/3 1/3)) -3))
(.f32 (log1p.f32 (fma.f32 s -4/3 1/3)) (.f32 u -3))

Symmetry

(negabs s)

Compiler

Compiled 136 to 114 computations (16.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.5s

Operation ival-sub, time spent: 917.0ms, 60.0% of total-time

Operation ival-div, time spent: 281.0ms, 18.0% of total-time

Operation ival-log, time spent: 140.0ms, 9.0% of total-time

Operation ival-mult, time spent: 97.0ms, 6.0% of total-time

Operation const, time spent: 84.0ms, 6.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 53 to 43 computations (18.9% saved)

prune13.0ms (0.1%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	98.4%	(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
▶	95.8%	(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
▶	96.3%	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
	98.0%	(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
▶	97.3%	(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
▶	97.0%	(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Compiler

Compiled 154 to 130 computations (15.6% saved)

localize4.7s (33.9%)

Compiler: Compiled 213 to 170 computations (20.2% saved)
Precisions: Click to see histograms. Total time spent on operations: 3.4s
Operation composed, time spent: 718.0ms, 21.0% of total-time
Operation ival-add, time spent: 657.0ms, 19.0% of total-time
Operation ival-sub, time spent: 656.0ms, 19.0% of total-time
Operation ival-log, time spent: 485.0ms, 14.0% of total-time
Operation ival-mult, time spent: 388.0ms, 11.0% of total-time
Operation ival-div, time spent: 307.0ms, 9.0% of total-time
Operation const, time spent: 152.0ms, 4.0% of total-time
Operation ival-neg, time spent: 20.0ms, 1.0% of total-time

eval0.0ms (0%)

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

prune7.0ms (0%)

Pruning

6 alts after pruning (1 fresh and 5 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	5	5
Done	0	0
Total	6	6

Accuracy

99.5%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
✓	95.8%	(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
✓	96.3%	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
▶	98.0%	(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
✓	97.3%	(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
✓	97.0%	(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Compiler

Compiled 77 to 65 computations (15.6% saved)

localize1.4s (10%)

Compiler: Compiled 33 to 26 computations (21.2% saved)
Precisions: Click to see histograms. Total time spent on operations: 1.2s
Operation composed, time spent: 595.0ms, 48.0% of total-time
Operation ival-add, time spent: 315.0ms, 25.0% of total-time
Operation ival-mult, time spent: 190.0ms, 15.0% of total-time
Operation ival-log, time spent: 115.0ms, 9.0% of total-time
Operation const, time spent: 35.0ms, 3.0% of total-time

eval0.0ms (0%)

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

prune5.0ms (0%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	1	1
Done	5	5
Total	6	6

Accuracy

99.5%

Counts

6 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	98.4%	(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
✓	95.8%	(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
✓	96.3%	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
✓	98.0%	(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))
✓	97.3%	(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
✓	97.0%	(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Compiler

Compiled 144 to 120 computations (16.7% saved)

regimes54.0ms (0.4%)

Counts

6 → 1

Calls

Call 1

Inputs
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 (.f32 3 s) (neg.f32 (log.f32 (-.f32 1 (-.f32 (/.f32 u 3/4) 1/3)))))
(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
(.f32 s (.f32 (log.f32 (fma.f32 u -4/3 4/3)) -3))
(.f32 s (.f32 (log1p.f32 (fma.f32 u -4/3 1/3)) -3))

Outputs
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))

Calls

9 calls:

10.0ms	(/.f32 (-.f32 u 1/4) 3/4)
7.0ms	(log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))))
6.0ms	u
5.0ms	(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))
5.0ms	(/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))

Results

Accuracy	Segments	Branch
98.4%	1	`s`
98.4%	1	`u`
98.4%	1	`(.f32 (.f32 3 s) (log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))))`
98.4%	1	`(*.f32 3 s)`
98.4%	1	`(log.f32 (/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))))`
98.4%	1	`(/.f32 1 (-.f32 1 (/.f32 (-.f32 u 1/4) 3/4)))`
98.4%	1	`(-.f32 1 (/.f32 (-.f32 u 1/4) 3/4))`
98.4%	1	`(/.f32 (-.f32 u 1/4) 3/4)`
98.4%	1	`(-.f32 u 1/4)`

Compiler

Compiled 71 to 61 computations (14.1% saved)

regimes5.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Outputs
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Calls

2 calls:

3.0ms	s
3.0ms	u

Results

Accuracy	Segments	Branch
97.0%	1	`u`
97.0%	1	`s`

Compiler

Compiled 6 to 4 computations (33.3% saved)

simplify326.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	70
1	30	70

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Outputs
(.f32 (.f32 s -3) (log1p.f32 (/.f32 (+.f32 u -1/4) -3/4)))
(.f32 s (.f32 -3 (log1p.f32 (+.f32 (*.f32 u -4/3) 1/3))))

Compiler

Compiled 24 to 20 computations (16.7% saved)

soundness1.4s (9.8%)

Rules

3500×	`fma-neg`
3500×	`fma-neg`
903×	`fma-define`
903×	`fma-define`
480×	`unsub-neg`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	38	331
1	105	261
2	258	245
3	633	229
4	1162	217
5	1955	217
6	2676	217
7	3662	217
8	5168	217
9	6476	217
10	7069	217
11	7480	217
12	7644	217
13	7747	217
14	7762	217
15	7763	217
16	7763	217
17	7813	217
18	7825	217
19	7825	217
20	7977	217
21	7977	217
0	38	331
1	105	261
2	258	245
3	633	229
4	1162	217
5	1955	217
6	2676	217
7	3662	217
8	5168	217
9	6476	217
10	7069	217
11	7480	217
12	7644	217
13	7747	217
14	7762	217
15	7763	217
16	7763	217
17	7813	217
18	7825	217
19	7825	217
20	7977	217
21	7977	217

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 434 to 368 computations (15.2% saved)

end0.0ms (0%)

preprocess33.0ms (0.2%)

Remove: (negabs s)
Compiler: Compiled 148 to 124 computations (16.2% saved)

analyze67.0ms (0.5%)

sample2.7s (19.1%)

preprocess3.3s (23.5%)

eval1.0ms (0%)

prune13.0ms (0.1%)

localize4.7s (33.9%)

eval0.0ms (0%)

prune7.0ms (0%)

localize1.4s (10%)

eval0.0ms (0%)

prune5.0ms (0%)

regimes54.0ms (0.4%)

regimes5.0ms (0%)

simplify326.0ms (2.3%)

soundness1.4s (9.8%)

end0.0ms (0%)

preprocess33.0ms (0.2%)

Profiling