Metrics for HairBSDF, Mp, lower

analyze525.0ms (6%)

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)

sample2.3s (26.8%)

Results

2.3s	8256×	body	256	valid
30.0ms	127×	body	256	invalid

Bogosity

preprocess69.0ms (0.8%)

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	1205
1	461	1129
2	1373	1037
3	6228	1037

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 30 to 22 computations (26.7% saved)

eval1.0ms (0%)

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

prune4.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.5%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.5%	(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)))))
▶	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.5%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.5%	(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)))))

Compiler

Compiled 170 to 122 computations (28.2% saved)

localize548.0ms (6.3%)

Localize:

Found 12 expressions with local error:

New	Accuracy	Program
✓	99.7%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.6%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
✓	99.5%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.2%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.9%	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.3%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.2%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
✓	99.7%	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	99.6%	(log.f32 (/.f32 1 (*.f32 2 v)))
✓	81.1%	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	77.8%	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 351 to 141 computations (59.8% saved)

series94.0ms (1.1%)

Counts

12 → 480

Calls

120 calls:

Time	Variable		Point	Expression
25.0ms	v	@	0	(log.f32 (/.f32 1 (*.f32 2 v)))
15.0ms	v	@	-inf	(log.f32 (/.f32 1 (*.f32 2 v)))
8.0ms	v	@	inf	(log.f32 (/.f32 1 (*.f32 2 v)))
6.0ms	cosTheta_i	@	-inf	(.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))
6.0ms	cosTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite142.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

874×	`add-sqr-sqrt`
854×	`pow1`
854×	`*-un-lft-identity`
816×	`add-exp-log`
814×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	268
1	1032	268

Stop Event

1×	node limit

Counts

12 → 248

Calls

Call 1

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

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

simplify218.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

662×	`fma-def`
540×	`associate-r`
538×	`associate-l`
458×	`sub-neg`
448×	`distribute-lft-neg-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	461	20800
1	1336	20184
2	5222	19098

Stop Event

1×	node limit

Counts

728 → 243

Calls

Call 1

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

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

eval135.0ms (1.6%)

Compiler: Compiled 9037 to 4462 computations (50.6% saved)

prune53.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	238	5	243
Fresh	0	0	0
Picked	2	1	3
Done	0	0	0
Total	240	6	246

Accuracy

99.9%

Counts

246 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.7%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
✓	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.7%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
▶	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))
▶	4.7%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
✓	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.7%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
▶	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))))

Compiler

Compiled 382 to 298 computations (22% saved)

localize436.0ms (5%)

Localize:

Found 15 expressions with local error:

New	Accuracy	Program
✓	99.8%	(+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v)))
✓	99.8%	(-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (*.f32 cosTheta_i (/.f32 cosTheta_O v))) (/.f32 1 v))
✓	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.2%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	100.0%	(/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v)
✓	100.0%	(*.f32 sinTheta_O sinTheta_i)
✓	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
✓	99.3%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
✓	99.0%	(/.f32 v (exp.f32 6931/10000))
✓	99.2%	(/.f32 (exp.f32 6931/10000) v)
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	81.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 243 to 124 computations (49% saved)

series24.0ms (0.3%)

Counts

15 → 289

Calls

117 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta_O	@	-inf	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
1.0ms	sinTheta_O	@	0	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
1.0ms	cosTheta_O	@	0	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
1.0ms	v	@	0	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
0.0ms	cosTheta_O	@	0	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))

rewrite101.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

766×	`add-sqr-sqrt`
750×	`pow1`
750×	`*-un-lft-identity`
716×	`add-exp-log`
714×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	321
1	772	301

Stop Event

1×	node limit

Counts

15 → 300

Calls

Call 1

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

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

simplify207.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1396×	`log-prod`
828×	`associate-r`
800×	`associate-l`
724×	`fma-def`
506×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	739	17857
1	1829	16193
2	7944	16193

Stop Event

1×	node limit

Counts

589 → 443

Calls

Call 1

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

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

eval173.0ms (2%)

Compiler: Compiled 9537 to 6144 computations (35.6% saved)

prune87.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	450	6	456
Fresh	0	0	0
Picked	5	0	5
Done	0	1	1
Total	455	7	462

Accuracy

100.0%

Counts

462 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) v))
▶	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	12.9%	(exp.f32 (/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i)))
▶	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.5%	1
✓	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.8%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) v))
▶	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	12.9%	(exp.f32 (/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i)))
▶	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.5%	1

Compiler

Compiled 374 to 298 computations (20.3% saved)

localize436.0ms (5%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
✓	99.8%	(+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))
✓	99.8%	(-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	100.0%	(/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	100.0%	(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	99.8%	(exp.f32 (/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i)))
✓	99.4%	(/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i))
✓	100.0%	(/.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))) v)
✓	99.9%	(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v))
✓	99.8%	(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 1 v)))
✓	99.6%	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)

Compiler

Compiled 204 to 118 computations (42.2% saved)

series26.0ms (0.3%)

Counts

14 → 311

Calls

90 calls:

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

rewrite105.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`add-sqr-sqrt`
792×	`pow1`
792×	`*-un-lft-identity`
758×	`add-exp-log`
756×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	320
1	798	320

Stop Event

1×	node limit

Counts

14 → 266

Calls

Call 1

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

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

simplify146.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

882×	`associate-r`
862×	`fma-def`
778×	`associate-l`
502×	`times-frac`
480×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	780	17899
1	1969	16809

Stop Event

1×	node limit

Counts

577 → 476

Calls

Call 1

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

eval213.0ms (2.5%)

Compiler: Compiled 10944 to 7784 computations (28.9% saved)

prune106.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	513	6	519
Fresh	0	1	1
Picked	3	2	5
Done	1	0	1
Total	517	9	526

Accuracy

100.0%

Counts

526 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2)
▶	6.3%	(-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
	99.5%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
▶	99.8%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v))
✓	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
▶	99.4%	(.f32 1/2 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v)))
▶	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.5%	1
▶	99.5%	(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2)
▶	6.3%	(-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
	99.5%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
▶	99.8%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v))
✓	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
▶	99.4%	(.f32 1/2 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v)))
▶	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.5%	1

Compiler

Compiled 494 to 430 computations (13% saved)

localize397.0ms (4.6%)

Localize:

Found 13 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	99.9%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.0%	(sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
	99.9%	(-.f32 6931/10000 (/.f32 1 v))
	99.8%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	99.6%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v))
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	100.0%	(-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
	99.5%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	100.0%	(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))

Compiler

Compiled 182 to 133 computations (26.9% saved)

series21.0ms (0.2%)

Counts

8 → 108

Calls

30 calls:

Time	Variable		Point	Expression
15.0ms	v	@	inf	(sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
1.0ms	v	@	-inf	(sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
1.0ms	v	@	inf	(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
1.0ms	v	@	inf	(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
0.0ms	v	@	-inf	(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)

rewrite98.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

594×	`add-sqr-sqrt`
576×	`pow1`
576×	`*-un-lft-identity`
556×	`add-exp-log`
554×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	192
1	641	192

Stop Event

1×	node limit

Counts

8 → 264

Calls

Call 1

Inputs
(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
(-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
(exp.f32 (/.f32 -1 v))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v))
(sqrt.f32 (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))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Outputs
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))) 1)
(*.f32 1 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 1)
(*.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1 (exp.f32 (/.f32 1 v))))
(*.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))))
(*.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) 1))
(*.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) 1))
(*.f32 (pow.f32 1 (+.f32 6931/10000 (/.f32 1 v))) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 6931/10000 (/.f32 1 v))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (pow.f32 (sqrt.f32 (E.f32)) (+.f32 6931/10000 (/.f32 1 v))) (pow.f32 (sqrt.f32 (E.f32)) (+.f32 6931/10000 (/.f32 1 v))))
(/.f32 1 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 6931/10000)))
(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
(/.f32 (*.f32 (exp.f32 6931/10000) 1) (exp.f32 (/.f32 1 v)))
(/.f32 (neg.f32 (exp.f32 6931/10000)) (neg.f32 (exp.f32 (/.f32 1 v))))
(sqrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v))))
(log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (+.f32 6931/10000 (/.f32 1 v)))
(log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v))) 1)
(*.f32 1 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (/.f32 1 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v))
(*.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 1)
(.f32 (cbrt.f32 (pow.f32 v -2)) (.f32 (/.f32 1 (cbrt.f32 v)) (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (/.f32 1 v)))
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)) (cbrt.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 2)))
(*.f32 (cbrt.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 2)) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (pow.f32 v -1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (sqrt.f32 v)))
(.f32 (pow.f32 v -1/2) (.f32 (pow.f32 v -1/2) (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (/.f32 1 v)))
(*.f32 (sqrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)) (sqrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (neg.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (/.f32 1 v))
(*.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (sqrt.f32 v)) (pow.f32 v -1/2))
(*.f32 (/.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) 1) (/.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) v))
(*.f32 (/.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (/.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 v)) (/.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 v)))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) 1) (/.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) v))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 1) (/.f32 1 v))
(*.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (pow.f32 (cbrt.f32 v) 2)) (/.f32 1 (cbrt.f32 v)))
(.f32 (.f32 (/.f32 1 v) (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (.f32 (/.f32 1 v) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))))
(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)))
(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (pow.f32 v -1/2)) (pow.f32 v -1/2))
(pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)) 3)
(pow.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)) 2)
(pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) -1)
(neg.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (neg.f32 v)))
(sqrt.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 2))
(log.f32 (exp.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v))))
(cbrt.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v) 3))
(cbrt.f32 (*.f32 (pow.f32 v -3) (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 3)))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 3) (pow.f32 v -3)))
(cbrt.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 1 v)) (log.f32 v)))
(exp.f32 (*.f32 (-.f32 (+.f32 6931/10000 (/.f32 1 v)) (log.f32 v)) 1))
(log1p.f32 (expm1.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) v)))
(+.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
(+.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i) 1)
(.f32 1 (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)))
(.f32 (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) 1)
(.f32 (cbrt.f32 (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) (cbrt.f32 (pow.f32 (+.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) 2)))
(.f32 (cbrt.f32 (pow.f32 (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i)) 2)) (cbrt.f32 (+.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
(.f32 (sqrt.f32 (+.f32 1 (.f32 (/.f32 sinTheta_O v) sinTheta_i))) (sqrt.f32 (+.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))))
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(/.f32 (neg.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) (pow.f32 v -3))) (neg.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (+.f32 (pow.f32 v -2) (/.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) v)))))
(/.f32 (neg.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) (neg.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)) 3)) (+.f32 48038761/100000000 (-.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) (.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))))
(/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) (pow.f32 v -3)) (+.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) (-.f32 (pow.f32 v -2) (/.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) v))))
(/.f32 (-.f32 48038761/100000000 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) (-.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 1)
(pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) 3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) 2)
(sqrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2))
(log.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(exp.f32 (log.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) 1))
(log1p.f32 (expm1.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(fma.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
(fma.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)))) (/.f32 1 v))
(fma.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 1 v))
(-.f32 (exp.f32 (log1p.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))) 1)
(.f32 1 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1)
(.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (sqrt.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))
(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(.f32 (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (cbrt.f32 (pow.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2)))
(.f32 (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (.f32 (cbrt.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))) (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(.f32 (cbrt.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2)) (cbrt.f32 (.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1/4) (.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1/4) (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(.f32 (.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1/4)) (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1/4))
(.f32 (.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(/.f32 1 (/.f32 (exp.f32 (/.f32 1 v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(/.f32 (neg.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (neg.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1)
(pow.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) 2)
(pow.f32 (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) 3)
(pow.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2) 1/2)
(pow.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 3) 1/3)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))) (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2))
(log.f32 (exp.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(cbrt.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 3))
(expm1.f32 (log1p.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))

simplify183.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

768×	`associate-r`
690×	`times-frac`
648×	`associate-l`
638×	`fma-def`
534×	`associate-/l*`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	696	15202
1	1757	13806
2	7772	13798

Stop Event

1×	node limit

Counts

372 → 453

Calls

Call 1

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

Outputs
(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v))))
(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(pow.f32 (pow.f32 (E.f32) 6931) 1/10000)
(+.f32 (.f32 -1 (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(fma.f32 -1 (*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(-.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 2)))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(fma.f32 -1 (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (*.f32 v v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(-.f32 (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (+.f32 (.f32 -1/6 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 3) (pow.f32 v 3)))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 2)))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
(fma.f32 -1 (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (fma.f32 -1/6 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 3))) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
(-.f32 (fma.f32 -1/6 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(pow.f32 (pow.f32 (E.f32) 6931) 1/10000)
(+.f32 (.f32 -1 (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(fma.f32 -1 (*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(-.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 2)))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(fma.f32 -1 (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (*.f32 v v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(-.f32 (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) v))) (+.f32 (.f32 -1/6 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 3) (pow.f32 v 3)))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 2)))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
(fma.f32 -1 (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)) (fma.f32 -1/6 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 3))) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
(-.f32 (fma.f32 -1/6 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))
(/.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v)))) v)
(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
(/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)
(/.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v)))) v)
(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
(/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)
(/.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v)))) v)
(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
(/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)
(/.f32 (exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (/.f32 1 v)))) v)
(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
(/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)
(.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v))
(*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v)
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) (pow.f32 v 2)))) (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v)))
(fma.f32 -1 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(-.f32 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) (pow.f32 v 2)))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 3)))) (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v))))
(fma.f32 -1 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 3))) (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
(-.f32 (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (pow.f32 v 3)) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v)) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) (pow.f32 v 2)))) (+.f32 (.f32 -1/6 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 3) (pow.f32 v 4)))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 3)))) (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v)))))
(fma.f32 -1 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (fma.f32 -1/6 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 4))) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 3))) (*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))))
(-.f32 (fma.f32 -1/6 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (pow.f32 v 4)) (fma.f32 1/2 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (pow.f32 v 3)) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v))) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)))
(.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v))
(*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))
(/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v)
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) (pow.f32 v 2)))) (.f32 (pow.f32 (*.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v)))
(fma.f32 -1 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (*.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000)))
(-.f32 (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) v) (/.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (*.f32 v v)))
(+.f32 (.f32 -1 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (log.f32 (E.f32)) (pow.f32 v 2)))) (+.f32 (.f32 1/2 (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 (pow.f32 (log.f32 (E.f32)) 2) (pow.f32 v 3)))) (.f32 (pow.f32 (.f32 1 (pow.f32 (E.f32) 6931)) 1/10000) (/.f32 1 v))))
(fma.f32 -1 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (.f32 v v))) (fma.f32 1/2 (.f32 (pow.f32 (pow.f32 (E.f32) 6931) 1/10000) (/.f32 1 (pow.f32 v 3))) (.f32 (/.f32 1 v) (pow.f32 (pow.f32 (E.f32) 6931) 1/10000))))
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(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(.f32 (.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))) (cbrt.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))) (.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))) (cbrt.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))))))
(.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))) (pow.f32 (cbrt.f32 (sqrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))) 4))
(/.f32 1 (/.f32 (exp.f32 (/.f32 1 v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(/.f32 (neg.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (neg.f32 (exp.f32 (/.f32 1 v))))
(/.f32 (*.f32 (/.f32 1/2 v) (neg.f32 (exp.f32 6931/10000))) (neg.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (/.f32 (/.f32 -1/2 v) -1) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 1)
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (sqrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) 2)
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (cbrt.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))) 3)
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2) 1/2)
(sqrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) 2))
(fabs.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))
(pow.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 3) 1/3)
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))) (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(sqrt.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 2))
(sqrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v)))) 2))
(fabs.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v)))
(log.f32 (exp.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(log.f32 (+.f32 1 (expm1.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(cbrt.f32 (pow.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))) 3))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(expm1.f32 (log1p.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(log1p.f32 (expm1.f32 (.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))

eval323.0ms (3.7%)

Compiler: Compiled 12672 to 10298 computations (18.7% saved)

prune112.0ms (1.3%)

Pruning

13 alts after pruning (6 fresh and 7 done)

	Pruned	Kept	Total
New	596	4	600
Fresh	0	2	2
Picked	0	5	5
Done	0	2	2
Total	596	13	609

Accuracy

100.0%

Counts

609 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.5%	(pow.f32 (sqrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2)
✓	6.3%	(-.f32 1 (*.f32 (/.f32 sinTheta_O v) sinTheta_i))
	6.3%	(+.f32 (*.f32 (/.f32 sinTheta_O v) sinTheta_i) 1)
	99.5%	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 2) (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
	21.3%	(*.f32 sinTheta_i (/.f32 (neg.f32 sinTheta_O) v))
✓	99.8%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v))
✓	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
✓	99.4%	(.f32 1/2 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v)))
	37.8%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
	21.3%	(neg.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
✓	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.5%	(exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	6.5%	1

Compiler

Compiled 474 to 350 computations (26.2% saved)

regimes104.0ms (1.2%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

9 calls:

13.0ms	sinTheta_O
12.0ms	cosTheta_O
12.0ms	cosTheta_i
12.0ms	sinTheta_i
12.0ms	v

Results

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

Compiler

Compiled 391 to 272 computations (30.4% saved)

regimes50.0ms (0.6%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	cosTheta_O
10.0ms	sinTheta_O
9.0ms	sinTheta_i
9.0ms	cosTheta_i
9.0ms	v

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`

Compiler

Compiled 183 to 121 computations (33.9% saved)

regimes38.0ms (0.4%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	sinTheta_i
7.0ms	v
7.0ms	cosTheta_i
7.0ms	sinTheta_O
7.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
98.2%	1	`cosTheta_i`
98.2%	1	`cosTheta_O`
98.2%	1	`sinTheta_i`
98.2%	1	`sinTheta_O`
98.2%	1	`v`

Compiler

Compiled 100 to 67 computations (33% saved)

regimes27.0ms (0.3%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
37.8%	1	`cosTheta_i`
37.8%	1	`cosTheta_O`
37.8%	1	`sinTheta_i`
37.8%	1	`sinTheta_O`
37.8%	1	`v`

Compiler

Compiled 69 to 47 computations (31.9% saved)

regimes21.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

5.0ms	cosTheta_i
4.0ms	cosTheta_O
4.0ms	sinTheta_i
4.0ms	sinTheta_O
4.0ms	v

Results

Accuracy	Segments	Branch
21.3%	1	`sinTheta_i`
21.3%	1	`sinTheta_O`
21.3%	1	`cosTheta_O`
21.3%	1	`cosTheta_i`
21.3%	1	`v`

Compiler

Compiled 48 to 37 computations (22.9% saved)

regimes15.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
6.5%	1	`v`
6.5%	1	`sinTheta_i`
6.5%	1	`sinTheta_O`
6.5%	1	`cosTheta_i`
6.5%	1	`cosTheta_O`

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	108
1	42	108
2	54	108
3	69	108
4	80	108
5	83	108
6	84	108

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 68 to 57 computations (16.2% saved)

soundness1.1s (12.3%)

Rules

1396×	`log-prod`
882×	`associate-r`
862×	`fma-def`
838×	`distribute-neg-in`
838×	`distribute-neg-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	33	321
1	772	301
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	461	20800
1	1336	20184
2	5222	19098
0	739	17857
1	1829	16193
2	7944	16193
0	780	17899
1	1969	16809
0	696	15202
1	1757	13806
2	7772	13798

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 320 to 192 computations (40% saved)

end0.0ms (0%)

preprocess53.0ms (0.6%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 210 to 164 computations (21.9% saved)

analyze525.0ms (6%)

sample2.3s (26.8%)

preprocess69.0ms (0.8%)

eval1.0ms (0%)

prune4.0ms (0%)

localize548.0ms (6.3%)

series94.0ms (1.1%)

rewrite142.0ms (1.6%)

simplify218.0ms (2.5%)

eval135.0ms (1.6%)

prune53.0ms (0.6%)

localize436.0ms (5%)

series24.0ms (0.3%)

rewrite101.0ms (1.2%)

simplify207.0ms (2.4%)

eval173.0ms (2%)

prune87.0ms (1%)

localize436.0ms (5%)

series26.0ms (0.3%)

rewrite105.0ms (1.2%)

simplify146.0ms (1.7%)

eval213.0ms (2.5%)

prune106.0ms (1.2%)

localize397.0ms (4.6%)

series21.0ms (0.2%)

rewrite98.0ms (1.1%)

simplify183.0ms (2.1%)

eval323.0ms (3.7%)

prune112.0ms (1.3%)

regimes104.0ms (1.2%)

regimes50.0ms (0.6%)

regimes38.0ms (0.4%)

regimes27.0ms (0.3%)

regimes21.0ms (0.2%)

regimes15.0ms (0.2%)

simplify8.0ms (0.1%)

soundness1.1s (12.3%)

end0.0ms (0%)

preprocess53.0ms (0.6%)

Profiling