Metrics for Disney BSSRDF, PDF of scattering profile

analyze34.0ms (0.1%)

Memory

-3.5MiB live, 12.3MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	2.1%	97.9%	0%	0%	0%	0
0%	0%	2.1%	97.9%	0%	0%	0%	1
50%	1%	1%	97.9%	0%	0%	0%	2
50%	1%	1%	97.9%	0%	0%	0%	3
75%	1.5%	0.5%	97.9%	0%	0%	0%	4
75%	1.5%	0.5%	97.9%	0%	0%	0%	5
87.5%	1.8%	0.3%	97.9%	0%	0%	0%	6
87.5%	1.8%	0.3%	97.9%	0%	0%	0%	7
93.7%	1.9%	0.1%	97.9%	0%	0%	0%	8
93.7%	1.9%	0.1%	97.9%	0%	0%	0%	9
96.9%	2%	0.1%	97.9%	0%	0%	0%	10
96.9%	2%	0.1%	97.9%	0%	0%	0%	11
98.4%	2%	0%	97.9%	0%	0%	0%	12

Compiler

Compiled 71 to 53 computations (25.4% saved)

sample25.7s (99.3%)

Memory

55.7MiB live, 5 331.8MiB allocated

Samples

5.6s	7 765×	valid-sollya
1.2s	7 765×	valid-baseline
1.1s	7 765×	valid-rival
78.0ms	491×	valid-rival+baseline-zero

Precisions

Click to see Rival histograms. Total time spent on operations: 918.0ms

ival-mult: 413.0ms (45% of total)

ival-div: 226.0ms (24.6% of total)

ival-exp: 134.0ms (14.6% of total)

ival-neg: 46.0ms (5% of total)

ival-add: 37.0ms (4% of total)

ival-pi: 31.0ms (3.4% of total)

...in/eval/compile.rkt:110:19: 16.0ms (1.7% of total)

ival-true: 10.0ms (1.1% of total)

ival-assert: 5.0ms (0.5% of total)

Precisions

Click to see Base histograms. Total time spent on operations: 949.0ms

ival-mult: 431.0ms (45.4% of total)

ival-div: 231.0ms (24.3% of total)

ival-exp: 129.0ms (13.6% of total)

ival-neg: 44.0ms (4.6% of total)

ival-add: 41.0ms (4.3% of total)

ival-pi: 39.0ms (4.1% of total)

const: 33.0ms (3.5% of total)

Bogosity

preprocess93.0ms (0.4%)

Memory

-8.4MiB live, 22.1MiB allocated

Algorithm

1×	egg-herbie

Rules

1 764×	`times-frac`
1 088×	`fmm-def`
976×	`distribute-frac-neg2`
820×	`distribute-lft-neg-out`
646×	`distribute-rgt-neg-out`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	74	943
1	230	771
2	1095	606
3	5165	606

Stop Event

1×	node limit

Calls

Call 1

Inputs
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (neg.f32 s)))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 s)) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s))))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) (neg.f32 s)) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) (neg.f32 r))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) (neg.f32 r))))
(neg.f32 (+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (neg.f32 s)))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 s)) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s))))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) (neg.f32 s)) r))))
(neg.f32 (+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) (neg.f32 r))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) (neg.f32 r)))))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 s) r))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) r) s)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 s) (.f32 #s(literal 3 binary32) r)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) r) s)))

Outputs
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))
(+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 s (.f32 #s(literal 2 binary32) (PI.f32)))) (/.f32 (exp.f32 (neg.f32 (/.f32 r s))) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 s #s(literal 3 binary32)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) s))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (.f32 #s(literal -1/3 binary32) (/.f32 r s))) r) (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (neg.f32 s))) r)))
(.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (exp.f32 (/.f32 r (neg.f32 s))) r) (/.f32 (pow.f32 (exp.f32 #s(literal -1/3 binary32)) (/.f32 r s)) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))
(+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 s (.f32 #s(literal 2 binary32) (PI.f32)))) (/.f32 (exp.f32 (neg.f32 (/.f32 r s))) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 s #s(literal 3 binary32)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) s))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (.f32 #s(literal -1/3 binary32) (/.f32 r s))) r) (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (neg.f32 s))) r)))
(.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (exp.f32 (/.f32 r (neg.f32 s))) r) (/.f32 (pow.f32 (exp.f32 #s(literal -1/3 binary32)) (/.f32 r s)) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (neg.f32 s)))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 s)) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s))))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) (neg.f32 s)) r)))
(+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (neg.f32 s)))) (/.f32 (exp.f32 (/.f32 r s)) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) (neg.f32 s)))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r s)) (neg.f32 r)) (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (.f32 s #s(literal 3 binary32)))) (neg.f32 r))))
(.f32 (/.f32 #s(literal -1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (exp.f32 (/.f32 r s)) r) (/.f32 (cbrt.f32 (exp.f32 (/.f32 r s))) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) (neg.f32 r))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) (neg.f32 r))))
(+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (neg.f32 s)))) (/.f32 (exp.f32 (/.f32 r s)) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) (neg.f32 s)))))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r s)) (neg.f32 r)) (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (.f32 s #s(literal 3 binary32)))) (neg.f32 r))))
(.f32 (/.f32 #s(literal -1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (exp.f32 (/.f32 r s)) r) (/.f32 (cbrt.f32 (exp.f32 (/.f32 r s))) r)))
(neg.f32 (+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (neg.f32 s)))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 s)) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s))))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) (neg.f32 s)) r))))
(neg.f32 (+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (neg.f32 s)))) (/.f32 (exp.f32 (/.f32 r s)) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) (neg.f32 s))))))))
(+.f32 (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (.f32 s #s(literal 3 binary32)))) r)) (.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r s)) r)))
(.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (cbrt.f32 (exp.f32 (/.f32 r s))) r) (/.f32 (exp.f32 (/.f32 r s)) r)))
(neg.f32 (+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) (neg.f32 r))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 (neg.f32 r)) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) (neg.f32 r)))))
(neg.f32 (+.f32 (.f32 (/.f32 #s(literal 1/4 binary32) (.f32 #s(literal 2 binary32) (.f32 (PI.f32) (neg.f32 s)))) (/.f32 (exp.f32 (/.f32 r s)) r)) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) (neg.f32 s)))) (.f32 r (.f32 #s(literal 6 binary32) (.f32 (PI.f32) (neg.f32 s))))))))
(+.f32 (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r (.f32 s #s(literal 3 binary32)))) r)) (.f32 (/.f32 #s(literal 1/8 binary32) (*.f32 s (PI.f32))) (/.f32 (exp.f32 (/.f32 r s)) r)))
(.f32 (/.f32 #s(literal 1/8 binary32) (.f32 s (PI.f32))) (+.f32 (/.f32 (cbrt.f32 (exp.f32 (/.f32 r s))) r) (/.f32 (exp.f32 (/.f32 r s)) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 s) r))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) r) s)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 s) (.f32 #s(literal 3 binary32) r)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) r) s)))
(+.f32 (.f32 #s(literal 1/4 binary32) (/.f32 (exp.f32 (neg.f32 (/.f32 s r))) (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) (.f32 r s)))) (.f32 #s(literal 3/4 binary32) (/.f32 (exp.f32 (/.f32 (neg.f32 s) (.f32 r #s(literal 3 binary32)))) (.f32 (.f32 (PI.f32) #s(literal 6 binary32)) (*.f32 r s)))))
(fma.f32 (/.f32 #s(literal 1/8 binary32) (.f32 r (PI.f32))) (/.f32 (exp.f32 (.f32 #s(literal -1/3 binary32) (/.f32 s r))) s) (.f32 (/.f32 #s(literal 1/8 binary32) (.f32 r (PI.f32))) (/.f32 (exp.f32 (/.f32 s (neg.f32 r))) s)))
(.f32 (/.f32 #s(literal 1/8 binary32) (.f32 r (PI.f32))) (+.f32 (/.f32 (exp.f32 (/.f32 s (neg.f32 r))) s) (/.f32 (pow.f32 (exp.f32 #s(literal -1/3 binary32)) (/.f32 s r)) s)))

Compiler

Compiled 35 to 25 computations (28.6% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 2 to 2 computations (0% saved)

prune1.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))

Status

Accuracy

Program

99.5%

(+.f32 (/.f32 (*.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (*.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (*.f32 #s(literal 3 binary32) s)))) (*.f32 (*.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))

Compiler

Compiled 70 to 50 computations (28.6% saved)

simplify4.0ms (0%)

Memory

1.2MiB live, 1.2MiB allocated

Algorithm

1×	egg-herbie

Rules

30×	`*-commutative`
14×	`+-commutative`
12×	`sub-neg`
12×	`neg-sub0`
12×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	129
1	49	129
2	59	129
3	73	129
4	81	129
5	85	129
6	86	129

Stop Event

1×

saturated

Calls

Call 1

Inputs

(+.f32 (/.f32 (*.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (*.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (*.f32 #s(literal 3 binary32) s)))) (*.f32 (*.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))

Outputs
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 (.f32 (.f32 #s(literal 2 binary32) (PI.f32)) s) r)) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 #s(literal 3 binary32) s)))) (.f32 (.f32 (*.f32 #s(literal 6 binary32) (PI.f32)) s) r)))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 (neg.f32 r) s))) (.f32 r (.f32 s (.f32 #s(literal 2 binary32) (PI.f32))))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 s #s(literal 3 binary32))))) (.f32 r (.f32 s (*.f32 (PI.f32) #s(literal 6 binary32))))))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 r (neg.f32 s)))) (.f32 r (.f32 s (.f32 #s(literal 2 binary32) (PI.f32))))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 (neg.f32 r) (.f32 s #s(literal 3 binary32))))) (.f32 r (.f32 s (*.f32 (PI.f32) #s(literal 6 binary32))))))
(+.f32 (/.f32 (.f32 #s(literal 1/4 binary32) (exp.f32 (/.f32 r (neg.f32 s)))) (.f32 r (.f32 s (.f32 #s(literal 2 binary32) (PI.f32))))) (/.f32 (.f32 #s(literal 3/4 binary32) (exp.f32 (/.f32 r (.f32 s (neg.f32 #s(literal 3 binary32)))))) (.f32 r (.f32 s (*.f32 (PI.f32) #s(literal 6 binary32))))))

soundness0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 35 to 26 computations (25.7% saved)

preprocess36.0ms (0.1%)

Memory: -6.0MiB live, 28.2MiB allocated
Compiler: Compiled 140 to 102 computations (27.1% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

analyze34.0ms (0.1%)

sample25.7s (99.3%)

preprocess93.0ms (0.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify4.0ms (0%)

soundness0.0ms (0%)

preprocess36.0ms (0.1%)

end0.0ms (0%)

Profiling