Metrics for UniformSampleCone, x

analyze204.0ms (8.2%)

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
0%	0%	0.1%	99.9%	0%	0%	0%	3
50%	0%	0%	99.9%	0%	0%	0%	4
50%	0%	0%	99.9%	0%	0%	0%	5
50%	0%	0%	99.9%	0%	0%	0%	6
75%	0.1%	0%	99.9%	0%	0%	0%	7
75%	0.1%	0%	99.9%	0%	0%	0%	8
75%	0.1%	0%	99.9%	0%	0%	0%	9
87.5%	0.1%	0%	99.9%	0%	0%	0%	10
87.5%	0.1%	0%	99.9%	0%	0%	0%	11
87.5%	0.1%	0%	99.9%	0%	0%	0%	12

Compiler

Compiled 51 to 37 computations (27.5% saved)

sample2.0s (81.1%)

Results

2.0s

8256×

body

256

valid

Bogosity

preprocess266.0ms (10.7%)

Algorithm

1×	egg-herbie

Rules

1102×	`+-commutative`
882×	`distribute-neg-in`
776×	`distribute-rgt-in`
772×	`distribute-lft-in`
720×	`associate-+l-`

Problems

217×	`(-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (*.f32 ux maxCos))))`
37×	No Errors
2×	`(cos.f32 (.f32 (.f32 uy 2) (PI.f32)))`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	72	1142
1	224	1034
2	736	973
3	3528	967

Stop Event

1×	node limit

Calls

Call 1

Inputs
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos))))))
(.f32 (cos.f32 (.f32 (.f32 (neg.f32 uy) 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos)))))))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)))))))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 (neg.f32 uy) 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))))))))
(.f32 (cos.f32 (.f32 (.f32 ux 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 uy) (.f32 uy maxCos)) (+.f32 (-.f32 1 uy) (.f32 uy maxCos))))))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 maxCos) (.f32 maxCos ux)) (+.f32 (-.f32 1 maxCos) (.f32 maxCos ux))))))
(.f32 (cos.f32 (.f32 (.f32 maxCos 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux uy)) (+.f32 (-.f32 1 ux) (.f32 ux uy))))))

Outputs
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (fma.f32 ux maxCos (-.f32 1 ux))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 -1 (.f32 ux (-.f32 1 maxCos))) 1)))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 (.f32 ux (-.f32 1 maxCos)) -1) 1)))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (fma.f32 ux maxCos (-.f32 1 ux))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 -1 (.f32 ux (-.f32 1 maxCos))) 1)))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 (.f32 ux (-.f32 1 maxCos)) -1) 1)))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 ux (neg.f32 maxCos)))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 1 (-.f32 ux (.f32 ux maxCos))) (+.f32 1 (-.f32 ux (.f32 ux maxCos)))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (+.f32 1 (.f32 ux (-.f32 1 maxCos))) (+.f32 -1 (*.f32 ux (+.f32 maxCos -1))) 1)))
(.f32 (cos.f32 (.f32 uy (*.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 ux (fma.f32 ux maxCos -1)) (fma.f32 ux maxCos (-.f32 -1 ux)) 1)))
(.f32 (cos.f32 (.f32 (.f32 (neg.f32 uy) 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (fma.f32 ux maxCos (-.f32 1 ux))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 -1 (.f32 ux (-.f32 1 maxCos))) 1)))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 (.f32 ux (-.f32 1 maxCos)) -1) 1)))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos)))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos)))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (-.f32 1 (+.f32 ux (.f32 ux maxCos))) (-.f32 1 (+.f32 ux (.f32 ux maxCos)))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 1 (.f32 ux (+.f32 1 maxCos))) (+.f32 -1 (*.f32 ux (+.f32 1 maxCos))) 1)))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 1 (.f32 ux (+.f32 1 maxCos))) (+.f32 ux (fma.f32 ux maxCos -1)) 1)))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 (neg.f32 ux) maxCos)))))))
(.f32 (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 (neg.f32 ux)) (.f32 ux (neg.f32 maxCos)))))))
(.f32 (sqrt.f32 (-.f32 1 (.f32 (+.f32 1 (-.f32 ux (.f32 ux maxCos))) (+.f32 1 (-.f32 ux (.f32 ux maxCos)))))) (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))))
(.f32 (sqrt.f32 (fma.f32 (+.f32 1 (.f32 ux (-.f32 1 maxCos))) (+.f32 -1 (.f32 ux (+.f32 maxCos -1))) 1)) (neg.f32 (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))
(.f32 (sqrt.f32 (fma.f32 (-.f32 ux (fma.f32 ux maxCos -1)) (fma.f32 ux maxCos (-.f32 -1 ux)) 1)) (neg.f32 (cos.f32 (.f32 uy (*.f32 2 (PI.f32))))))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 (neg.f32 uy) 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 (neg.f32 uy)))) (neg.f32 (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux maxCos)) (+.f32 (-.f32 1 ux) (.f32 ux maxCos)))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 uy -2))) (neg.f32 (sqrt.f32 (-.f32 1 (.f32 (fma.f32 ux maxCos (-.f32 1 ux)) (fma.f32 ux maxCos (-.f32 1 ux)))))))
(.f32 (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 -1 (.f32 ux (-.f32 1 maxCos))) 1)) (neg.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32))))))
(.f32 (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) ux) (+.f32 (.f32 ux (-.f32 1 maxCos)) -1) 1)) (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))))
(neg.f32 (.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))))))))
(.f32 (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos))) (+.f32 (-.f32 1 ux) (.f32 ux (neg.f32 maxCos)))))))
(.f32 (sqrt.f32 (-.f32 1 (.f32 (-.f32 1 (+.f32 ux (.f32 ux maxCos))) (-.f32 1 (+.f32 ux (.f32 ux maxCos)))))) (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))))
(.f32 (sqrt.f32 (fma.f32 (-.f32 1 (.f32 ux (+.f32 1 maxCos))) (+.f32 -1 (.f32 ux (+.f32 1 maxCos))) 1)) (neg.f32 (cos.f32 (.f32 2 (*.f32 uy (PI.f32))))))
(.f32 (sqrt.f32 (fma.f32 (-.f32 1 (.f32 ux (+.f32 1 maxCos))) (+.f32 ux (fma.f32 ux maxCos -1)) 1)) (neg.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32))))))
(.f32 (cos.f32 (.f32 (.f32 ux 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 uy) (.f32 uy maxCos)) (+.f32 (-.f32 1 uy) (.f32 uy maxCos))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 ux))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 uy) (.f32 uy maxCos)) (+.f32 (-.f32 1 uy) (.f32 uy maxCos))))))
(.f32 (cos.f32 (.f32 2 (.f32 ux (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 uy maxCos (-.f32 1 uy)) (fma.f32 uy maxCos (-.f32 1 uy))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 ux))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 uy maxCos 1) uy) (+.f32 -1 (.f32 (-.f32 1 maxCos) uy)) 1)))
(.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) ux))) (sqrt.f32 (fma.f32 (fma.f32 uy maxCos (-.f32 1 uy)) (+.f32 (.f32 uy (-.f32 1 maxCos)) -1) 1)))
(.f32 (cos.f32 (.f32 (.f32 uy 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 maxCos) (.f32 maxCos ux)) (+.f32 (-.f32 1 maxCos) (.f32 maxCos ux))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 maxCos)) (+.f32 (.f32 ux maxCos) (-.f32 1 maxCos))))))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 ux maxCos (-.f32 1 maxCos)) (fma.f32 ux maxCos (-.f32 1 maxCos))))))
(.f32 (cos.f32 (.f32 2 (.f32 uy (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) maxCos) (+.f32 -1 (.f32 (-.f32 1 ux) maxCos)) 1)))
(.f32 (cos.f32 (.f32 uy (.f32 2 (PI.f32)))) (sqrt.f32 (fma.f32 (-.f32 (fma.f32 ux maxCos 1) maxCos) (+.f32 -1 (.f32 (-.f32 1 ux) maxCos)) 1)))
(.f32 (cos.f32 (.f32 (.f32 maxCos 2) (PI.f32))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 ux uy)) (+.f32 (-.f32 1 ux) (.f32 ux uy))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 maxCos))) (sqrt.f32 (-.f32 1 (.f32 (+.f32 (-.f32 1 ux) (.f32 uy ux)) (+.f32 (-.f32 1 ux) (.f32 uy ux))))))
(.f32 (cos.f32 (.f32 2 (.f32 maxCos (PI.f32)))) (sqrt.f32 (-.f32 1 (.f32 (fma.f32 uy ux (-.f32 1 ux)) (fma.f32 uy ux (-.f32 1 ux))))))
(.f32 (cos.f32 (.f32 (PI.f32) (.f32 2 maxCos))) (sqrt.f32 (fma.f32 (fma.f32 uy ux (-.f32 1 ux)) (-.f32 -1 (.f32 ux (+.f32 -1 uy))) 1)))
(.f32 (cos.f32 (.f32 2 (.f32 (PI.f32) maxCos))) (sqrt.f32 (fma.f32 (fma.f32 uy ux (-.f32 1 ux)) (+.f32 (.f32 ux (-.f32 1 uy)) -1) 1)))

Symmetry

(abs uy)

Compiler

Compiled 112 to 63 computations (43.8% saved)

UniformSampleCone, x

analyze204.0ms (8.2%)

sample2.0s (81.1%)

preprocess266.0ms (10.7%)

end0.0ms (0%)

Profiling