Metrics for HairBSDF, Mp, lower

analyze782.0ms (4.3%)

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
50%	0.7%	0.7%	97%	0%	1.5%	0%	11
50%	0.7%	0.7%	97%	0%	1.5%	0%	12

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.9s (15.7%)

Results

2.8s	8256×	body	256	valid
32.0ms	131×	body	256	invalid

Bogosity

preprocess406.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

838×	`distribute-neg-in`
784×	`associate-+l-`
766×	`times-frac`
676×	`associate-+l+`
622×	`associate-+r-`

Problems

96×	No Errors
77×	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
74×	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
8×	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
1×	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037

Stop Event

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 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 (neg.f32 cosTheta_i) cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i (neg.f32 cosTheta_O)) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 (neg.f32 sinTheta_i) sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (neg.f32 v)) (/.f32 (.f32 sinTheta_i sinTheta_O) (neg.f32 v))) (/.f32 1 (neg.f32 v))) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 (neg.f32 v))))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 sinTheta_i cosTheta_O) v) (/.f32 (.f32 cosTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 sinTheta_O cosTheta_O) v) (/.f32 (.f32 sinTheta_i cosTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 v cosTheta_O) cosTheta_i) (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_i)) (/.f32 1 cosTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_i)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i sinTheta_i) v) (/.f32 (.f32 cosTheta_O sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i sinTheta_O) v) (/.f32 (.f32 sinTheta_i cosTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i v) cosTheta_O) (/.f32 (.f32 sinTheta_i sinTheta_O) cosTheta_O)) (/.f32 1 cosTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 cosTheta_O)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_i) (/.f32 (.f32 v sinTheta_O) sinTheta_i)) (/.f32 1 sinTheta_i)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_i)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) sinTheta_O) (/.f32 (.f32 sinTheta_i v) sinTheta_O)) (/.f32 1 sinTheta_O)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 sinTheta_O)))))

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 169 to 80 computations (52.7% saved)

eval1.0ms (0%)

Compiler: Compiled 71 to 45 computations (36.6% saved)

prune3.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.6%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.6%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize783.0ms (4.3%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.7%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.7%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.4%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.4%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.7%	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.7%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.3%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.3%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series164.0ms (0.9%)

Counts

8 → 384

Calls

96 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
19.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
8.0ms	cosTheta_O	@	0	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
8.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
8.0ms	sinTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite171.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

764×	`add-sqr-sqrt`
748×	`pow1`
748×	`*-un-lft-identity`
714×	`add-exp-log`
712×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	270
1	803	262

Stop Event

1×	node limit

Counts

8 → 192

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))) 1)
(*.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)))
(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
(.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 2)
(pow.f32 (/.f32 (/.f32 v cosTheta_i) cosTheta_O) -1)
(log.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (log.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (.f32 (log.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 1))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(.f32 1 (.f32 sinTheta_i (/.f32 sinTheta_O v)))
(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
(.f32 (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(.f32 (sqrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(*.f32 (/.f32 sinTheta_i v) sinTheta_O)
(pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)
(pow.f32 (/.f32 (/.f32 v sinTheta_O) sinTheta_i) -1)
(log.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (.f32 (log.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) 1)
(.f32 1 (exp.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(.f32 (exp.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2) (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(pow.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1)
(pow.f32 (exp.f32 1) (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
(pow.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log.f32 (exp.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 1)
(.f32 1 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2) (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(.f32 (sqrt.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(/.f32 (+.f32 (pow.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 3) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)) (+.f32 (pow.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2) (-.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(/.f32 (-.f32 (pow.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (-.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1)
(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
(pow.f32 (pow.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)
(log.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(log.f32 (.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(expm1.f32 (log1p.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (log.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (.f32 (log.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1))
(log1p.f32 (expm1.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (neg.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
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(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 1)
(pow.f32 (exp.f32 1) (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3)
(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(log.f32 (exp.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))

simplify230.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1664×	`fma-neg`
774×	`log-prod`
590×	`associate-r`
574×	`fma-def`
536×	`exp-prod`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	545	24882
1	1488	23158
2	5976	23158

Stop Event

1×	node limit

Counts

576 → 317

Calls

Call 1

Inputs
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v)))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_O 3) (.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i)))) v))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2))) (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i)))) v)))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (+.f32 (.f32 1/6 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) 3)) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2))) (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 1 (*.f32 sinTheta_O sinTheta_i)))) v))))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2))))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v)))
(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_O 3) (.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))
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(pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 2)
(pow.f32 (/.f32 (/.f32 v cosTheta_i) cosTheta_O) -1)
(log.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (log.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(exp.f32 (.f32 (log.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 1))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(/.f32 sinTheta_i (/.f32 v sinTheta_O))
(/.f32 1 (/.f32 (/.f32 v sinTheta_O) sinTheta_i))
(/.f32 (neg.f32 sinTheta_i) (neg.f32 (/.f32 v sinTheta_O)))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)
(pow.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 3)
(pow.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)
(pow.f32 (/.f32 (/.f32 v sinTheta_O) sinTheta_i) -1)
(log.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(cbrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (.f32 (log.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (fma.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (fma.f32 (neg.f32 (sqrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (sqrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (neg.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))
(+.f32 (fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (.f32 sinTheta_O (/.f32 sinTheta_i v))))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (.f32 sinTheta_O (/.f32 sinTheta_i v))))
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(+.f32 (fma.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (*.f32 sinTheta_O (/.f32 sinTheta_i v))))
(+.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (neg.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))
(+.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (.f32 sinTheta_O (/.f32 sinTheta_i v))))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (.f32 sinTheta_O (/.f32 sinTheta_i v))))
(+.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 1 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))
(+.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))) 2))))
(+.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)))) (fma.f32 (neg.f32 sinTheta_O) (/.f32 sinTheta_i v) (.f32 sinTheta_O (/.f32 sinTheta_i v))))
(.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(/.f32 (-.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 3)) (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (+.f32 (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 2) (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(/.f32 (-.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 2)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))) 3)
(pow.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))) 2)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))))
(log.f32 (/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))))
(cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 3))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(exp.f32 (.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) 1))
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 cosTheta_O (/.f32 1 (/.f32 v cosTheta_i)) (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(fma.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(fma.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(fma.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(fma.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) 1)
(.f32 1 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 1)
(pow.f32 (exp.f32 1) (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3)
(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(log.f32 (exp.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))

Outputs
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
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(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(fma.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (fma.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (*.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) 0))
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (*.f32 (neg.f32 (/.f32 sinTheta_O v)) sinTheta_i))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) 1)
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(.f32 1 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v))))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 1)
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (exp.f32 1) (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))
(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3)
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 2)
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))) (sqrt.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))))
(log.f32 (exp.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v))))

eval168.0ms (0.9%)

Compiler: Compiled 11173 to 5987 computations (46.4% saved)

prune68.0ms (0.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	308	9	317
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	310	9	319

Accuracy

99.8%

Counts

319 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.4%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
▶	99.6%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	97.4%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
▶	14.0%	(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
	14.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	98.4%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
▶	99.6%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	97.4%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
▶	14.0%	(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
	14.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))

Compiler

Compiled 728 to 548 computations (24.7% saved)

localize514.0ms (2.8%)

Localize:

Found 15 expressions with local error:

New	Accuracy	Program
✓	99.7%	(exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.5%	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
✓	99.4%	(*.f32 sinTheta_i (/.f32 sinTheta_O v))
✓	98.6%	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.7%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	99.7%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	76.7%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.9%	(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
✓	99.4%	(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
✓	98.9%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	99.8%	(-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))
✓	99.7%	(+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v)))
✓	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
✓	99.4%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))

Compiler

Compiled 336 to 148 computations (56% saved)

series53.0ms (0.3%)

Counts

15 → 481

Calls

147 calls:

Time	Variable		Point	Expression
5.0ms	sinTheta_O	@	inf	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
2.0ms	cosTheta_i	@	0	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
2.0ms	cosTheta_i	@	inf	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
2.0ms	sinTheta_i	@	0	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
2.0ms	sinTheta_O	@	0	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))

rewrite106.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`add-sqr-sqrt`
858×	`pow1`
858×	`*-un-lft-identity`
816×	`add-exp-log`
814×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	441
1	916	441

Stop Event

1×	node limit

Counts

15 → 194

Calls

Call 1

Inputs
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
(+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v)))
(-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
(cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))

Outputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))) 1)
(/.f32 cosTheta_O (/.f32 v cosTheta_i))
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (neg.f32 (*.f32 cosTheta_i cosTheta_O)) (neg.f32 v))
(pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 1)
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(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))) 1)
(.f32 1 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))
(.f32 (.f32 (cbrt.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (cbrt.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))) (cbrt.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(.f32 (sqrt.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (sqrt.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (-.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v))) (.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))))
(/.f32 (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (-.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))
(pow.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) 1)
(log.f32 (exp.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))
(cbrt.f32 (.f32 (.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(expm1.f32 (log1p.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(exp.f32 (log.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(log1p.f32 (expm1.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))
(+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))
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(.f32 (.f32 (cbrt.f32 (-.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))) (cbrt.f32 (-.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)))) (cbrt.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(.f32 (sqrt.f32 (-.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))) (sqrt.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
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(/.f32 (-.f32 (.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (.f32 (/.f32 1 v) (/.f32 1 v))) (+.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)))
(pow.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)) 1)
(log.f32 (exp.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)))))
(cbrt.f32 (.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v)) (-.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))) (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(expm1.f32 (log1p.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(exp.f32 (log.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(log1p.f32 (expm1.f32 (-.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000) (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) 1)
(.f32 1 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 1/3)
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 1)
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(exp.f32 (log.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
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(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)
(log.f32 (exp.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(cbrt.f32 (.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
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(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
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(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))) 1)
(.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))
(.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) 1)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
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(.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
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(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))

simplify217.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1376×	`fma-def`
784×	`times-frac`
550×	`associate-*r/`
510×	`associate-+r+`
508×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	913	33453
1	2542	29603

Stop Event

1×	node limit

Counts

675 → 452

Calls

Call 1

Inputs
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
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6931/10000
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(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
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Outputs
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
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1
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(exp.f32 6931/10000)
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(exp.f32 6931/10000)
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6931/10000
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
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(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
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(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(exp.f32 (log.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(log.f32 (exp.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(cbrt.f32 (.f32 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(cbrt.f32 (.f32 (/.f32 (.f32 sinTheta_O sinTheta_i) v) (.f32 (/.f32 (.f32 sinTheta_O sinTheta_i) v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
(cbrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3))
(expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(*.f32 sinTheta_i (/.f32 sinTheta_O v))
(+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(.f32 (.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(cbrt.f32 (.f32 (.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(cbrt.f32 (.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) (.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))
(cbrt.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 3))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) 1)
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(.f32 1 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 1)
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(log.f32 (exp.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(cbrt.f32 (.f32 (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(cbrt.f32 (.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))) (exp.f32 (+.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))) (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))

eval444.0ms (2.5%)

Compiler: Compiled 19434 to 12520 computations (35.6% saved)

prune187.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	442	10	452
Fresh	2	2	4
Picked	5	0	5
Done	0	0	0
Total	449	12	461

Accuracy

99.8%

Counts

461 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.3%	(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
	99.6%	(.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
	98.4%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) 3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
▶	91.4%	(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.7%	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
▶	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	14.0%	(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.4%	1
▶	6.3%	(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
	99.6%	(.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
	98.4%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) 3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
▶	91.4%	(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.7%	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
▶	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	14.0%	(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 1284 to 920 computations (28.3% saved)

localize1.2s (6.5%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
	99.7%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
	99.7%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	98.6%	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	76.7%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.7%	(+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
✓	99.7%	(exp.f32 (/.f32 1 v))
	99.4%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	97.3%	(/.f32 (exp.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v)))
✓	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.7%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	100.0%	(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
✓	99.4%	(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))
✓	99.7%	(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
	99.4%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	98.6%	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))

Compiler

Compiled 419 to 229 computations (45.3% saved)

series106.0ms (0.6%)

Counts

12 → 319

Calls

84 calls:

Time	Variable		Point	Expression
21.0ms	cosTheta_O	@	inf	(/.f32 (exp.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v)))
7.0ms	cosTheta_i	@	0	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
6.0ms	cosTheta_i	@	-inf	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
5.0ms	cosTheta_i	@	inf	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
4.0ms	v	@	-inf	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))

rewrite157.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

812×	`add-sqr-sqrt`
794×	`pow1`
794×	`*-un-lft-identity`
760×	`add-exp-log`
758×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	338
1	864	334

Stop Event

1×	node limit

Counts

12 → 203

Calls

Call 1

Inputs
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
(+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))
(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(-.f32 6931/10000 (/.f32 1 v))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(/.f32 (exp.f32 (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v)))
(exp.f32 (/.f32 1 v))
(+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))

Outputs
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))) 1)
(*.f32 1 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(*.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(*.f32 (pow.f32 1 1/3) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(*.f32 (pow.f32 (exp.f32 6931/10000) 1/3) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(*.f32 (pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 1/3) (pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 1/3))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 1/3)
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 1)
(pow.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 2)
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3))
(exp.f32 (.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 1))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 1)
(*.f32 1 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 2) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(*.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 2) (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))) 2)
(log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 2) (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))
(-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))) 1)
(*.f32 1 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))
(*.f32 (pow.f32 (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 2) (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(*.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(/.f32 (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))) 3)) (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (-.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))) 2) (*.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))) 2)) (-.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))
(pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) 1)
(pow.f32 (*.f32 (pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) 2) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)
(pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 2)
(log.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(log.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(log.f32 (*.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) (/.f32 1/2 v)))
(cbrt.f32 (*.f32 (pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) 2) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(expm1.f32 (log1p.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(exp.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(exp.f32 (*.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1))
(log1p.f32 (expm1.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))
(fma.f32 1 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))
(fma.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) (cbrt.f32 (log.f32 (/.f32 1/2 v))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))
(fma.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))
(fma.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))) (log.f32 (/.f32 1/2 v)))
(-.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 1)
(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
(pow.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 1)
(pow.f32 (.f32 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1/3)
(pow.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 2)
(log.f32 (exp.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(cbrt.f32 (.f32 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(exp.f32 (.f32 (log.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1))
(log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1))) 1)
(*.f32 1 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1))
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) 2) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(/.f32 (+.f32 1 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 3)) (+.f32 1 (-.f32 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(/.f32 (-.f32 1 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2)) (-.f32 1 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 1)
(pow.f32 (*.f32 (pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 2) (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) 2)
(log.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1))))
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 2) (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(expm1.f32 (log1p.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(exp.f32 (.f32 (log1p.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1))
(log1p.f32 (expm1.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(fma.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 1)
(fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)
(fma.f32 (/.f32 (neg.f32 sinTheta_O) v) sinTheta_i 1)
(fma.f32 (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 2) (cbrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1)
(fma.f32 (sqrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) (sqrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1)
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
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(*.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1)
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(log.f32 (exp.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
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(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
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(log1p.f32 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 6931/10000 (neg.f32 (/.f32 1 v)))
(+.f32 0 (-.f32 6931/10000 (/.f32 1 v)))
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(+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2)) (log.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(*.f32 1 (-.f32 6931/10000 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (cbrt.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))) (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))))
(/.f32 (-.f32 332956652491/1000000000000 (pow.f32 v -3)) (+.f32 48038761/100000000 (+.f32 (pow.f32 v -2) (*.f32 6931/10000 (/.f32 1 v)))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (+.f32 6931/10000 (/.f32 1 v)))
(pow.f32 (-.f32 6931/10000 (/.f32 1 v)) 1)
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(pow.f32 (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)
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(log.f32 (+.f32 1 (expm1.f32 (-.f32 6931/10000 (/.f32 1 v)))))
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(exp.f32 (log.f32 (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (*.f32 (log.f32 (-.f32 6931/10000 (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (-.f32 6931/10000 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) 1)
(/.f32 (*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/2) v)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1)
(pow.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 2)
(log.f32 (exp.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))
(cbrt.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))
(*.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (neg.f32 (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 2) (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2)
(pow.f32 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) -1)
(log.f32 (exp.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 2) (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2) (cbrt.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)
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(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))))
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(log1p.f32 (expm1.f32 (exp.f32 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)
(*.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(*.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))))
(/.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2)) (-.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) 48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
(pow.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i 6931/10000)
(fma.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
(fma.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))) 1)
(*.f32 1 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3))
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(*.f32 (pow.f32 1 1/3) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3) (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3))
(pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1/3)
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1)
(pow.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2)
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(exp.f32 (*.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3))
(exp.f32 (.f32 (.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))

simplify338.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

1314×	`associate-r`
1114×	`fma-def`
832×	`times-frac`
550×	`sqr-pow`
536×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	964	27758
1	2719	24892

Stop Event

1×	node limit

Counts

522 → 445

Calls

Call 1

Inputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
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(*.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(/.f32 (+.f32 1 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 3)) (+.f32 1 (-.f32 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2) (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))))
(/.f32 (-.f32 1 (pow.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 2)) (-.f32 1 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 1)
(pow.f32 (*.f32 (pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 2) (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)) 2)
(log.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1))))
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1) 2) (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(expm1.f32 (log1p.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))))
(exp.f32 (.f32 (log1p.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1))
(log1p.f32 (expm1.f32 (fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)))
(fma.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)) 1)
(fma.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v) 1)
(fma.f32 (/.f32 (neg.f32 sinTheta_O) v) sinTheta_i 1)
(fma.f32 (pow.f32 (cbrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 2) (cbrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1)
(fma.f32 (sqrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) (sqrt.f32 (.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))) 1)
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
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(*.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1)
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(pow.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2)
(log.f32 (exp.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 6931/10000 (neg.f32 (/.f32 1 v)))
(+.f32 0 (-.f32 6931/10000 (/.f32 1 v)))
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(+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2)) (log.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(*.f32 1 (-.f32 6931/10000 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (cbrt.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))) (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))))
(/.f32 (-.f32 332956652491/1000000000000 (pow.f32 v -3)) (+.f32 48038761/100000000 (+.f32 (pow.f32 v -2) (*.f32 6931/10000 (/.f32 1 v)))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (+.f32 6931/10000 (/.f32 1 v)))
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(pow.f32 (*.f32 (pow.f32 (-.f32 6931/10000 (/.f32 1 v)) 2) (-.f32 6931/10000 (/.f32 1 v))) 1/3)
(pow.f32 (sqrt.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)
(log.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(cbrt.f32 (*.f32 (pow.f32 (-.f32 6931/10000 (/.f32 1 v)) 2) (-.f32 6931/10000 (/.f32 1 v))))
(expm1.f32 (log1p.f32 (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (log.f32 (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (*.f32 (log.f32 (-.f32 6931/10000 (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (-.f32 6931/10000 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) 1)
(/.f32 (*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/2) v)
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1)
(pow.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 2)
(log.f32 (exp.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))
(cbrt.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))
(*.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (neg.f32 (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 2) (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2)
(pow.f32 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) -1)
(log.f32 (exp.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 2) (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2) (cbrt.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) 2)
(log.f32 (exp.f32 (exp.f32 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 1 v)))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)
(*.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(*.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))))
(/.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2)) (-.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) 48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
(pow.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i 6931/10000)
(fma.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
(fma.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))) 1)
(*.f32 1 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3))
(*.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (pow.f32 1 1/3) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3) (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3))
(pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1/3)
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1)
(pow.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2)
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(exp.f32 (*.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3))
(exp.f32 (.f32 (.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))

Outputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3)
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(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(exp.f32 (/.f32 1 v))
(pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)
(exp.f32 (/.f32 1 v))
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) 2)
(exp.f32 (/.f32 1 v))
(log.f32 (exp.f32 (exp.f32 (/.f32 1 v))))
(exp.f32 (/.f32 1 v))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 1 v)))))
(exp.f32 (/.f32 1 v))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))))
(exp.f32 (/.f32 1 v))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v))))
(exp.f32 (/.f32 1 v))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 1 v))))
(exp.f32 (/.f32 1 v))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(*.f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(*.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (.f32 -6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))))
(/.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (-.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) 48038761/100000000) (.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3)) (+.f32 48038761/100000000 (+.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) -6931/10000) (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 2)) (-.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v))))
(/.f32 (-.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) 48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))
(/.f32 (+.f32 (pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 2) -48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(pow.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1/3)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 (/.f32 cosTheta_O v) cosTheta_i 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v) 6931/10000)
(fma.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 1 v) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 2) (cbrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) (sqrt.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v))) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))) 1)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 1 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3))
(*.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (cbrt.f32 (exp.f32 (/.f32 -1 v))))
(*.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (pow.f32 1 1/3) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(*.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2)))
(*.f32 (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3) (pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1/3))
(*.f32 (cbrt.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))) 1)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))) 2)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(exp.f32 (*.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(exp.f32 (.f32 (.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) 1))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))

eval1.8s (9.8%)

Compiler: Compiled 62588 to 44215 computations (29.4% saved)

prune354.0ms (2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	943	13	956
Fresh	3	4	7
Picked	4	1	5
Done	0	0	0
Total	950	18	968

Accuracy

99.9%

Counts

968 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.3%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	99.6%	(*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
	98.4%	(.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
	91.4%	(.f32 (pow.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3)) 3) (/.f32 1/2 v))
	99.7%	(.f32 (pow.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2))) 3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (exp.f32 (.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)) 3) (/.f32 1/2 v))
	99.6%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
	90.2%	(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
▶	91.4%	(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.6%	(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.8%	(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
	99.7%	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))))
	97.7%	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	14.0%	(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.4%	1
▶	6.3%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	99.6%	(*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
	98.4%	(.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
	91.4%	(.f32 (pow.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3)) 3) (/.f32 1/2 v))
	99.7%	(.f32 (pow.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2))) 3) (/.f32 1/2 v))
▶	99.6%	(.f32 (pow.f32 (exp.f32 (.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)) 3) (/.f32 1/2 v))
	99.6%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
	90.2%	(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
▶	91.4%	(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.6%	(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.8%	(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
	99.7%	(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))))
	97.7%	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	14.0%	(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 1858 to 1454 computations (21.7% saved)

localize1.1s (6.2%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
	99.7%	(exp.f32 (/.f32 1 v))
✓	97.7%	(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
✓	97.4%	(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
✓	97.3%	(/.f32 (exp.f32 (*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v)))
✓	99.9%	(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))
✓	99.8%	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
✓	99.6%	(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3))
✓	98.8%	(*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)
✓	99.9%	(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
✓	99.9%	(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
	99.7%	(exp.f32 (/.f32 1 v))
✓	100.0%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
✓	99.5%	(/.f32 sinTheta_O (/.f32 v sinTheta_i))
✓	99.7%	(exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3))
	99.4%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	98.8%	(*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)
	98.6%	(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))

Compiler

Compiled 552 to 328 computations (40.6% saved)

series35.0ms (0.2%)

Counts

13 → 396

Calls

105 calls:

Time	Variable		Point	Expression
4.0ms	v	@	inf	(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
2.0ms	cosTheta_i	@	0	(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
2.0ms	v	@	inf	(/.f32 sinTheta_O (/.f32 v sinTheta_i))
2.0ms	cosTheta_O	@	0	(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
1.0ms	v	@	-inf	(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)

rewrite122.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

842×	`add-sqr-sqrt`
822×	`pow1`
818×	`*-un-lft-identity`
792×	`add-exp-log`
790×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	363
1	872	363

Stop Event

1×	node limit

Counts

13 → 201

Calls

Call 1

Inputs
(*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)
(exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3))
(/.f32 sinTheta_O (/.f32 v sinTheta_i))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
(*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)
(exp.f32 (*.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))
(/.f32 (exp.f32 (*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v)))
(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))

Outputs
(+.f32 0 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))
(+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))) (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))) (log.f32 (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))))
(+.f32 (log.f32 (sqrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))) (log.f32 (sqrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))) 1)
(pow.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3) 1)
(log.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(cbrt.f32 (.f32 (pow.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3) 2) (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(expm1.f32 (log1p.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(exp.f32 (log.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(exp.f32 (.f32 (log.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)) 1))
(log1p.f32 (expm1.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))) 1)
(.f32 1 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))
(.f32 (.f32 (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))) (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))) (cbrt.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(.f32 (sqrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))) (sqrt.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(pow.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)) 1)
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v))))) 1/3)
(log.f32 (exp.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)))))
(cbrt.f32 (.f32 (pow.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3)) 2) (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(expm1.f32 (log1p.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(log1p.f32 (expm1.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 1/3))))
(-.f32 (+.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) 1)
(.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i))
(*.f32 sinTheta_O (/.f32 1 (/.f32 v sinTheta_i)))
(.f32 (.f32 (cbrt.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (cbrt.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) (cbrt.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(.f32 (sqrt.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (sqrt.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
(pow.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i) 1)
(pow.f32 (/.f32 (/.f32 v sinTheta_i) sinTheta_O) -1)
(log.f32 (exp.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(cbrt.f32 (.f32 (pow.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i) 2) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(exp.f32 (log.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(exp.f32 (.f32 (log.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) 1))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(+.f32 1 (neg.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(.f32 1 (-.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(.f32 (.f32 (cbrt.f32 (-.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) (cbrt.f32 (-.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)))) (cbrt.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(.f32 (sqrt.f32 (-.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) (sqrt.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(/.f32 (-.f32 1 (pow.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i) 3)) (+.f32 1 (+.f32 (pow.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i) 2) (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(/.f32 (-.f32 1 (pow.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i) 2)) (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(pow.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) 1)
(log.f32 (exp.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)))))
(cbrt.f32 (.f32 (pow.f32 (-.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) 2) (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(expm1.f32 (log1p.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(exp.f32 (log1p.f32 (neg.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(exp.f32 (.f32 (log1p.f32 (neg.f32 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) 1))
(log1p.f32 (expm1.f32 (-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) 1)
(/.f32 (.f32 (exp.f32 6931/10000) 1/2) (.f32 (exp.f32 (/.f32 1 v)) v))
(/.f32 (*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/2) v)
(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 1 v)))
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1)
(log.f32 (exp.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))
(cbrt.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
(exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))) 1))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v)))
(.f32 (.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1)
(pow.f32 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 6931/10000)) -1)
(log.f32 (exp.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (*.f32 (-.f32 6931/10000 (/.f32 1 v)) 1))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 0 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))
(+.f32 (log.f32 (sqrt.f32 (exp.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))) (log.f32 (sqrt.f32 (exp.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))))
(+.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))))) (log.f32 (cbrt.f32 (exp.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))) 1)
(pow.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 1)
(log.f32 (exp.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))))
(cbrt.f32 (.f32 (pow.f32 (.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2) (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))
(expm1.f32 (log1p.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))
(exp.f32 (log.f32 (*.f32 1/3 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))
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(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 3)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))
(exp.f32 (*.f32 (log.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 3))
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)

simplify179.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1070×	`fma-def`
1022×	`associate-r`
876×	`associate-l`
776×	`times-frac`
606×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	828	22365
1	2214	20193

Stop Event

1×	node limit

Counts

597 → 424

Calls

Call 1

Inputs
(.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))
(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (.f32 -1 (log.f32 v))))) (.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (.f32 -1 (log.f32 v))))) (.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (.f32 -1 (log.f32 v))))) (.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
(*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))
(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (.f32 1/3 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))
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(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (.f32 1/3 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))
(*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))
(+.f32 (.f32 -1/3 (/.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i))) v)) (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))))
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(*.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
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(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(.f32 1/3 (/.f32 (.f32 cosTheta_O cosTheta_i) v))
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(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(.f32 1/3 (/.f32 (.f32 cosTheta_O cosTheta_i) v))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(*.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
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(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(.f32 1/3 (/.f32 (.f32 cosTheta_O cosTheta_i) v))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(.f32 1/3 (/.f32 (.f32 cosTheta_O cosTheta_i) v))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(+.f32 (.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (.f32 1/3 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))))
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(+.f32 (exp.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (+.f32 (.f32 1/162 (/.f32 (.f32 (exp.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) 3)) (pow.f32 v 3))) (+.f32 (.f32 1/18 (/.f32 (.f32 (exp.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) 2)) (pow.f32 v 2))) (.f32 1/3 (/.f32 (.f32 (exp.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (-.f32 (*.f32 cosTheta_O cosTheta_i) 1)) v)))))
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(exp.f32 (*.f32 1/3 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
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(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
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(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
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(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
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(*.f32 1 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))
(.f32 (.f32 (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))) (cbrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))
(*.f32 (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (sqrt.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))
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(/.f32 (-.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2) (pow.f32 v -2)) (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))
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(fma.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (/.f32 -1 v))
(fma.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (/.f32 -1 v))
(fma.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (/.f32 -1 v))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))) 1)
(*.f32 1 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))
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(-.f32 (exp.f32 (log1p.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2))) 1)
(*.f32 1 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2))
(*.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
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(log.f32 (exp.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)))
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(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)

Outputs
(.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))
(*.f32 1/3 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (.f32 -1 (log.f32 v))))) (.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
(*.f32 1/3 (+.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v)))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
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(+.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (.f32 -1 (log.f32 v))))) (.f32 1/3 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
(*.f32 1/3 (+.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v)))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
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(*.f32 1/3 (+.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v)))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
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(*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))
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(*.f32 1/3 (+.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v)))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
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(+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(+.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (log.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))
(+.f32 (.f32 2 (.f32 1/3 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (*.f32 1/3 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(+.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))
(*.f32 2 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 3)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(exp.f32 (*.f32 (log.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 3))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)

eval1.2s (6.6%)

Compiler: Compiled 39472 to 28548 computations (27.7% saved)

prune205.0ms (1.1%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	717	9	726
Fresh	3	9	12
Picked	4	1	5
Done	0	1	1
Total	724	20	744

Accuracy

99.9%

Counts

744 → 20

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	6.3%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	99.6%	(*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
	98.4%	(.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
	91.4%	(.f32 (pow.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3)) 3) (/.f32 1/2 v))
	99.6%	(*.f32 (pow.f32 (exp.f32 (+.f32 6931/30000 (/.f32 -1/3 v))) 3) (/.f32 1/2 v))
	99.6%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 3) (/.f32 1/2 v))
	99.6%	(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
	85.9%	(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 6931/10000))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
	98.4%	(.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 (.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
	21.6%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
	99.6%	(*.f32 (/.f32 1 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
	99.7%	(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
	99.7%	(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
	97.7%	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	39.4%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
	14.0%	(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
	99.7%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 1463 to 1040 computations (28.9% saved)

regimes224.0ms (1.2%)

Counts

44 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
(*.f32 (/.f32 1 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000))) (/.f32 1/2 v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(*.f32 (pow.f32 (exp.f32 (+.f32 6931/30000 (/.f32 -1/3 v))) 3) (/.f32 1/2 v))
(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 3) (/.f32 1/2 v))
(*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 (.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 6931/10000))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (pow.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3)) 3) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (pow.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2))) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))))) 3) (/.f32 1/2 v))
(.f32 (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (*.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v)))))))) 2) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))))))))

Outputs

(*.f32 (*.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (*.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))

Calls

9 calls:

22.0ms	sinTheta_i
21.0ms	sinTheta_O
21.0ms	cosTheta_i
21.0ms	cosTheta_O
17.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
99.8%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.8%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.8%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.8%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 1101 to 742 computations (32.6% saved)

regimes149.0ms (0.8%)

Counts

37 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
(*.f32 (/.f32 1 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000))) (/.f32 1/2 v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(*.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(*.f32 (pow.f32 (exp.f32 (+.f32 6931/30000 (/.f32 -1/3 v))) 3) (/.f32 1/2 v))
(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 3) (/.f32 1/2 v))
(*.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)) 1/3)) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) 1/3) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 (.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)) (pow.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 1 v))) 1/3)) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 6931/10000))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (pow.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (pow.f32 (exp.f32 (neg.f32 (/.f32 1 v))) 1/3)) 3) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (exp.f32 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (.f32 (exp.f32 (.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (/.f32 1 v))))) 1/3)) (cbrt.f32 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))

Outputs
(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))

Calls

9 calls:

19.0ms	sinTheta_i
19.0ms	sinTheta_O
19.0ms	cosTheta_i
18.0ms	cosTheta_O
15.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

Accuracy	Segments	Branch
99.7%	1	`cosTheta_i`
99.7%	1	`cosTheta_O`
99.7%	1	`sinTheta_i`
99.7%	1	`sinTheta_O`
99.7%	1	`v`
99.7%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.7%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.7%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.7%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 707 to 487 computations (31.1% saved)

regimes63.0ms (0.3%)

Counts

15 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
(*.f32 (/.f32 1 (exp.f32 (-.f32 (/.f32 1 v) 6931/10000))) (/.f32 1/2 v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))

Outputs
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))

Calls

5 calls:

25.0ms	sinTheta_i
9.0ms	cosTheta_i
9.0ms	cosTheta_O
9.0ms	sinTheta_O
8.0ms	v

Results

Accuracy	Segments	Branch
99.6%	1	`cosTheta_i`
99.6%	1	`cosTheta_O`
99.6%	1	`sinTheta_i`
99.6%	1	`sinTheta_O`
99.6%	1	`v`

Compiler

Compiled 171 to 113 computations (33.9% saved)

regimes60.0ms (0.3%)

Counts

10 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))

Outputs
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))

Calls

5 calls:

29.0ms	cosTheta_O
7.0ms	sinTheta_O
7.0ms	sinTheta_i
7.0ms	cosTheta_i
6.0ms	v

Results

Accuracy	Segments	Branch
97.7%	1	`cosTheta_i`
97.7%	1	`cosTheta_O`
97.7%	1	`sinTheta_i`
97.7%	1	`sinTheta_O`
97.7%	1	`v`

Compiler

Compiled 99 to 66 computations (33.3% saved)

regimes48.0ms (0.3%)

Counts

9 → 2

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(exp.f32 (*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v)))
(exp.f32 (/.f32 (*.f32 (neg.f32 sinTheta_i) sinTheta_O) v))

Outputs
(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))

Calls

5 calls:

15.0ms	sinTheta_i
12.0ms	sinTheta_O
7.0ms	v
6.0ms	cosTheta_i
6.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
39.4%	1	`cosTheta_O`
43.1%	2	`sinTheta_i`
43.7%	2	`sinTheta_O`
39.4%	1	`v`
39.4%	1	`cosTheta_i`

Compiler

Compiled 91 to 60 computations (34.1% saved)

regimes18.0ms (0.1%)

Counts

6 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
(+.f32 1 (*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))

Outputs
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))

Calls

3 calls:

6.0ms	sinTheta_i
5.0ms	sinTheta_O
5.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
39.4%	1	`cosTheta_i`
39.4%	1	`sinTheta_i`
39.4%	1	`sinTheta_O`

Compiler

Compiled 58 to 42 computations (27.6% saved)

regimes57.0ms (0.3%)

Counts

2 → 1

Calls

Call 1

Inputs
1
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))

Outputs
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))

Calls

5 calls:

43.0ms	sinTheta_O
3.0ms	sinTheta_i
3.0ms	cosTheta_O
3.0ms	v
3.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
21.6%	1	`sinTheta_O`
21.6%	1	`cosTheta_O`
21.6%	1	`sinTheta_i`
21.6%	1	`v`
21.6%	1	`cosTheta_i`

Compiler

Compiled 42 to 34 computations (19% saved)

regimes27.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

5 calls:

5.0ms	sinTheta_i
5.0ms	cosTheta_O
5.0ms	sinTheta_O
5.0ms	cosTheta_i
5.0ms	v

Results

Accuracy	Segments	Branch
6.4%	1	`cosTheta_i`
6.4%	1	`cosTheta_O`
6.4%	1	`sinTheta_O`
6.4%	1	`v`
6.4%	1	`sinTheta_i`

Compiler

Compiled 36 to 31 computations (13.9% saved)

bsearch1.0ms (0%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
0.0ms	-2.8602053715331473e-21	-7.125290832011438e-23

Compiler

Compiled 38 to 29 computations (23.7% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

42×	`*-commutative`
34×	`+-commutative`
26×	`sub-neg`
22×	`neg-sub0`
20×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	326
1	84	326
2	108	326
3	135	326
4	151	326
5	156	326
6	157	326

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f32 (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(if (<=.f32 sinTheta_O -309485/154742504910672534362390528) (exp.f32 (.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
1

Outputs
(.f32 (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))))
(.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))) (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))))
(.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 -1 v)))))) (.f32 (exp.f32 (+.f32 (+.f32 6931/30000 (.f32 (log.f32 (/.f32 1/2 v)) 1/3)) (/.f32 -1/3 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 -1 v))))))))
(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(if (<=.f32 sinTheta_O -309485/154742504910672534362390528) (exp.f32 (.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (.f32 -1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
(if (<=.f32 sinTheta_O -309485/154742504910672534362390528) (exp.f32 (.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (neg.f32 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
(if (<=.f32 sinTheta_O -309485/154742504910672534362390528) (exp.f32 (.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) (/.f32 (.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(neg.f32 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
(*.f32 (neg.f32 sinTheta_i) (/.f32 sinTheta_O v))
1

Compiler

Compiled 150 to 116 computations (22.7% saved)

soundness3.4s (18.5%)

Rules

1664×	`fma-neg`
1664×	`fma-neg`
1664×	`fma-neg`
1376×	`fma-def`
1376×	`fma-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	545	24882
1	1488	23158
2	5976	23158
0	41	441
1	916	441
0	38	338
1	864	334
0	828	22365
1	2214	20193
0	545	24882
1	1488	23158
2	5976	23158
0	913	33453
1	2542	29603
0	964	27758
1	2719	24892
0	828	22365
1	2214	20193
0	545	24882
1	1488	23158
2	5976	23158
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	913	33453
1	2542	29603

Stop Event

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

Compiler

Compiled 1286 to 852 computations (33.7% saved)

end0.0ms (0%)

preprocess160.0ms (0.9%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 514 to 366 computations (28.8% saved)

analyze782.0ms (4.3%)

sample2.9s (15.7%)

preprocess406.0ms (2.2%)

eval1.0ms (0%)

prune3.0ms (0%)

localize783.0ms (4.3%)

series164.0ms (0.9%)

rewrite171.0ms (0.9%)

simplify230.0ms (1.3%)

eval168.0ms (0.9%)

prune68.0ms (0.4%)

localize514.0ms (2.8%)

series53.0ms (0.3%)

rewrite106.0ms (0.6%)

simplify217.0ms (1.2%)

eval444.0ms (2.5%)

prune187.0ms (1%)

localize1.2s (6.5%)

series106.0ms (0.6%)

rewrite157.0ms (0.9%)

simplify338.0ms (1.9%)

eval1.8s (9.8%)

prune354.0ms (2%)

localize1.1s (6.2%)

series35.0ms (0.2%)

rewrite122.0ms (0.7%)

simplify179.0ms (1%)

eval1.2s (6.6%)

prune205.0ms (1.1%)

regimes224.0ms (1.2%)

regimes149.0ms (0.8%)

regimes63.0ms (0.3%)

regimes60.0ms (0.3%)

regimes48.0ms (0.3%)

regimes18.0ms (0.1%)

regimes57.0ms (0.3%)

regimes27.0ms (0.1%)

bsearch1.0ms (0%)

simplify22.0ms (0.1%)

soundness3.4s (18.5%)

end0.0ms (0%)

preprocess160.0ms (0.9%)

Profiling