Metrics for HairBSDF, Mp, lower

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated

analyze328.0ms (14.3%)

Memory

4.5MiB live, 123.7MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	3%	97%	0%	0%	0%	0
0%	0%	3%	97%	0%	0%	0%	1
0%	0%	3%	97%	0%	0%	0%	2
0%	0%	3%	97%	0%	0%	0%	3
0%	0%	3%	97%	0%	0%	0%	4
0%	0%	3%	97%	0%	0%	0%	5
0%	0%	1.5%	97%	0%	1.5%	0%	6
0%	0%	1.5%	97%	0%	1.5%	0%	7
0%	0%	1.5%	97%	0%	1.5%	0%	8
0%	0%	1.5%	97%	0%	1.5%	0%	9
0%	0%	1.5%	97%	0%	1.5%	0%	10
0%	0%	1.5%	97%	0%	1.5%	0%	11
0%	0%	1.5%	97%	0%	1.5%	0%	12

Compiler

Compiled 65 to 44 computations (32.3% saved)

sample59.0ms (2.6%)

Memory

0.3MiB live, 24.0MiB allocated

Samples

44.0ms	260×	0	valid
1.0ms	5×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 36.0ms

const: 10.0ms (27.4% of total)

ival-div: 6.0ms (16.4% of total)

ival-<=: 5.0ms (13.7% of total)

ival-mult: 4.0ms (11% of total)

ival-log: 3.0ms (8.2% of total)

ival-exp: 2.0ms (5.5% of total)

ival-add: 2.0ms (5.5% of total)

ival-sub: 2.0ms (5.5% of total)

ival-and: 2.0ms (5.5% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

Bogosity

explain1.7s (75.5%)

Memory

8.2MiB live, 1 377.0MiB allocated

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
98	14	(2.164914851938718e-32 -7.226218549759047e-29 0.0012382048880681396 1.0635658041401585e-37 6.640054454761303e-38)	17	(-1.487494988294813e-10 2.838171653252175e-8 -5.262123604001002e-33 4.316611821444389e-27 1.1439316437470397e-18)	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
92	17	(-5.863633148331052e-22 6.127387950371774e-19 -7.732310791652708e-9 -9.20257569716379e-31 7.73577757895943e-20)	18	(-1.0035430316295058e-20 -8.481488435304059e-38 -1.0955745999738974e-36 -1.0835636884112222e-21 9.999607418099116e-20)	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
0	0	-	0	-	`(/.f32 #s(literal 1 binary32) v)`
0	0	-	0	-	`(/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))`
0	0	-	0	-	`#s(literal 2 binary32)`
0	230	(-2.722882282687799e-21 -9.93129368465097e-28 -9.184807982501676e-32 -1.2406339289228185e-9 7.450516997388376e-26)	0	-	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`
0	0	-	0	-	`sinTheta_i`
0	0	-	0	-	`v`
0	0	-	0	-	`cosTheta_i`
0	220	(-2.722882282687799e-21 -9.93129368465097e-28 -9.184807982501676e-32 -1.2406339289228185e-9 7.450516997388376e-26)	0	-	`(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))`
0	0	-	0	-	`sinTheta_O`
0	0	-	0	-	`(*.f32 #s(literal 2 binary32) v)`
0	0	-	0	-	`(*.f32 sinTheta_i sinTheta_O)`
0	0	-	0	-	`(log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))`
0	0	-	0	-	`#s(literal 1 binary32)`
0	0	-	0	-	`(*.f32 cosTheta_i cosTheta_O)`
0	0	-	0	-	`#s(literal 6931/10000 binary32)`
0	41	(1.2849414781837902e-37 1.4674641057865756e-8 2.503614094639257e-36 1.466102239611189e-11 3.3108813000254367e-13)	0	-	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`
0	0	-	0	-	`(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v))`
0	4	(7.515275501646101e-5 -6.2148623920788015e-12 -1.0036289905585517e-17 4.0257309431038796e-38 0.02156539261341095)	0	-	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`
0	0	-	0	-	`cosTheta_O`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`+.f32`	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))))`	cancellation	230	0
`+.f32`	`(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32))`	cancellation	220	0
`-.f32`	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`	cancellation	20	0
`/.f32`	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`	u/n	17	0
↳	`(*.f32 sinTheta_i sinTheta_O)`	underflow	143
`/.f32`	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`	u/n	16	0
↳	`(*.f32 cosTheta_i cosTheta_O)`	underflow	138
`exp.f32`	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))`	sensitivity	4	0

Confusion

	Predicted +	Predicted -
+	2	0
-	233	21

Precision

0.00851063829787234

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	2	0	0
-	233	0	21

Precision?

0.00851063829787234

Recall?

1.0

Freqs

test

number	freq
0	21
1	12
2	180
3	37
4	6

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	1	0	0
-	0	0	0

Precision?

1.0

Recall?

1.0

Total Time

12.79443359375

Average Time

0.04997825622558594

Samples

395.0ms

3 072×

valid

Compiler

Compiled 5 112 to 1 032 computations (79.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 271.0ms

ival-div: 75.0ms (27.7% of total)

ival-mult: 52.0ms (19.2% of total)

const: 38.0ms (14% of total)

ival-log: 30.0ms (11.1% of total)

ival-add: 25.0ms (9.2% of total)

ival-sub: 23.0ms (8.5% of total)

ival-exp: 20.0ms (7.4% of total)

exact: 3.0ms (1.1% of total)

ival-true: 2.0ms (0.7% of total)

adjust: 1.0ms (0.4% of total)

ival-assert: 1.0ms (0.4% of total)

preprocess138.0ms (6%)

Memory

-0.9MiB live, 34.0MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	159	481
1	462	447
2	1368	440
3	4990	440
0	21	25
0	34	23
1	63	22
2	151	22
3	471	22
4	1717	22
5	5047	22
0	8134	19

Stop Event

1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Inputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Outputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i #s(literal 6931/10000 binary32)))))

Outputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

(*.f32 (/.f32 #s(literal 1/2 binary32) v) (exp.f32 (fma.f32 (fma.f32 sinTheta_O sinTheta_i #s(literal 1 binary32)) (/.f32 #s(literal -1 binary32) v) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i #s(literal 6931/10000 binary32)))))

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 25 to 21 computations (16% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated
Compiler: Compiled 0 to 5 computations (-∞% saved)

prune1.0ms (0%)

Memory

0.6MiB live, 0.6MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Status

Accuracy

Program

99.8%

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Compiler

Compiled 50 to 42 computations (16% saved)

simplify30.0ms (1.3%)

Memory

-9.3MiB live, 18.2MiB allocated

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	25
1	33	25
2	47	25
3	63	25
4	77	25
5	106	25
6	148	25
7	152	25

Stop Event

1×

saturated

Calls

Call 1

Inputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Inputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

Outputs
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))
(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1 binary32) (.f32 #s(literal 2 binary32) v))) (+.f32 #s(literal 6931/10000 binary32) (-.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 #s(literal 1 binary32) v)))))

Outputs

(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 #s(literal 1 binary32) v)) #s(literal 6931/10000 binary32)) (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v)))))

(exp.f32 (+.f32 (log.f32 (/.f32 #s(literal 1 binary32) (*.f32 #s(literal 2 binary32) v))) (+.f32 #s(literal 6931/10000 binary32) (-.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (/.f32 #s(literal 1 binary32) v)))))

soundness0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 25 to 21 computations (16% saved)

preprocess6.0ms (0.2%)

Memory

4.2MiB live, 4.2MiB allocated

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 300 to 252 computations (16% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

start0.0ms (0%)

analyze328.0ms (14.3%)

sample59.0ms (2.6%)

explain1.7s (75.5%)

preprocess138.0ms (6%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify30.0ms (1.3%)

soundness0.0ms (0%)

preprocess6.0ms (0.2%)

end0.0ms (0%)

Profiling