Metrics for HairBSDF, Mp, lower

analyze700.0ms (4.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	3%	97%	0%	0%	0%	0
0%	0%	3%	97%	0%	0%	0%	1
0%	0%	3%	97%	0%	0%	0%	2
0%	0%	3%	97%	0%	0%	0%	3
0%	0%	3%	97%	0%	0%	0%	4
0%	0%	3%	97%	0%	0%	0%	5
0%	0%	1.5%	97%	0%	1.5%	0%	6
0%	0%	1.5%	97%	0%	1.5%	0%	7
0%	0%	1.5%	97%	0%	1.5%	0%	8
0%	0%	1.5%	97%	0%	1.5%	0%	9
0%	0%	1.5%	97%	0%	1.5%	0%	10
50%	0.7%	0.7%	97%	0%	1.5%	0%	11
50%	0.7%	0.7%	97%	0%	1.5%	0%	12

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample4.4s (27.5%)

Results

4.4s	8256×	body	256	valid
55.0ms	134×	body	256	invalid

Bogosity

preprocess71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 30 to 22 computations (26.7% saved)

eval1.0ms (0%)

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

prune3.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.3%	(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)))))
▶	99.4%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
▶	99.3%	(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)

localize345.0ms (2.1%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	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)))
✓	99.6%	(.f32 (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))) (/.f32 1/2 v))
✓	99.3%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.3%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.7%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.4%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
✓	99.4%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series85.0ms (0.5%)

Counts

8 → 336

Calls

84 calls:

Time	Variable		Point	Expression
26.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
20.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))
6.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
1.0ms	cosTheta_O	@	0	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
1.0ms	sinTheta_O	@	0	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))

rewrite78.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`add-sqr-sqrt`
770×	`pow1`
770×	`*-un-lft-identity`
734×	`add-exp-log`
732×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	250
1	825	246

Stop Event

1×	node limit

Counts

8 → 126

Calls

Call 1

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

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

simplify406.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

774×	`fma-neg`
628×	`unswap-sqr`
536×	`times-frac`
502×	`fma-def`
486×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	459	21994
1	1229	20438
2	5047	20174

Stop Event

1×	node limit

Counts

462 → 283

Calls

Call 1

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

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

eval178.0ms (1.1%)

Compiler: Compiled 11299 to 6575 computations (41.8% saved)

prune79.0ms (0.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	273	10	283
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	275	10	285

Accuracy

99.8%

Counts

285 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))
	99.4%	(.f32 (+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)) (/.f32 1/2 v))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
	99.4%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
	99.4%	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.3%	(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 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))) v))
	99.4%	(.f32 (+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)) (/.f32 1/2 v))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
	99.4%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
	99.4%	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.3%	(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 964 to 708 computations (26.6% saved)

localize616.0ms (3.8%)

Localize:

Found 16 expressions with local error:

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

Compiler

Compiled 303 to 162 computations (46.5% saved)

series62.0ms (0.4%)

Counts

16 → 252

Calls

132 calls:

Time	Variable		Point	Expression
17.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
2.0ms	sinTheta_i	@	0	(/.f32 v (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))
1.0ms	cosTheta_i	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
1.0ms	cosTheta_O	@	inf	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
1.0ms	v	@	-inf	(/.f32 v (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))

rewrite124.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

900×	`add-sqr-sqrt`
884×	`pow1`
884×	`*-un-lft-identity`
838×	`add-exp-log`
836×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	498
1	887	498

Stop Event

1×	node limit

Counts

16 → 208

Calls

Call 1

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

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

simplify185.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1414×	`associate-r`
1214×	`fma-def`
948×	`times-frac`
682×	`associate-+r+`
626×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	881	24880
1	2482	22316

Stop Event

1×	node limit

Counts

460 → 519

Calls

Call 1

Inputs
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 -1 (/.f32 (.f32 sinTheta_O (*.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_O 2) (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_O 3) (.f32 (pow.f32 sinTheta_i 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_O 2) (*.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 -1 (/.f32 (.f32 sinTheta_O (*.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_O 2) (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O (.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_O 3) (.f32 (pow.f32 sinTheta_i 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_O 2) (*.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 6931/10000)
(+.f32 (exp.f32 6931/10000) (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (+.f32 1 (.f32 sinTheta_O sinTheta_i)) 2)) (pow.f32 v 2)))))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (+.f32 1 (.f32 sinTheta_O sinTheta_i)) 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (+.f32 1 (*.f32 sinTheta_O sinTheta_i)) 2)) (pow.f32 v 2))))))
(exp.f32 6931/10000)
(+.f32 (exp.f32 6931/10000) (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2)))))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i)))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (-.f32 1 (.f32 -1 (.f32 sinTheta_O sinTheta_i))) 2)) (pow.f32 v 2))))))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))) (/.f32 1 v))
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(/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (/.f32 1 v) 3)) (+.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v)))))
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(log.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))))
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(exp.f32 (log.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
(log1p.f32 (expm1.f32 (+.f32 6931/10000 (-.f32 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))))) 1)
(.f32 1 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))))
(.f32 (.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(.f32 (sqrt.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
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(/.f32 (-.f32 48038761/100000000 (.f32 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))) (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (-.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))))
(pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 1)
(log.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))))))
(cbrt.f32 (.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(expm1.f32 (log1p.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(exp.f32 (log.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(log1p.f32 (expm1.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))) 1)
(*.f32 1 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
(.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))) (cbrt.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(*.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))) (sqrt.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(pow.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))) 1)
(log.f32 (exp.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))))
(cbrt.f32 (.f32 (.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(expm1.f32 (log1p.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(log1p.f32 (expm1.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (exp.f32 6931/10000) v))) 1)
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(.f32 (.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v))) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)))
(*.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)) (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)))
(pow.f32 (/.f32 (exp.f32 6931/10000) v) 1)
(log.f32 (exp.f32 (/.f32 (exp.f32 6931/10000) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (exp.f32 6931/10000) v))))
(cbrt.f32 (.f32 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (exp.f32 6931/10000) v)) (/.f32 (exp.f32 6931/10000) v)))
(expm1.f32 (log1p.f32 (/.f32 (exp.f32 6931/10000) v)))
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(log1p.f32 (expm1.f32 (/.f32 (exp.f32 6931/10000) v)))
(-.f32 (exp.f32 (log1p.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))))) 1)
(pow.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))) 1)
(log.f32 (exp.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))))
(log.f32 (+.f32 1 (expm1.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))))))
(cbrt.f32 (.f32 (.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))) (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))) (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))))
(expm1.f32 (log1p.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))))
(exp.f32 (log.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v)))))))
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Outputs
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 -1 (/.f32 (.f32 sinTheta_O (*.f32 sinTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v)))
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(-.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 (.f32 (.f32 sinTheta_O sinTheta_i) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v))
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(+.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (fma.f32 1/2 (/.f32 (.f32 (.f32 (.f32 sinTheta_O sinTheta_O) (.f32 sinTheta_i sinTheta_i)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (.f32 v v)) (/.f32 (.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)))
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(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
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(exp.f32 6931/10000)
(+.f32 (exp.f32 6931/10000) (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (*.f32 sinTheta_O sinTheta_i))) v)))
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(-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) (/.f32 v (fma.f32 sinTheta_O sinTheta_i 1))))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 sinTheta_O sinTheta_i))) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (+.f32 1 (.f32 sinTheta_O sinTheta_i)) 2)) (pow.f32 v 2)))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) (/.f32 v (+.f32 1 (.f32 sinTheta_O sinTheta_i)))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (+.f32 1 (.f32 sinTheta_O sinTheta_i)) 2)) (*.f32 v v)))))
(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) (/.f32 v (fma.f32 sinTheta_O sinTheta_i 1)))) (.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (fma.f32 sinTheta_O sinTheta_i 1) 2) v))))
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eval472.0ms (2.9%)

Compiler: Compiled 17160 to 11696 computations (31.8% saved)

prune228.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	538	9	547
Fresh	3	2	5
Picked	4	1	5
Done	0	0	0
Total	545	12	557

Accuracy

99.8%

Counts

557 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
	4.6%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))) v))
	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (exp.f32 (/.f32 -1 v))) v)))
	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
	99.0%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
▶	99.4%	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
▶	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.7%	(.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))))
	50.5%	(exp.f32 (/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (/.f32 1 v) 3)) (+.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v))))))
▶	99.3%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
	4.6%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))) v))
	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (exp.f32 (/.f32 -1 v))) v)))
	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
	99.0%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
▶	99.4%	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
▶	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.7%	(.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))))
	50.5%	(exp.f32 (/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (/.f32 1 v) 3)) (+.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v))))))
▶	99.3%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 1146 to 884 computations (22.9% saved)

localize1.0s (6.4%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
✓	99.9%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	99.8%	(exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	99.0%	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000))
✓	99.8%	(exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
✓	99.8%	(exp.f32 (log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v)))
	99.1%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	85.8%	(log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))
	100.0%	(log.f32 (/.f32 1/2 v))
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
✓	99.7%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	99.8%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	100.0%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
✓	99.9%	(/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))

Compiler

Compiled 311 to 181 computations (41.8% saved)

series818.0ms (5.1%)

Counts

15 → 351

Calls

93 calls:

Time	Variable		Point	Expression
350.0ms	sinTheta_O	@	inf	(.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 (log.f32 (/.f32 1/2 v)) 6931/10000)))
94.0ms	v	@	0	(log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))
84.0ms	v	@	0	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
60.0ms	cosTheta_O	@	inf	(log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))
57.0ms	cosTheta_O	@	-inf	(log.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v)))) v))

rewrite159.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

856×	`add-sqr-sqrt`
844×	`pow1`
840×	`*-un-lft-identity`
808×	`add-exp-log`
804×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	415
1	911	403

Stop Event

1×	node limit

Counts

15 → 203

Calls

Call 1

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

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

simplify290.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1192×	`associate-l`
1088×	`fma-def`
846×	`times-frac`
632×	`associate-+r+`
602×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	847	28122
1	2234	23736

Stop Event

1×	node limit

Counts

554 → 507

Calls

Call 1

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

Outputs
(exp.f32 6931/10000)
(+.f32 (exp.f32 6931/10000) (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (exp.f32 6931/10000) (neg.f32 (/.f32 (exp.f32 6931/10000) v)))
(-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) v) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)))))
(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v)) (*.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 1/2 v)))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) v) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v))))))
(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v)) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (*.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 1/2 v))))
(exp.f32 6931/10000)
(+.f32 (exp.f32 6931/10000) (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (exp.f32 6931/10000) (neg.f32 (/.f32 (exp.f32 6931/10000) v)))
(-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) v) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)))))
(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v)) (*.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 1/2 v)))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) v) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v))))))
(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v)) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (*.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 1/2 v))))
(/.f32 -1 v)
6931/10000
6931/10000
(/.f32 v (exp.f32 6931/10000))
(+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000)))
(+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 v (exp.f32 6931/10000)))) (+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000))))
(+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (/.f32 1/2 (*.f32 (exp.f32 6931/10000) v)))
(+.f32 (/.f32 v (exp.f32 6931/10000)) (+.f32 (exp.f32 -6931/10000) (/.f32 1/2 (*.f32 (exp.f32 6931/10000) v))))
(+.f32 (.f32 1/6 (/.f32 1 (.f32 (pow.f32 v 2) (exp.f32 6931/10000)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 v (exp.f32 6931/10000)))) (+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000)))))
(+.f32 (+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (/.f32 1/2 (.f32 (exp.f32 6931/10000) v))) (/.f32 1/6 (.f32 (exp.f32 6931/10000) (*.f32 v v))))
(+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (+.f32 (/.f32 1/2 (.f32 (exp.f32 6931/10000) v)) (/.f32 1/6 (.f32 (exp.f32 6931/10000) (*.f32 v v)))))
(/.f32 v (exp.f32 6931/10000))
(+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000)))
(+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 v (exp.f32 6931/10000)))) (+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000))))
(+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (/.f32 1/2 (*.f32 (exp.f32 6931/10000) v)))
(+.f32 (/.f32 v (exp.f32 6931/10000)) (+.f32 (exp.f32 -6931/10000) (/.f32 1/2 (*.f32 (exp.f32 6931/10000) v))))
(+.f32 (.f32 1/6 (/.f32 1 (.f32 (pow.f32 v 2) (exp.f32 6931/10000)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 v (exp.f32 6931/10000)))) (+.f32 (/.f32 1 (exp.f32 6931/10000)) (/.f32 v (exp.f32 6931/10000)))))
(+.f32 (+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (/.f32 1/2 (.f32 (exp.f32 6931/10000) v))) (/.f32 1/6 (.f32 (exp.f32 6931/10000) (*.f32 v v))))
(+.f32 (+.f32 (/.f32 v (exp.f32 6931/10000)) (exp.f32 -6931/10000)) (+.f32 (/.f32 1/2 (.f32 (exp.f32 6931/10000) v)) (/.f32 1/6 (.f32 (exp.f32 6931/10000) (*.f32 v v)))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))
(fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (*.f32 (/.f32 -1/2 v) (/.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))))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (fma.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(fma.f32 (/.f32 (exp.f32 6931/10000) (.f32 v v)) -1/2 (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) 1/4)))
(+.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)))))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
(fma.f32 (/.f32 (exp.f32 6931/10000) (.f32 v v)) -1/2 (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) 1/4))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))
(fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (*.f32 (/.f32 -1/2 v) (/.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))))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (fma.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(fma.f32 (/.f32 (exp.f32 6931/10000) (.f32 v v)) -1/2 (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) 1/4)))
(+.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)))))
(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (.f32 v v)) (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
(fma.f32 (/.f32 (exp.f32 6931/10000) (.f32 v v)) -1/2 (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) 1/4))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 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 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v))))) (neg.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 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)))))
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(exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(cbrt.f32 (.f32 (.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 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))
(cbrt.f32 (.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 (-.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)))))))
(cbrt.f32 (pow.f32 (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 3))
(expm1.f32 (log1p.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 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(log1p.f32 (expm1.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 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))) 1)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 1 (/.f32 v (*.f32 cosTheta_O cosTheta_i)))
(.f32 (/.f32 1 v) (.f32 cosTheta_O cosTheta_i))
(/.f32 (.f32 1 (.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_i (/.f32 cosTheta_O v))
(/.f32 (neg.f32 (*.f32 cosTheta_O cosTheta_i)) (neg.f32 v))
(/.f32 (*.f32 (neg.f32 cosTheta_O) cosTheta_i) (neg.f32 v))
(.f32 1 (.f32 cosTheta_i (/.f32 cosTheta_O v)))
(pow.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) 1)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(log.f32 (exp.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))))
(*.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))))
(cbrt.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (*.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))))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(exp.f32 (log.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(log1p.f32 (expm1.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v))))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(-.f32 (exp.f32 (log1p.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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))))))) 1)
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(pow.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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))))) 1)
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(log.f32 (exp.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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)))))))
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(log.f32 (+.f32 1 (expm1.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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))))))))
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(cbrt.f32 (.f32 (.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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))))) (.f32 (.f32 (exp.f32 6931/10000) (/.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)))))) (.f32 (.f32 (exp.f32 6931/10000) (/.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 (.f32 (.f32 (exp.f32 6931/10000) (.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)))))) (.f32 (.f32 (.f32 (exp.f32 6931/10000) (exp.f32 6931/10000)) (.f32 (/.f32 1/2 v) (/.f32 1/2 v))) (exp.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))))))))
(cbrt.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))) 3))
(expm1.f32 (log1p.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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)))))))
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))
(log1p.f32 (expm1.f32 (.f32 (.f32 (exp.f32 6931/10000) (/.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)))))))
(exp.f32 (+.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)))))
(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))

eval546.0ms (3.4%)

Compiler: Compiled 16547 to 11497 computations (30.5% saved)

prune227.0ms (1.4%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	576	3	579
Fresh	0	6	6
Picked	2	3	5
Done	0	1	1
Total	578	13	591

Accuracy

99.8%

Counts

591 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 1/2 (/.f32 v (exp.f32 (/.f32 -1 v))))
✓	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
▶	4.6%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))) v))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (exp.f32 (/.f32 -1 v))) v)))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
▶	99.0%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
	99.4%	(.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)))
✓	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.7%	(*.f32 1/2 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v))))
	50.5%	(exp.f32 (/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (/.f32 1 v) 3)) (+.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v))))))
✓	99.3%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	98.3%	(/.f32 1/2 (/.f32 v (exp.f32 (/.f32 -1 v))))
✓	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
▶	4.6%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
	99.3%	(+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))) v))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (exp.f32 (/.f32 -1 v))) v)))
▶	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
▶	99.0%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
	99.4%	(.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)))
✓	4.6%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.7%	(*.f32 1/2 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v))))
	50.5%	(exp.f32 (/.f32 (-.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) 3) (pow.f32 (/.f32 1 v) 3)) (+.f32 (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (+.f32 6931/10000 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v))))) (+.f32 (.f32 (/.f32 1 v) (/.f32 1 v)) (.f32 (+.f32 6931/10000 (+.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (log.f32 (/.f32 1/2 v)))) (/.f32 1 v))))))
✓	99.3%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 1066 to 830 computations (22.1% saved)

localize1.4s (8.8%)

Localize:

Found 18 expressions with local error:

New	Accuracy	Program
✓	99.5%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 -1 v))))
✓	99.2%	(log.f32 (/.f32 (exp.f32 6931/10000) v))
	99.0%	(/.f32 (exp.f32 6931/10000) v)
✓	90.3%	(exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	99.7%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
✓	99.5%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (exp.f32 (/.f32 -1 v))) v)))
	99.0%	(/.f32 (exp.f32 6931/10000) v)
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	99.7%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
✓	99.6%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
	99.0%	(/.f32 (exp.f32 6931/10000) v)
✓	99.1%	(/.f32 1/2 (/.f32 v (exp.f32 6931/10000)))
✓	99.0%	(/.f32 v (exp.f32 6931/10000))
✓	100.0%	(log.f32 v)
	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v))
✓	99.8%	(exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v)))

Compiler

Compiled 252 to 172 computations (31.7% saved)

series153.0ms (1%)

Counts

14 → 168

Calls

54 calls:

Time	Variable		Point	Expression
26.0ms	v	@	-inf	(log.f32 (/.f32 (exp.f32 6931/10000) v))
23.0ms	v	@	0	(log.f32 (/.f32 (exp.f32 6931/10000) v))
21.0ms	v	@	inf	(log.f32 (/.f32 (exp.f32 6931/10000) v))
18.0ms	v	@	0	(log.f32 v)
16.0ms	v	@	-inf	(log.f32 v)

rewrite193.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

714×	`add-sqr-sqrt`
700×	`pow1`
698×	`*-un-lft-identity`
668×	`add-exp-log`
664×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	304
1	765	304

Stop Event

1×	node limit

Counts

14 → 327

Calls

Call 1

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

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

simplify414.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1204×	`associate-r`
1136×	`associate-l`
832×	`fma-def`
674×	`times-frac`
430×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	763	19343
1	2020	17433

Stop Event

1×	node limit

Counts

495 → 452

Calls

Call 1

Inputs
(exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (*.f32 -1 (log.f32 (/.f32 1 v)))))
(+.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (*.f32 -1 (log.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) v)) (.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (*.f32 -1 (log.f32 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 (-.f32 6931/10000 (.f32 -1 (log.f32 (/.f32 1 v))))) (pow.f32 v 3))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (*.f32 -1 (log.f32 (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v))))))
(+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v)))))) v)))
(+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) v)) (.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v)))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 v)))))) (pow.f32 v 3))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v)))))) (pow.f32 v 2))))))
(/.f32 -1 v)
(-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v)))
(-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v)))
(-.f32 6931/10000 (+.f32 (log.f32 v) (/.f32 1 v)))
(-.f32 6931/10000 (*.f32 -1 (log.f32 (/.f32 1 v))))
(-.f32 6931/10000 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 v))) (/.f32 1 v)))
(-.f32 6931/10000 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 v))) (/.f32 1 v)))
(-.f32 6931/10000 (+.f32 (*.f32 -1 (log.f32 (/.f32 1 v))) (/.f32 1 v)))
(-.f32 6931/10000 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v)))))
(-.f32 6931/10000 (+.f32 (log.f32 -1) (+.f32 (*.f32 -1 (log.f32 (/.f32 -1 v))) (/.f32 1 v))))
(-.f32 6931/10000 (+.f32 (log.f32 -1) (+.f32 (*.f32 -1 (log.f32 (/.f32 -1 v))) (/.f32 1 v))))
(-.f32 6931/10000 (+.f32 (log.f32 -1) (+.f32 (*.f32 -1 (log.f32 (/.f32 -1 v))) (/.f32 1 v))))
(*.f32 -1 (log.f32 (/.f32 1 v)))
(*.f32 -1 (log.f32 (/.f32 1 v)))
(*.f32 -1 (log.f32 (/.f32 1 v)))
(*.f32 -1 (log.f32 (/.f32 1 v)))
(+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v))))
(+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v))))
(+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v))))
(+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 v))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(.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)))))
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 1 (.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 1 (*.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 1 (.f32 1/2 (/.f32 1 (pow.f32 v 2)))) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.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) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 cosTheta_O cosTheta_i) 1)) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1/2 (.f32 -1 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 cosTheta_O cosTheta_i) 1)) (pow.f32 v 2)))))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1/2 (.f32 -1 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 1/2 (.f32 cosTheta_O cosTheta_i)) 1/6)) (pow.f32 v 4))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 cosTheta_O cosTheta_i) 1)) (pow.f32 v 2))))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 2))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1/2 (.f32 -1 (*.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 3)))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1/6 (.f32 -1/2 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 4))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1 (.f32 -1 (.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (+.f32 1/2 (.f32 -1 (*.f32 cosTheta_O cosTheta_i)))) (pow.f32 v 3))))))
(.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.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 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))) v)))
(.f32 1/2 (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v))))) (pow.f32 v 2)))
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(exp.f32 (log.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 1 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))))
(exp.f32 (.f32 (log.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (exp.f32 (/.f32 1 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))) 1))
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(fma.f32 1 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 1 v))) (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))
(fma.f32 1 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 1 v))) (.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v)))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (/.f32 1 v))) (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))
(fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (exp.f32 (/.f32 1 v))) (.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v)))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(fma.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 1 v)) (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))
(fma.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 1 v)) (.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v)))) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(fma.f32 (exp.f32 (/.f32 1 v)) (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (/.f32 (.f32 cosTheta_O cosTheta_i) (/.f32 v (exp.f32 (/.f32 1 v))))))
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(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))) 1)
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(/.f32 1/2 (*.f32 v (exp.f32 -6931/10000)))
(/.f32 1/2 (neg.f32 (neg.f32 (*.f32 v (exp.f32 -6931/10000)))))
(/.f32 -1 (neg.f32 (/.f32 (*.f32 v (exp.f32 -6931/10000)) 1/2)))
(/.f32 -1/2 (neg.f32 (*.f32 v (exp.f32 -6931/10000))))
(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
(/.f32 (neg.f32 (*.f32 1/2 (exp.f32 6931/10000))) (neg.f32 v))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))) 2)
(pow.f32 (/.f32 (*.f32 v (exp.f32 -6931/10000)) 1/2) -1)
(sqrt.f32 (/.f32 1/4 (/.f32 (*.f32 v v) (exp.f32 6931/5000))))
(log.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 6931/10000) v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3))
(expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000))
(exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 1))
(log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2) (cbrt.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(pow.f32 (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))) (cbrt.f32 (/.f32 1 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 6931/10000) v))) 1)
(*.f32 1 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1 v))
(*.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)))
(*.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)) (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)))
(*.f32 (pow.f32 v -1/2) (/.f32 (exp.f32 6931/10000) (sqrt.f32 v)))
(*.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 6931/10000) (cbrt.f32 v)))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) 1) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) v))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (sqrt.f32 v)) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) (sqrt.f32 v)))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) 1) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) v))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (cbrt.f32 v)))
(/.f32 1 (*.f32 v (exp.f32 -6931/10000)))
(/.f32 (exp.f32 6931/10000) v)
(/.f32 -1 (neg.f32 (*.f32 v (exp.f32 -6931/10000))))
(/.f32 (neg.f32 (exp.f32 6931/10000)) (neg.f32 v))
(/.f32 (neg.f32 (neg.f32 (exp.f32 6931/10000))) (neg.f32 (neg.f32 v)))
(pow.f32 (*.f32 v (exp.f32 -6931/10000)) -1)
(pow.f32 (/.f32 (exp.f32 6931/10000) v) 1)
(pow.f32 (E.f32) (-.f32 6931/10000 (log.f32 v)))
(pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 3)
(pow.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2)
(pow.f32 (exp.f32 (sqrt.f32 (-.f32 6931/10000 (log.f32 v)))) (sqrt.f32 (-.f32 6931/10000 (log.f32 v))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (log.f32 v))) 2)) (cbrt.f32 (-.f32 6931/10000 (log.f32 v))))
(sqrt.f32 (/.f32 (exp.f32 6931/5000) (*.f32 v v)))
(log.f32 (exp.f32 (/.f32 (exp.f32 6931/10000) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (exp.f32 6931/10000) v))))
(cbrt.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) v) 3))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 6931/10000) 3) (pow.f32 v -3)))
(cbrt.f32 (/.f32 (pow.f32 (exp.f32 6931/10000) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (/.f32 (exp.f32 6931/10000) v)))
(log1p.f32 (expm1.f32 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 6931/10000 (neg.f32 (log.f32 v)))
(+.f32 0 (-.f32 6931/10000 (log.f32 v)))
(+.f32 (log.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2)) (log.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v))))
(+.f32 (log.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v))) (log.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v))))
(-.f32 6931/10000 (log.f32 v))
(-.f32 0 (-.f32 (log.f32 v) 6931/10000))
(-.f32 (log.f32 (neg.f32 (exp.f32 6931/10000))) (log.f32 (neg.f32 v)))
(-.f32 (exp.f32 (log1p.f32 (-.f32 6931/10000 (log.f32 v)))) 1)
(*.f32 1 (-.f32 6931/10000 (log.f32 v)))
(*.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (log.f32 v))) 2) (cbrt.f32 (-.f32 6931/10000 (log.f32 v))))
(*.f32 (sqrt.f32 (-.f32 6931/10000 (log.f32 v))) (sqrt.f32 (-.f32 6931/10000 (log.f32 v))))
(pow.f32 (-.f32 6931/10000 (log.f32 v)) 1)
(pow.f32 (cbrt.f32 (-.f32 6931/10000 (log.f32 v))) 3)
(pow.f32 (pow.f32 (-.f32 6931/10000 (log.f32 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 6931/10000 (log.f32 v))) 2)
(neg.f32 (-.f32 (log.f32 v) 6931/10000))
(sqrt.f32 (pow.f32 (-.f32 6931/10000 (log.f32 v)) 2))
(cbrt.f32 (pow.f32 (-.f32 6931/10000 (log.f32 v)) 3))
(expm1.f32 (log1p.f32 (-.f32 6931/10000 (log.f32 v))))
(exp.f32 (log.f32 (-.f32 6931/10000 (log.f32 v))))
(exp.f32 (*.f32 (log.f32 (-.f32 6931/10000 (log.f32 v))) 1))
(log1p.f32 (expm1.f32 (-.f32 6931/10000 (log.f32 v))))
(-.f32 (exp.f32 (log1p.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))))) 1)
(pow.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))) 1)
(pow.f32 (cbrt.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))))) 3)
(pow.f32 (pow.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))) 3) 1/3)
(pow.f32 (sqrt.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))))) 2)
(sqrt.f32 (pow.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))) 2))
(log.f32 (pow.f32 (exp.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(log.f32 (+.f32 1 (expm1.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))))))
(cbrt.f32 (pow.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)))) 3))
(cbrt.f32 (.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3) (pow.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))) 3)))
(cbrt.f32 (.f32 (pow.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))) 3) (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3)))
(expm1.f32 (log1p.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))))))
(exp.f32 (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)) (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)))
(exp.f32 (*.f32 (+.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v)) (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) 1))
(log1p.f32 (expm1.f32 (.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) (/.f32 1 v))))))

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

eval540.0ms (3.4%)

Compiler: Compiled 14840 to 10963 computations (26.1% saved)

prune404.0ms (2.5%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	666	6	672
Fresh	2	2	4
Picked	3	2	5
Done	2	2	4
Total	673	12	685

Accuracy

99.9%

Counts

685 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	98.3%	(/.f32 1/2 (/.f32 v (exp.f32 (/.f32 -1 v))))
✓	99.8%	(/.f32 1/2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
	98.9%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (pow.f32 (exp.f32 -1) (/.f32 1 v)))
✓	99.0%	(.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 (/.f32 -1 v)))
	99.0%	(.f32 (.f32 1/2 (exp.f32 (log.f32 (/.f32 (exp.f32 6931/10000) v)))) (exp.f32 (/.f32 -1 v)))
	99.4%	(.f32 (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)))
	98.9%	(*.f32 1/2 (pow.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 3) 1/3))
	99.7%	(*.f32 1/2 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (log.f32 v)))) 2)) (cbrt.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (log.f32 v))))))
	99.3%	(*.f32 1/2 (exp.f32 (/.f32 (-.f32 (pow.f32 (-.f32 6931/10000 (/.f32 1 v)) 2) (pow.f32 (log.f32 v) 2)) (+.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v)))))
	98.1%	(*.f32 1/2 (exp.f32 (/.f32 -1 v)))
✓	99.7%	(*.f32 1/2 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v))))
✓	99.3%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 817 to 597 computations (26.9% saved)

regimes385.0ms (2.4%)

Counts

31 → 1

Calls

Call 1

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

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

Calls

9 calls:

79.0ms	v
49.0ms	sinTheta_O
48.0ms	cosTheta_i
46.0ms	cosTheta_O
45.0ms	sinTheta_i

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 699 to 486 computations (30.5% saved)

regimes91.0ms (0.6%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

29.0ms	sinTheta_i
15.0ms	sinTheta_O
15.0ms	cosTheta_O
14.0ms	v
9.0ms	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 67 to 56 computations (16.4% saved)

regimes49.0ms (0.3%)

Accuracy

Total -29.9b remaining (-5024.3%)

Threshold costs -29.9b (-5024.3%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

12.0ms	v
10.0ms	sinTheta_i
9.0ms	cosTheta_i
8.0ms	sinTheta_O
8.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
98.1%	1	`cosTheta_i`
98.1%	1	`cosTheta_O`
98.1%	1	`sinTheta_i`
98.1%	1	`sinTheta_O`
98.1%	1	`v`

Compiler

Compiled 59 to 50 computations (15.3% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	69
1	23	69
2	28	69
3	32	69
4	37	69

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 39 to 34 computations (12.8% saved)

soundness1.2s (7.3%)

Rules

1192×	`associate-l`
1088×	`fma-def`
900×	`add-sqr-sqrt`
884×	`pow1`
884×	`*-un-lft-identity`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	459	21994
1	1229	20438
2	5047	20174
0	40	498
1	887	498
0	847	28122
1	2234	23736

Stop Event

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

Compiler

Compiled 318 to 212 computations (33.3% saved)

end0.0ms (0%)

preprocess132.0ms (0.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 178 to 144 computations (19.1% saved)

analyze700.0ms (4.4%)

sample4.4s (27.5%)

preprocess71.0ms (0.4%)

eval1.0ms (0%)

prune3.0ms (0%)

localize345.0ms (2.1%)

series85.0ms (0.5%)

rewrite78.0ms (0.5%)

simplify406.0ms (2.5%)

eval178.0ms (1.1%)

prune79.0ms (0.5%)

localize616.0ms (3.8%)

series62.0ms (0.4%)

rewrite124.0ms (0.8%)

simplify185.0ms (1.2%)

eval472.0ms (2.9%)

prune228.0ms (1.4%)

localize1.0s (6.4%)

series818.0ms (5.1%)

rewrite159.0ms (1%)

simplify290.0ms (1.8%)

eval546.0ms (3.4%)

prune227.0ms (1.4%)

localize1.4s (8.8%)

series153.0ms (1%)

rewrite193.0ms (1.2%)

simplify414.0ms (2.6%)

eval540.0ms (3.4%)

prune404.0ms (2.5%)

regimes385.0ms (2.4%)

regimes91.0ms (0.6%)

regimes49.0ms (0.3%)

simplify10.0ms (0.1%)

soundness1.2s (7.3%)

end0.0ms (0%)

preprocess132.0ms (0.8%)

Profiling