Metrics for HairBSDF, Mp, lower

analyze568.0ms (5.5%)

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)

sample2.4s (23.1%)

Results

2.3s	8256×	body	256	valid
28.0ms	119×	body	256	invalid

Bogosity

preprocess315.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

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

Problems

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 169 to 80 computations (52.7% saved)

eval1.0ms (0%)

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

prune3.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize356.0ms (3.5%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.8%	(+.f32 (/.f32 -1 v) 6931/10000)
✓	99.8%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.5%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.3%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.8%	(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)))))
✓	99.8%	(+.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))))
✓	99.4%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.2%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series54.0ms (0.5%)

Counts

8 → 336

Calls

84 calls:

Time	Variable		Point	Expression
15.0ms	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))))
6.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
3.0ms	sinTheta_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))))
2.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	v	@	inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite81.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	252
1	803	244

Stop Event

1×	node limit

Counts

8 → 158

Calls

Call 1

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

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

simplify202.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1526×	`fma-neg`
768×	`log-prod`
628×	`exp-prod`
542×	`associate-r`
506×	`exp-sum`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	480	21660
1	1331	20136
2	5654	20036

Stop Event

1×	node limit

Counts

494 → 283

Calls

Call 1

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

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

eval165.0ms (1.6%)

Compiler: Compiled 9904 to 5624 computations (43.2% saved)

prune65.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	274	9	283
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	276	9	285

Accuracy

99.9%

Counts

285 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
▶	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
	12.0%	(exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
▶	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
	12.0%	(exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))

Compiler

Compiled 844 to 608 computations (28% saved)

localize729.0ms (7.1%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
✓	99.8%	(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.7%	(cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.5%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	97.8%	(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
✓	99.8%	(+.f32 6931/10000 (/.f32 -1 v))
✓	99.8%	(pow.f32 (E.f32) (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.5%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	99.4%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	100.0%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
✓	99.0%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
✓	99.7%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	78.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 404 to 183 computations (54.7% saved)

series98.0ms (1%)

Counts

15 → 436

Calls

156 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta_O	@	0	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v)
12.0ms	sinTheta_O	@	0	(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
7.0ms	sinTheta_i	@	0	(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
6.0ms	v	@	inf	(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)
4.0ms	v	@	-inf	(pow.f32 (cbrt.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3)

rewrite139.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1084×	`pow1`
1036×	`add-exp-log`
1034×	`add-log-exp`
1026×	`add-cube-cbrt`
1024×	`add-cbrt-cube`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	501
1	1132	501

Stop Event

1×	node limit

Counts

15 → 158

Calls

Call 1

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

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

simplify334.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1058×	`associate-+r+`
922×	`distribute-lft-in`
884×	`distribute-rgt-in`
816×	`times-frac`
646×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1033	47094
1	3591	40548

Stop Event

1×	node limit

Counts

594 → 463

Calls

Call 1

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

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

eval693.0ms (6.7%)

Compiler: Compiled 31461 to 21129 computations (32.8% saved)

prune128.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	486	9	495
Fresh	1	3	4
Picked	4	1	5
Done	0	0	0
Total	491	13	504

Accuracy

99.9%

Counts

504 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
▶	50.4%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000)))))) (/.f32 1/2 v))
✓	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
▶	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	12.0%	(exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v))
	98.2%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	12.0%	(exp.f32 (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))
	6.4%	1
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
▶	50.4%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000)))))) (/.f32 1/2 v))
✓	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
▶	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3))
▶	98.2%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	12.0%	(exp.f32 (/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v))
	98.2%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	12.0%	(exp.f32 (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))
	6.4%	1

Compiler

Compiled 1168 to 844 computations (27.7% saved)

localize699.0ms (6.8%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
	99.5%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	99.4%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.1%	(*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000))
✓	33.2%	(/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000))))
✓	99.8%	(-.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)))
✓	99.7%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
	78.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	99.9%	(exp.f32 (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))
✓	99.3%	(*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))
✓	100.0%	(log.f32 (/.f32 1/2 v))
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))

Compiler

Compiled 368 to 203 computations (44.8% saved)

series61.0ms (0.6%)

Counts

12 → 193

Calls

72 calls:

Time	Variable		Point	Expression
18.0ms	v	@	0	(/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000))))
16.0ms	v	@	0	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
11.0ms	v	@	-inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
4.0ms	v	@	inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
1.0ms	v	@	inf	(/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000))))

rewrite101.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

922×	`add-sqr-sqrt`
898×	`pow1`
896×	`*-un-lft-identity`
864×	`add-exp-log`
862×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	292
1	932	292

Stop Event

1×	node limit

Counts

12 → 116

Calls

Call 1

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

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

simplify128.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

650×	`associate-r`
602×	`associate-l`
574×	`unswap-sqr`
522×	`fma-neg`
448×	`fma-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	449	9565
1	1164	9131
2	5213	8951

Stop Event

1×	node limit

Counts

309 → 274

Calls

Call 1

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

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

eval190.0ms (1.9%)

Compiler: Compiled 8253 to 5484 computations (33.6% saved)

prune82.0ms (0.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	323	3	326
Fresh	2	5	7
Picked	3	2	5
Done	0	1	1
Total	328	11	339

Accuracy

99.9%

Counts

339 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	6.3%	(-.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
✓	50.4%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000)))))) (/.f32 1/2 v))
✓	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2))) (/.f32 1/2 v))
▶	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
▶	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3))
▶	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1
▶	6.3%	(-.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
	99.7%	(.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (cbrt.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (/.f32 1/2 v))
✓	50.4%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000)))))) (/.f32 1/2 v))
✓	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2))) (/.f32 1/2 v))
▶	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
▶	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3))
▶	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1

Compiler

Compiled 896 to 644 computations (28.1% saved)

localize437.0ms (4.3%)

Localize:

Found 13 expressions with local error:

New	Accuracy	Program
	99.7%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	99.7%	(cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
✓	97.8%	(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3)
	78.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	100.0%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.8%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	100.0%	(-.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
✓	99.3%	(*.f32 sinTheta_i (/.f32 sinTheta_O v))
✓	100.0%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
✓	99.8%	(exp.f32 (/.f32 -1 v))
	99.0%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))

Compiler

Compiled 217 to 134 computations (38.2% saved)

series32.0ms (0.3%)

Counts

10 → 155

Calls

54 calls:

Time	Variable		Point	Expression
7.0ms	v	@	-inf	(cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
6.0ms	v	@	inf	(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3)
4.0ms	v	@	-inf	(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3)
3.0ms	cosTheta_O	@	0	(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3)
3.0ms	cosTheta_i	@	0	(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 3)

rewrite92.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`add-sqr-sqrt`
710×	`pow1`
708×	`*-un-lft-identity`
684×	`add-exp-log`
682×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	244
1	750	244

Stop Event

1×	node limit

Counts

10 → 213

Calls

Call 1

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

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

simplify164.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1134×	`fma-def`
602×	`associate-+r+`
564×	`distribute-rgt-in`
560×	`times-frac`
550×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	849	23782
1	2599	20508

Stop Event

1×	node limit

Counts

368 → 397

Calls

Call 1

Inputs
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))
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(-.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 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))) (+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))) (+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) 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)
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 (/.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
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Outputs
1
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1
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(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 2) 1/3) (cbrt.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))))
(.f32 (cbrt.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v))))) 2)) (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))))
(*.f32 (cbrt.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v))))) 2)) (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))))
(*.f32 (pow.f32 (sqrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 1/3) (pow.f32 (sqrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 1/3))
(.f32 (cbrt.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))) (cbrt.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))))
(*.f32 (cbrt.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))) (cbrt.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 3) (pow.f32 v -3))) (cbrt.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 2) (+.f32 (pow.f32 v -2) (*.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O v) cosTheta_i)) 3) (pow.f32 v -3))) (cbrt.f32 (+.f32 (pow.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O v) cosTheta_i)) 2) (+.f32 (pow.f32 v -2) (.f32 (/.f32 -1 v) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O v) cosTheta_i)))))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 v -3))) (cbrt.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v)))) 2) (fma.f32 (/.f32 -1 v) (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v)))) (pow.f32 v -2)))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 2) (pow.f32 v -2))) (cbrt.f32 (+.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O v) cosTheta_i)) 2) (pow.f32 v -2))) (cbrt.f32 (+.f32 (/.f32 -1 v) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O v) cosTheta_i)))))
(/.f32 (cbrt.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v)))) 2) (pow.f32 v -2))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(pow.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)) 1/3)
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 1)
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(pow.f32 (cbrt.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))) 3)
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)) 1/6) 2)
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(sqrt.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 2))
(sqrt.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v))))) 2))
(fabs.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v))))))
(log.f32 (exp.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(expm1.f32 (log1p.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(exp.f32 (log.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(exp.f32 (*.f32 (log.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v))) 1/3))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(exp.f32 (*.f32 (log.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))) 1))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i) (/.f32 -1 v)))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (/.f32 1 v)))))

eval396.0ms (3.9%)

Compiler: Compiled 19394 to 14759 computations (23.9% saved)

prune105.0ms (1%)

Pruning

17 alts after pruning (10 fresh and 7 done)

	Pruned	Kept	Total
New	471	8	479
Fresh	1	2	3
Picked	1	4	5
Done	0	3	3
Total	473	17	490

Accuracy

99.9%

Counts

490 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	21.6%	(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
✓	6.3%	(-.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
✓	50.4%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 (+.f32 332956652491/1000000000000 (/.f32 -1 (pow.f32 v 3))) (+.f32 48038761/100000000 (*.f32 (/.f32 -1 v) (-.f32 (/.f32 -1 v) 6931/10000)))))) (/.f32 1/2 v))
✓	99.8%	(.f32 (pow.f32 (E.f32) (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))
	21.6%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
	99.8%	(.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 sinTheta_i (/.f32 sinTheta_O v))) (+.f32 6931/10000 (/.f32 -1 v))) 2))) (/.f32 1/2 v))
	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 v -2))) (/.f32 -1 (cbrt.f32 v))))
	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (pow.f32 (cbrt.f32 (exp.f32 (/.f32 -1 v))) 3))
✓	99.8%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
	98.3%	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	99.8%	(.f32 (exp.f32 (log.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) (exp.f32 (/.f32 -1 v)))
	38.0%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
	99.7%	(exp.f32 (pow.f32 (cbrt.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 3))
✓	98.2%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1

Compiler

Compiled 822 to 558 computations (32.1% saved)

regimes128.0ms (1.2%)

Counts

32 → 1

Calls

Call 1

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

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

Calls

9 calls:

16.0ms	sinTheta_i
16.0ms	cosTheta_O
16.0ms	sinTheta_O
15.0ms	cosTheta_i
13.0ms	(*.f32 cosTheta_i cosTheta_O)

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 606 to 386 computations (36.3% saved)

regimes48.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	cosTheta_O
9.0ms	sinTheta_i
9.0ms	cosTheta_i
9.0ms	sinTheta_O
7.0ms	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 174 to 110 computations (36.8% saved)

regimes40.0ms (0.4%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	cosTheta_O
7.0ms	v
7.0ms	sinTheta_O
7.0ms	sinTheta_i
7.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta_i`
98.3%	1	`cosTheta_O`
98.3%	1	`sinTheta_i`
98.3%	1	`sinTheta_O`
98.3%	1	`v`

Compiler

Compiled 102 to 68 computations (33.3% saved)

regimes40.0ms (0.4%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	cosTheta_i
9.0ms	sinTheta_O
6.0ms	sinTheta_i
6.0ms	cosTheta_O
6.0ms	v

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 94 to 62 computations (34% saved)

regimes26.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	cosTheta_O
5.0ms	sinTheta_O
5.0ms	cosTheta_i
5.0ms	v
5.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
38.0%	1	`cosTheta_i`
38.0%	1	`cosTheta_O`
38.0%	1	`sinTheta_i`
38.0%	1	`sinTheta_O`
38.0%	1	`v`

Compiler

Compiled 62 to 43 computations (30.6% saved)

regimes21.0ms (0.2%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

6.0ms	cosTheta_O
4.0ms	v
4.0ms	sinTheta_i
4.0ms	cosTheta_i
4.0ms	sinTheta_O

Results

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

Compiler

Compiled 48 to 36 computations (25% saved)

regimes16.0ms (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:

5.0ms	sinTheta_O
3.0ms	cosTheta_O
3.0ms	sinTheta_i
3.0ms	v
3.0ms	cosTheta_i

Results

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

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	131
1	44	131
2	61	131
3	80	131
4	93	131
5	97	131
6	98	131

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 81 to 68 computations (16% saved)

soundness1.1s (10.7%)

Rules

1526×	`fma-neg`
1134×	`fma-def`
1058×	`associate-+r+`
1058×	`associate-+r+`
922×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	1033	47094
1	3591	40548
0	480	21660
1	1331	20136
2	5654	20036
0	1033	47094
1	3591	40548
0	449	9565
1	1164	9131
2	5213	8951
0	849	23782
1	2599	20508
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037

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 254 to 160 computations (37% saved)

end0.0ms (0%)

preprocess56.0ms (0.5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 226 to 176 computations (22.1% saved)

analyze568.0ms (5.5%)

sample2.4s (23.1%)

preprocess315.0ms (3.1%)

eval1.0ms (0%)

prune3.0ms (0%)

localize356.0ms (3.5%)

series54.0ms (0.5%)

rewrite81.0ms (0.8%)

simplify202.0ms (2%)

eval165.0ms (1.6%)

prune65.0ms (0.6%)

localize729.0ms (7.1%)

series98.0ms (1%)

rewrite139.0ms (1.4%)

simplify334.0ms (3.2%)

eval693.0ms (6.7%)

prune128.0ms (1.2%)

localize699.0ms (6.8%)

series61.0ms (0.6%)

rewrite101.0ms (1%)

simplify128.0ms (1.2%)

eval190.0ms (1.9%)

prune82.0ms (0.8%)

localize437.0ms (4.3%)

series32.0ms (0.3%)

rewrite92.0ms (0.9%)

simplify164.0ms (1.6%)

eval396.0ms (3.9%)

prune105.0ms (1%)

regimes128.0ms (1.2%)

regimes48.0ms (0.5%)

regimes40.0ms (0.4%)

regimes40.0ms (0.4%)

regimes26.0ms (0.3%)

regimes21.0ms (0.2%)

regimes16.0ms (0.2%)

simplify9.0ms (0.1%)

soundness1.1s (10.7%)

end0.0ms (0%)

preprocess56.0ms (0.5%)

Profiling