Metrics for Beckmann Sample, near normal, slope

analyze63.0ms (1.9%)

Memory

6.5MiB live, 22.1MiB allocated

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
50%	0%	0%	100%	0%	0%	0%	3
50%	0%	0%	100%	0%	0%	0%	4
50%	0%	0%	100%	0%	0%	0%	5
75%	0%	0%	100%	0%	0%	0%	6
75%	0%	0%	100%	0%	0%	0%	7
75%	0%	0%	100%	0%	0%	0%	8
87.5%	0%	0%	100%	0%	0%	0%	9
87.5%	0%	0%	100%	0%	0%	0%	10
87.5%	0%	0%	100%	0%	0%	0%	11
93.8%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 32 to 31 computations (3.1% saved)

sample3.2s (93.7%)

Memory

39.9MiB live, 887.4MiB allocated

Samples

1.1s	8 256×	valid-baseline
762.0ms	8 256×	valid-rival
504.0ms	8 256×	valid-sollya

Precisions

Click to see Rival histograms. Total time spent on operations: 553.0ms

ival-log: 144.0ms (26% of total)

ival-mult: 136.0ms (24.6% of total)

ival-cos: 86.0ms (15.5% of total)

ival-sqrt: 50.0ms (9% of total)

ival-neg: 48.0ms (8.7% of total)

ival-sub: 44.0ms (7.9% of total)

ival-pi: 29.0ms (5.2% of total)

ival-true: 8.0ms (1.4% of total)

...in/eval/compile.rkt:76:19: 6.0ms (1.1% of total)

ival-assert: 3.0ms (0.5% of total)

Precisions

Click to see Base histograms. Total time spent on operations: 708.0ms

ival-mult: 190.0ms (26.8% of total)

ival-log: 171.0ms (24.1% of total)

ival-cos: 106.0ms (15% of total)

ival-sqrt: 71.0ms (10% of total)

ival-sub: 57.0ms (8% of total)

ival-neg: 55.0ms (7.8% of total)

ival-pi: 39.0ms (5.5% of total)

const: 19.0ms (2.7% of total)

Bogosity

preprocess128.0ms (3.8%)

Memory

-6.2MiB live, 26.2MiB allocated

Algorithm

1×	egg-herbie

Rules

1 672×	`fma-define`
322×	`associate-r`
286×	`fmm-def`
254×	`distribute-lft-in`
238×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	559
1	109	521
2	201	521
3	348	521
4	583	521
5	992	521
6	1214	521
7	1598	521
8	2234	521
9	2548	521
10	2561	521
11	2568	521
12	2569	521

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 u2))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 u2)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) cosTheta_i)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) cosTheta_i)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u2)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1)))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log1p.f32 u1))))
(.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))) (sqrt.f32 (neg.f32 (log1p.f32 u1))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2))))
(.f32 (neg.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (neg.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (neg.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32))))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) (neg.f32 u1))))) (neg.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2))))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (neg.f32 (sqrt.f32 (neg.f32 (log1p.f32 u1)))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 u1))) (neg.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32))))))
(neg.f32 (.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) (neg.f32 u2)))))
(.f32 (neg.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1))))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (neg.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1))))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (neg.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32))))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) cosTheta_i)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) cosTheta_i)))))
(.f32 (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 cosTheta_i)))))
(.f32 (cos.f32 (.f32 (PI.f32) (*.f32 u2 #s(literal -2 binary32)))) (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 cosTheta_i)))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) cosTheta_i)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 #s(literal 2 binary32) (*.f32 (PI.f32) cosTheta_i))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 #s(literal 2 binary32) (*.f32 (PI.f32) cosTheta_i))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) cosTheta_i)))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u1)))) (cos.f32 (.f32 (PI.f32) (*.f32 #s(literal 2 binary32) cosTheta_i))))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u2)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u1)))
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u2)))) (cos.f32 (.f32 u1 (*.f32 #s(literal 2 binary32) (PI.f32)))))
(.f32 (sqrt.f32 (neg.f32 (log1p.f32 (neg.f32 u2)))) (cos.f32 (.f32 u1 (*.f32 #s(literal 2 binary32) (PI.f32)))))

Symmetry

(abs cosTheta_i)

(abs u2)

Compiler

Compiled 16 to 14 computations (12.5% saved)

eval0.0ms (0%)

Memory: 0.2MiB live, 0.2MiB allocated
Compiler: Compiled 3 to 3 computations (0% saved)

prune1.0ms (0%)

Memory

0.9MiB live, 0.9MiB allocated

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.6%	(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))

Compiler

Compiled 32 to 28 computations (12.5% saved)

simplify2.0ms (0.1%)

Memory

0.6MiB live, 0.6MiB allocated

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	49
1	32	49
2	37	49
3	40	49
4	41	49

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))

Outputs
(.f32 (sqrt.f32 (neg.f32 (log.f32 (-.f32 #s(literal 1 binary32) u1)))) (cos.f32 (.f32 (*.f32 #s(literal 2 binary32) (PI.f32)) u2)))

soundness0.0ms (0%)

Memory

0.4MiB live, 0.4MiB allocated

Stop Event

1×

fuel

Compiler

Compiled 16 to 14 computations (12.5% saved)

preprocess21.0ms (0.6%)

Memory

-3.6MiB live, 27.8MiB allocated

Remove

(abs u2)

(abs cosTheta_i)

Compiler

Compiled 192 to 168 computations (12.5% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated

Beckmann Sample, near normal, slope_x

analyze63.0ms (1.9%)

sample3.2s (93.7%)

preprocess128.0ms (3.8%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify2.0ms (0.1%)

soundness0.0ms (0%)

preprocess21.0ms (0.6%)

end0.0ms (0%)

Profiling