Metrics for HairBSDF, Mp, lower

analyze523.0ms (5.4%)

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)

sample2.5s (25.9%)

Results

2.5s	8256×	body	256	valid
28.0ms	114×	body	256	invalid

Bogosity

preprocess65.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1136
1	461	1064
2	1373	976
3	6228	976

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 (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 (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 35 to 27 computations (22.9% saved)

simplify37.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1828×	`fma-def`
1016×	`exp-sum`
920×	`sub-neg`
824×	`exp-diff`
696×	`cancel-sign-sub-inv`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	55	65
2	149	61
3	580	57
4	2989	57

Stop Event

1×	node limit

Counts

1 → 6

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)))))

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

eval2.0ms (0%)

Compiler: Compiled 136 to 82 computations (39.7% saved)

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	4	2	6
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	5	2	7

Accurracy

99.9%

Counts

7 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.9%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize352.0ms (3.6%)

Local Accuracy

Found 8 expressions with local accuracy:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.8%	(-.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (/.f32 sinTheta_i v) sinTheta_O))
✓	99.4%	(*.f32 (/.f32 sinTheta_i v) sinTheta_O)
✓	99.4%	(*.f32 (/.f32 cosTheta_i v) cosTheta_O)
✓	99.8%	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.8%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.3%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	78.0%	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 218 to 89 computations (59.2% saved)

series50.0ms (0.5%)

Counts

8 → 348

Calls

96 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
5.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
3.0ms	cosTheta_i	@	0	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
3.0ms	v	@	inf	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite87.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

760×	`add-sqr-sqrt`
744×	`pow1`
744×	`*-un-lft-identity`
710×	`add-exp-log`
708×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	270
1	797	262

Stop Event

1×	node limit

Counts

8 → 192

Calls

Call 1

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

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

simplify225.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

756×	`log-prod`
630×	`fma-def`
604×	`associate-r`
580×	`exp-prod`
518×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	546	24442
1	1514	22598
2	6287	22518

Stop Event

1×	node limit

Counts

540 → 316

Calls

Call 1

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

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

eval159.0ms (1.6%)

Compiler: Compiled 11366 to 6133 computations (46% saved)

prune71.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	308	8	316
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	310	8	318

Accurracy

99.9%

Counts

318 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(pow.f32 (exp.f32 1) (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.9%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
▶	99.9%	(*.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	98.1%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	15.1%	(exp.f32 (*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v))))
▶	99.8%	(pow.f32 (exp.f32 1) (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.9%	(.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (+.f32 6931/10000 (/.f32 -1 v))))) 3) (/.f32 1/2 v))
▶	99.9%	(*.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	98.1%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	15.1%	(exp.f32 (*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v))))

Compiler

Compiled 680 to 508 computations (25.3% saved)

localize612.0ms (6.3%)

Local Accuracy

Found 16 expressions with local accuracy:

New	Accuracy	Program
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.8%	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.8%	(pow.f32 (exp.f32 1) (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
✓	76.8%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	100.0%	(*.f32 cosTheta_i cosTheta_O)
✓	100.0%	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v)
✓	99.9%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
✓	99.1%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.9%	(exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
	99.3%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	90.1%	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 354 to 169 computations (52.3% saved)

series70.0ms (0.7%)

Counts

14 → 352

Calls

129 calls:

Time	Variable		Point	Expression
21.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
8.0ms	v	@	-inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
4.0ms	v	@	inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
4.0ms	cosTheta_O	@	0	(exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
3.0ms	sinTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite100.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

884×	`add-sqr-sqrt`
866×	`pow1`
866×	`*-un-lft-identity`
832×	`add-exp-log`
830×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	450
1	900	450

Stop Event

1×	node limit

Counts

14 → 163

Calls

Call 1

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

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

simplify226.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1090×	`associate-r`
974×	`associate-l`
842×	`fma-def`
524×	`times-frac`
440×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	673	28965
1	1894	24017

Stop Event

1×	node limit

Counts

515 → 383

Calls

Call 1

Inputs
(exp.f32 (+.f32 (*.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))
(exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))
(exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))
(exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))
(exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))
(exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
(+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 3))) (pow.f32 v 3))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
1
(-.f32 (+.f32 1 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 1 (+.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) 2) (pow.f32 v 2))))) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 1 (+.f32 (.f32 1/6 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) 3) (pow.f32 v 3))) (+.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) 2) (pow.f32 v 2)))))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
1
(+.f32 1 (.f32 -1 (/.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (*.f32 sinTheta_i sinTheta_O))) v)))
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (.f32 sinTheta_i sinTheta_O))) 2) (pow.f32 v 2))) (.f32 -1 (/.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v))))
(+.f32 (.f32 -1/6 (/.f32 (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (.f32 sinTheta_i sinTheta_O))) 3) (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (.f32 sinTheta_i sinTheta_O))) 2) (pow.f32 v 2))) (.f32 -1 (/.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (*.f32 sinTheta_i sinTheta_O))) v)))))
(exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
(+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 3))) (pow.f32 v 3))) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (neg.f32 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v))))
(exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
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Outputs
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(exp.f32 (fma.f32 -1 (log.f32 v) (+.f32 6931/10000 (log.f32 1/2))))
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(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (+.f32 (*.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))
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(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
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(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
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(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) (+.f32 48038761/100000000 (*.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000))))
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(pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)
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(fma.f32 -1 (log.f32 v) (+.f32 6931/10000 (log.f32 1/2)))
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(-.f32 6931/10000 (log.f32 (/.f32 v 1/2)))
(exp.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(fma.f32 -1 (log.f32 v) (+.f32 6931/10000 (log.f32 1/2)))
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(log1p.f32 (expm1.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
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eval252.0ms (2.6%)

Compiler: Compiled 16504 to 9997 computations (39.4% saved)

prune96.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	484	9	493
Fresh	2	1	3
Picked	4	1	5
Done	0	0	0
Total	490	11	501

Accurracy

100.0%

Counts

501 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
▶	91.3%	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))
	99.8%	(*.f32 (pow.f32 (E.f32) (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
✓	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	98.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	12.8%	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
▶	15.1%	(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	12.8%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
	99.8%	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
▶	91.3%	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))
	99.8%	(*.f32 (pow.f32 (E.f32) (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (.f32 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
✓	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	98.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	12.8%	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
▶	15.1%	(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	12.8%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))

Compiler

Compiled 838 to 644 computations (23.2% saved)

localize614.0ms (6.3%)

Local Accuracy

Found 16 expressions with local accuracy:

New	Accuracy	Program
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
	99.4%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	96.2%	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))
✓	91.9%	(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	76.9%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	99.8%	(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
✓	99.5%	(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
✓	99.8%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
✓	99.4%	(*.f32 cosTheta_O (/.f32 cosTheta_i v))
	99.4%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	99.0%	(.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	98.6%	(*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	90.6%	(exp.f32 (cbrt.f32 (.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

Compiler

Compiled 377 to 205 computations (45.6% saved)

series25.0ms (0.3%)

Counts

13 → 325

Calls

99 calls:

Time	Variable		Point	Expression
3.0ms	v	@	inf	(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
2.0ms	v	@	-inf	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))
2.0ms	cosTheta_O	@	0	(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
1.0ms	v	@	inf	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))
1.0ms	cosTheta_O	@	0	(/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (exp.f32 (/.f32 1 v)))

rewrite99.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

804×	`add-sqr-sqrt`
788×	`pow1`
784×	`*-un-lft-identity`
758×	`add-exp-log`
756×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	339
1	857	315

Stop Event

1×	node limit

Counts

13 → 243

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 1)
(*.f32 1 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(*.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1)
(pow.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)
(log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(+.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6931/10000) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (log.f32 (/.f32 1/2 v))))
(+.f32 (.f32 6931/10000 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2))) 1)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) 1)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 2/3)
(pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6) 1/3)
(pow.f32 (*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 4) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) 1/3)
(pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) 2)
(log.f32 (exp.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2))))
(cbrt.f32 (*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 4) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(expm1.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(exp.f32 (*.f32 2 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (.f32 (.f32 2 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1))
(exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))
(log1p.f32 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(fma.f32 6931/10000 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(fma.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6931/10000 (*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (log.f32 (/.f32 1/2 v))))
(+.f32 (.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) 6931/10000) (.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (log.f32 (/.f32 1/2 v))))
(+.f32 (.f32 6931/10000 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (.f32 (log.f32 (/.f32 1/2 v)) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))) 1)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1)
(pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)
(pow.f32 (*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)) 1/3)
(pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)) 2)
(log.f32 (exp.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))))
(cbrt.f32 (*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(expm1.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(exp.f32 (*.f32 3 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(exp.f32 (.f32 (.f32 3 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1))
(exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(log1p.f32 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(fma.f32 6931/10000 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (*.f32 (log.f32 (/.f32 1/2 v)) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)))
(fma.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) 6931/10000 (*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (log.f32 (/.f32 1/2 v))))
(+.f32 0 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(+.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))))
(+.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))) 1)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
(/.f32 1 (/.f32 (/.f32 v cosTheta_O) cosTheta_i))
(/.f32 1 (/.f32 v (*.f32 cosTheta_O cosTheta_i)))
(/.f32 (neg.f32 cosTheta_i) (neg.f32 (/.f32 v cosTheta_O)))
(/.f32 (neg.f32 (*.f32 cosTheta_O cosTheta_i)) (neg.f32 v))
(pow.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) 1)
(pow.f32 (.f32 (pow.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) 2) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 1/3)
(pow.f32 (sqrt.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))) 2)
(pow.f32 (/.f32 (/.f32 v cosTheta_O) cosTheta_i) -1)
(pow.f32 (/.f32 v (*.f32 cosTheta_O cosTheta_i)) -1)
(log.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))))
(cbrt.f32 (.f32 (pow.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) 2) (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(expm1.f32 (log1p.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(exp.f32 (log.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(exp.f32 (.f32 (log.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v))) 1))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v))))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))) 1)
(*.f32 1 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))
(*.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))) 2) (cbrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(*.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))) (sqrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(pow.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) 1)
(pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))
(pow.f32 (exp.f32 cosTheta_O) (*.f32 (/.f32 cosTheta_i v) 1))
(pow.f32 (*.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) 2) (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))) 1/3)
(pow.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))) 2)
(pow.f32 (pow.f32 (exp.f32 cosTheta_O) cosTheta_i) (/.f32 1 v))
(pow.f32 (pow.f32 (exp.f32 cosTheta_O) (pow.f32 (cbrt.f32 (/.f32 cosTheta_i v)) 2)) (cbrt.f32 (/.f32 cosTheta_i v)))
(pow.f32 (pow.f32 (exp.f32 cosTheta_O) (sqrt.f32 (/.f32 cosTheta_i v))) (sqrt.f32 (/.f32 cosTheta_i v)))
(log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)))))
(cbrt.f32 (*.f32 (pow.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) 2) (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(expm1.f32 (log1p.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(log1p.f32 (expm1.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(+.f32 0 (*.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O))
(+.f32 (log.f32 (sqrt.f32 (exp.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)))) (log.f32 (sqrt.f32 (exp.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)))))
(+.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O))) 2)) (log.f32 (cbrt.f32 (exp.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O))) 1)
(*.f32 (neg.f32 sinTheta_i) (/.f32 1 (/.f32 v sinTheta_O)))
(.f32 1 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O))
(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)) 2) (cbrt.f32 (*.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)))
(.f32 (sqrt.f32 (.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)) (sqrt.f32 (*.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)))
(*.f32 (/.f32 (neg.f32 sinTheta_i) v) sinTheta_O)
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(exp.f32 (-.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))
(exp.f32 (*.f32 (-.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)) 1))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))))) 1)
(*.f32 1 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))))
(*.f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) 2) (cbrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(*.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(/.f32 (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) (pow.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) 3)) (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (-.f32 (pow.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) 2) (.f32 (log.f32 (/.f32 1/2 v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (pow.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) 2)) (-.f32 (log.f32 (/.f32 1/2 v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))))
(pow.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))) 1)
(pow.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))) 2) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) 1/3)
(pow.f32 (sqrt.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) 2)
(log.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))))))
(log.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v))))
(log.f32 (*.f32 (pow.f32 (exp.f32 cosTheta_O) (/.f32 cosTheta_i v)) (/.f32 1/2 v)))
(cbrt.f32 (*.f32 (pow.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v))) 2) (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(expm1.f32 (log1p.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(exp.f32 (log.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))) 1))
(log1p.f32 (expm1.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (log.f32 (/.f32 1/2 v)))
(fma.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)) (log.f32 (/.f32 1/2 v)))
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))
(fma.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 1 v) (log.f32 (/.f32 1/2 v)))
(fma.f32 1 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(fma.f32 1 (*.f32 cosTheta_O (/.f32 cosTheta_i v)) (log.f32 (/.f32 1/2 v)))
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v))) 2) (cbrt.f32 (.f32 cosTheta_O (/.f32 cosTheta_i 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))) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(fma.f32 (sqrt.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v))) (sqrt.f32 (.f32 cosTheta_O (/.f32 cosTheta_i 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))) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))

simplify194.0ms (2%)

Algorithm

1×	egg-herbie

Rules

718×	`times-frac`
702×	`associate-r`
666×	`fma-def`
650×	`associate-/l*`
538×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	801	4294988534
1	2098	18318

Stop Event

1×	node limit

Counts

568 → 430

Calls

Call 1

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

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

eval271.0ms (2.8%)

Compiler: Compiled 15488 to 10147 computations (34.5% saved)

prune108.0ms (1.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	517	6	523
Fresh	1	4	5
Picked	3	2	5
Done	1	0	1
Total	522	12	534

Accurracy

100.0%

Counts

534 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	99.9%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	6.1%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
▶	6.2%	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	99.8%	(*.f32 (pow.f32 (E.f32) (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (exp.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))))
	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	98.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
✓	15.1%	(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	12.8%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
	6.4%	1
▶	99.8%	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	99.9%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	6.1%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
▶	6.2%	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	99.8%	(*.f32 (pow.f32 (E.f32) (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.9%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (exp.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))))
	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	98.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
✓	15.1%	(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	12.8%	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
	6.4%	1

Compiler

Compiled 746 to 586 computations (21.4% saved)

localize659.0ms (6.8%)

Local Accuracy

Found 17 expressions with local accuracy:

New	Accuracy	Program
	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	99.8%	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
	76.8%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	100.0%	(log.f32 (/.f32 1/2 v))
	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	100.0%	(*.f32 cosTheta_i cosTheta_O)
✓	100.0%	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
✓	99.9%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	100.0%	(*.f32 cosTheta_i cosTheta_O)
	76.8%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	99.3%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	99.2%	(*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)
✓	94.7%	(exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
✓	90.1%	(exp.f32 (cbrt.f32 (exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))))

Compiler

Compiled 326 to 188 computations (42.3% saved)

series70.0ms (0.7%)

Counts

9 → 144

Calls

45 calls:

Time	Variable		Point	Expression
28.0ms	v	@	0	(*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)
17.0ms	v	@	-inf	(*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)
15.0ms	v	@	inf	(*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)
3.0ms	v	@	-inf	(pow.f32 (exp.f32 1) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
1.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

rewrite86.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

690×	`add-sqr-sqrt`
668×	`pow1`
668×	`*-un-lft-identity`
652×	`add-exp-log`
648×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	239
1	682	225

Stop Event

1×	node limit

Counts

9 → 226

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 1)
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(.f32 1 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 2) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 1)
(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3)
(pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 2)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(sqrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2))
(log.f32 (exp.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))
(cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3))
(expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))) 1)
(*.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2))
(*.f32 1 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))
(*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(*.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) 3) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
(*.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(/.f32 (pow.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) 3) (pow.f32 (+.f32 48038761/100000000 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (*.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
(/.f32 (pow.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) 3) (pow.f32 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))
(pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1)
(pow.f32 (E.f32) (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(pow.f32 (exp.f32 3) (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 3) 1/3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2) 2)
(pow.f32 (exp.f32 (sqrt.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))) (sqrt.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)) 2)) (cbrt.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))
(sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 6))
(log.f32 (exp.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))))
(cbrt.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 3))
(expm1.f32 (log1p.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(log1p.f32 (expm1.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3)))
(+.f32 0 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))
(+.f32 (log.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2)) (log.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2)))
(+.f32 (log.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))) 1)
(pow.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 1)
(pow.f32 (cbrt.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)) 3)
(pow.f32 (pow.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)) 2)
(sqrt.f32 (pow.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 2))
(log.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))
(log.f32 (+.f32 1 (-.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1)))
(cbrt.f32 (pow.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3) 3))
(expm1.f32 (log1p.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))
(exp.f32 (log.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))
(exp.f32 (.f32 (log.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)) 1))
(log1p.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1)
(*.f32 1 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(/.f32 (exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (exp.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1)
(pow.f32 (E.f32) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(pow.f32 (exp.f32 (fma.f32 cosTheta_i cosTheta_O -1)) (/.f32 1 v))
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2)
(pow.f32 (exp.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (sqrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2)) (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(sqrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))
(log.f32 (exp.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (fma.f32 (neg.f32 (pow.f32 v -1/2)) (pow.f32 v -1/2) (/.f32 1 v)))
(+.f32 0 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(+.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
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(*.f32 1 (log.f32 (/.f32 1/2 v)))
(*.f32 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) (cbrt.f32 (log.f32 (/.f32 1/2 v))))
(*.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))))
(pow.f32 (log.f32 (/.f32 1/2 v)) 1)
(pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 3)
(pow.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) 2)
(pow.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) 1/3)
(neg.f32 (log.f32 (/.f32 v 1/2)))
(sqrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))
(cbrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3))
(expm1.f32 (log1p.f32 (log.f32 (/.f32 1/2 v))))
(exp.f32 (log.f32 (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (log.f32 (log.f32 (/.f32 1/2 v))) 1))
(log1p.f32 (-.f32 (/.f32 1/2 v) 1))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))
(.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (exp.f32 (neg.f32 (/.f32 1 v))))
(.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (pow.f32 (E.f32) (neg.f32 (/.f32 1 v))))
(*.f32 (exp.f32 6931/10000) (exp.f32 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))) (sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))))
(*.f32 (pow.f32 (E.f32) 6931/10000) (pow.f32 (E.f32) (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))
(*.f32 (pow.f32 1 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))) (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))) (pow.f32 (cbrt.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))
(*.f32 (pow.f32 (sqrt.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))) (pow.f32 (sqrt.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))
(/.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (exp.f32 (/.f32 1 v)))
(/.f32 (neg.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O))))) (neg.f32 (exp.f32 (/.f32 1 v))))
(sqrt.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))) 2))
(log.f32 (exp.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 1 v)))))

simplify175.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1160×	`fma-neg`
674×	`associate-r`
626×	`associate-l`
550×	`fma-def`
432×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	673	16004
1	1765	13130
2	7595	13108

Stop Event

1×	node limit

Counts

370 → 409

Calls

Call 1

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

eval325.0ms (3.3%)

Compiler: Compiled 17766 to 12006 computations (32.4% saved)

prune158.0ms (1.6%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	713	4	717
Fresh	1	4	5
Picked	2	3	5
Done	2	0	2
Total	718	11	729

Accurracy

100.0%

Counts

729 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(pow.f32 (E.f32) (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	99.9%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	6.1%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
✓	6.2%	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	99.8%	(*.f32 (pow.f32 (E.f32) (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.9%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.9%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (exp.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))))
	99.8%	(.f32 (exp.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (exp.f32 (cbrt.f32 (exp.f32 (expm1.f32 (log1p.f32 (.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))))))
	98.1%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1

Compiler

Compiled 666 to 442 computations (33.6% saved)

regimes137.0ms (1.4%)

Counts

30 → 1

Calls

Call 1

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

Outputs

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

Calls

9 calls:

37.0ms	(+.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))))
14.0ms	sinTheta_i
14.0ms	sinTheta_O
13.0ms	cosTheta_i
13.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	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)))))`
99.9%	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))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 569 to 360 computations (36.7% saved)

regimes113.0ms (1.2%)

Counts

28 → 1

Calls

Call 1

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

Outputs

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

Calls

9 calls:

16.0ms	(*.f32 sinTheta_i sinTheta_O)
14.0ms	sinTheta_O
14.0ms	cosTheta_O
14.0ms	sinTheta_i
13.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	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)))))`
99.9%	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))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 501 to 316 computations (36.9% saved)

regimes145.0ms (1.5%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

9 calls:

52.0ms	cosTheta_O
13.0ms	sinTheta_O
12.0ms	sinTheta_i
12.0ms	cosTheta_i
10.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	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)))))`
99.9%	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))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 473 to 299 computations (36.8% saved)

regimes106.0ms (1.1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

9 calls:

22.0ms	(+.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))))
13.0ms	(*.f32 sinTheta_i sinTheta_O)
12.0ms	sinTheta_O
12.0ms	sinTheta_i
12.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	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)))))`
99.9%	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))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 401 to 262 computations (34.7% saved)

regimes76.0ms (0.8%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

9 calls:

11.0ms	sinTheta_i
10.0ms	sinTheta_O
9.0ms	cosTheta_i
9.0ms	cosTheta_O
8.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	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)))))`
99.9%	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))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 315 to 206 computations (34.6% saved)

regimes50.0ms (0.5%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

6 calls:

20.0ms	sinTheta_i
6.0ms	cosTheta_i
5.0ms	cosTheta_O
5.0ms	v
5.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
98.1%	1	`cosTheta_i`
98.1%	1	`cosTheta_O`
98.1%	1	`sinTheta_i`
98.1%	1	`sinTheta_O`
98.1%	1	`v`
98.1%	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 102 to 68 computations (33.3% saved)

regimes20.0ms (0.2%)

Accuracy

Total -0.1b remaining (-0.4%)

Threshold costs -0.1b (-0.4%)

Counts

3 → 1

Calls

Call 1

Inputs
1
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))

Outputs
1

Calls

6 calls:

4.0ms	cosTheta_i
3.0ms	sinTheta_O
3.0ms	sinTheta_i
3.0ms	v
3.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
6.4%	1	`sinTheta_i`
6.4%	1	`sinTheta_O`
6.4%	1	`cosTheta_i`
6.4%	1	`cosTheta_O`
6.4%	1	`v`
6.4%	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 58 to 45 computations (22.4% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	351
1	57	351
2	65	351
3	71	351
4	77	351

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 151 to 120 computations (20.5% saved)

soundness749.0ms (7.7%)

Rules

1828×	`fma-def`
1828×	`fma-def`
1090×	`associate-r`
1016×	`exp-sum`
1016×	`exp-sum`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	55	65
2	149	61
3	580	57
4	2989	57
0	33	270
1	797	262
0	39	450
1	900	450
0	673	28965
1	1894	24017
0	24	69
1	55	65
2	149	61
3	580	57
4	2989	57
0	39	450
1	900	450
0	38	339
1	857	315

Stop Event

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

Compiler

Compiled 820 to 515 computations (37.2% saved)

end0.0ms (0%)

preprocess106.0ms (1.1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 474 to 344 computations (27.4% saved)

analyze523.0ms (5.4%)

sample2.5s (25.9%)

preprocess65.0ms (0.7%)

simplify37.0ms (0.4%)

eval2.0ms (0%)

prune3.0ms (0%)

localize352.0ms (3.6%)

series50.0ms (0.5%)

rewrite87.0ms (0.9%)

simplify225.0ms (2.3%)

eval159.0ms (1.6%)

prune71.0ms (0.7%)

localize612.0ms (6.3%)

series70.0ms (0.7%)

rewrite100.0ms (1%)

simplify226.0ms (2.3%)

eval252.0ms (2.6%)

prune96.0ms (1%)

localize614.0ms (6.3%)

series25.0ms (0.3%)

rewrite99.0ms (1%)

simplify194.0ms (2%)

eval271.0ms (2.8%)

prune108.0ms (1.1%)

localize659.0ms (6.8%)

series70.0ms (0.7%)

rewrite86.0ms (0.9%)

simplify175.0ms (1.8%)

eval325.0ms (3.3%)

prune158.0ms (1.6%)

regimes137.0ms (1.4%)

regimes113.0ms (1.2%)

regimes145.0ms (1.5%)

regimes106.0ms (1.1%)

regimes76.0ms (0.8%)

regimes50.0ms (0.5%)

regimes20.0ms (0.2%)

simplify11.0ms (0.1%)

soundness749.0ms (7.7%)

end0.0ms (0%)

preprocess106.0ms (1.1%)

Profiling