Metrics for HairBSDF, Mp, lower

analyze709.0ms (3.7%)

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 (23.1%)

Results

4.3s	8256×	body	256	valid
76.0ms	164×	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
▶	99.9%	(.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))
▶	99.9%	(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)))))
▶	99.9%	(.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))
▶	99.9%	(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)

localize330.0ms (1.7%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.8%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.2%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.2%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.9%	(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)))))
✓	99.9%	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.4%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
✓	99.3%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series50.0ms (0.3%)

Counts

8 → 384

Calls

96 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
6.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
3.0ms	cosTheta_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)))
2.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	v	@	inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite88.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	270
1	803	262

Stop Event

1×	node limit

Counts

8 → 192

Calls

Call 1

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

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

simplify235.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1924×	`fma-neg`
766×	`log-prod`
594×	`associate-r`
556×	`exp-prod`
554×	`fma-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	545	24910
1	1475	23130
2	6088	23130

Stop Event

1×	node limit

Counts

576 → 310

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

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

eval367.0ms (1.9%)

Compiler: Compiled 10919 to 5847 computations (46.5% saved)

prune258.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	303	7	310
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	305	7	312

Accuracy

100.0%

Counts

312 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.9%	(.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))) (/.f32 1/2 v))
▶	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.1%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	16.4%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.9%	(.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))) (/.f32 1/2 v))
▶	99.9%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.1%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	16.4%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))

Compiler

Compiled 556 to 420 computations (24.5% saved)

localize1.4s (7.6%)

Localize:

Found 15 expressions with local error:

New	Accuracy	Program
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	74.8%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	100.0%	(*.f32 sinTheta_O sinTheta_i)
✓	100.0%	(/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v)
✓	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.9%	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) (.f32 sinTheta_O sinTheta_i)) v))
✓	99.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
✓	99.4%	(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
✓	98.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	99.9%	(exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.9%	(+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	98.5%	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
✓	74.8%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 305 to 139 computations (54.4% saved)

series177.0ms (0.9%)

Counts

15 → 421

Calls

153 calls:

Time	Variable		Point	Expression
62.0ms	v	@	inf	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
6.0ms	v	@	0	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
6.0ms	cosTheta_O	@	0	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
5.0ms	sinTheta_i	@	-inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
4.0ms	v	@	-inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

rewrite178.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	433
1	851	433

Stop Event

1×	node limit

Counts

15 → 187

Calls

Call 1

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

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

simplify807.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

1370×	`associate-l`
1112×	`fma-def`
768×	`times-frac`
484×	`distribute-lft-in`
476×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	901	39410
1	2552	34466

Stop Event

1×	node limit

Counts

608 → 454

Calls

Call 1

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

eval385.0ms (2%)

Compiler: Compiled 22120 to 14201 computations (35.8% saved)

prune98.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	482	6	488
Fresh	0	2	2
Picked	4	1	5
Done	0	0	0
Total	486	9	495

Accuracy

100.0%

Counts

495 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))) 3)
▶	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	6.2%	(+.f32 1 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	99.9%	(.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))) (/.f32 1/2 v))
▶	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
✓	16.4%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	6.4%	1
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))) 3)
▶	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	6.2%	(+.f32 1 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	99.9%	(.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (/.f32 -1 v) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))) (/.f32 1/2 v))
▶	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	99.1%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
✓	16.4%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	6.4%	1

Compiler

Compiled 540 to 422 computations (21.9% saved)

localize426.0ms (2.2%)

Localize:

Found 15 expressions with local error:

New	Accuracy	Program
✓	100.0%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.9%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	100.0%	(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.9%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	100.0%	(+.f32 1 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	99.4%	(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
✓	100.0%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
	100.0%	(*.f32 sinTheta_O sinTheta_i)
✓	71.9%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
✓	99.9%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	98.5%	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
	74.8%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 224 to 117 computations (47.8% saved)

series41.0ms (0.2%)

Counts

11 → 207

Calls

81 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta_O	@	inf	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
4.0ms	v	@	inf	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
2.0ms	cosTheta_O	@	0	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
2.0ms	v	@	-inf	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
2.0ms	cosTheta_i	@	0	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))

rewrite107.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

786×	`add-sqr-sqrt`
768×	`pow1`
768×	`*-un-lft-identity`
732×	`add-exp-log`
730×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	34	279
1	766	275

Stop Event

1×	node limit

Counts

11 → 243

Calls

Call 1

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

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

simplify150.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1020×	`associate-r`
840×	`associate-l`
736×	`fma-def`
542×	`sqr-pow`
338×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	796	19570
1	2049	17682

Stop Event

1×	node limit

Counts

450 → 410

Calls

Call 1

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

Outputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v))))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/9) (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v))))) 7) 1/18) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v))))) 7) 1/18)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (neg.f32 (log.f32 v)))))))
(fma.f32 (.f32 1/3 (.f32 (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 7) 1/18) (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 7) 1/18))) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
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(exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))) 1))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))

eval308.0ms (1.6%)

Compiler: Compiled 13613 to 9819 computations (27.9% saved)

prune103.0ms (0.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	460	9	469
Fresh	2	1	3
Picked	3	2	5
Done	1	0	1
Total	466	12	478

Accuracy

100.0%

Counts

478 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))))) 3)
▶	90.2%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) 2)) (/.f32 1 v)))) 3)
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)
	43.4%	(/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v)
▶	21.9%	(/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i))
✓	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	6.2%	(-.f32 1 (-.f32 (+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) 1))
	99.9%	(*.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	99.1%	(exp.f32 (/.f32 -1 v))
▶	99.9%	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
	6.4%	1
	99.9%	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))))) 3)
▶	90.2%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) 2)) (/.f32 1 v)))) 3)
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)
	43.4%	(/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v)
▶	21.9%	(/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i))
✓	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	6.2%	(-.f32 1 (-.f32 (+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) 1))
	99.9%	(*.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	99.1%	(exp.f32 (/.f32 -1 v))
▶	99.9%	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 766 to 624 computations (18.5% saved)

localize786.0ms (4.1%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.6%	(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
✓	98.5%	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) 2)) (/.f32 1 v))))
✓	98.4%	(pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) 2)
	74.9%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	100.0%	(log.f32 (/.f32 1/2 v))
✓	99.9%	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v)))
✓	100.0%	(+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
	100.0%	(*.f32 sinTheta_O sinTheta_i)
	75.0%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
✓	47.2%	(-.f32 (+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) 1)
✓	99.3%	(/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i))
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	99.9%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
✓	98.5%	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))

Compiler

Compiled 325 to 204 computations (37.2% saved)

series104.0ms (0.5%)

Counts

13 → 213

Calls

75 calls:

Time	Variable		Point	Expression
27.0ms	v	@	-inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
18.0ms	v	@	0	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
6.0ms	sinTheta_O	@	0	(+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
5.0ms	v	@	inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
4.0ms	cosTheta_O	@	inf	(cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) 2)) (/.f32 1 v))))

rewrite107.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

832×	`add-sqr-sqrt`
812×	`pow1`
810×	`*-un-lft-identity`
778×	`add-exp-log`
776×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	355
1	871	343

Stop Event

1×	node limit

Counts

13 → 250

Calls

Call 1

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

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

simplify253.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

1518×	`fma-def`
762×	`distribute-lft-in`
718×	`associate-+l+`
712×	`distribute-rgt-in`
676×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	929	25067
1	2670	21645

Stop Event

1×	node limit

Counts

463 → 427

Calls

Call 1

Inputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3)
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (*.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/9) (/.f32 1 v))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/9) (/.f32 1 v))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (.f32 1/3 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 17)) 1/9))) (pow.f32 v 2)))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3)))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/9) (/.f32 1 v))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 -1/6 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (+.f32 (.f32 -2/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 4)) 1/9) (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (.f32 1/3 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 17)) 1/9))))) (.f32 -1/27 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/3)))) (pow.f32 v 3)))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))) (.f32 1/3 (pow.f32 (*.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 17)) 1/9))) (pow.f32 v 2)))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 1/3)
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (*.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 7)) 1/9) (/.f32 1 v))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 1/3))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 7)) 1/9) (/.f32 1 v))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))) (.f32 1/3 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 17)) 1/9))) (pow.f32 v 2)))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 1/3)))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 7)) 1/9) (/.f32 1 v))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/6 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))) (+.f32 (.f32 1/27 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 7)) 1/3)) (.f32 2/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 4)) 1/9) (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))) (.f32 1/3 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 17)) 1/9))))))) (pow.f32 v 3)))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))) (.f32 1/3 (pow.f32 (*.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 17)) 1/9))) (pow.f32 v 2)))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) 1/3))))
(/.f32 -1 v)
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v)))) (/.f32 1 v))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))) (/.f32 1 v))
(+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))) (/.f32 1 v))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (*.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) v)))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) v)) (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (*.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) v)))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) v)) (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 v 2)))))
(+.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (+.f32 (.f32 -1 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))) (pow.f32 v 2))))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (*.f32 -1 (log.f32 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))
(+.f32 6931/10000 (+.f32 (log.f32 -1/2) (log.f32 (/.f32 -1 v))))
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(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 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
(+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (log.f32 (/.f32 1/2 v)))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) 1)
(*.f32 1 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(*.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(.f32 (.f32 (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(/.f32 (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) (pow.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 3)) (fma.f32 (log.f32 (/.f32 1/2 v)) (log.f32 (/.f32 1/2 v)) (-.f32 (.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(/.f32 (-.f32 (.f32 (log.f32 (/.f32 1/2 v)) (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(log.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(log.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(log.f32 (*.f32 (exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1/2 v)))
(cbrt.f32 (.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(expm1.f32 (log1p.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(exp.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(exp.f32 (*.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 1))
(log1p.f32 (expm1.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(fma.f32 1 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
(fma.f32 1 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (log.f32 (/.f32 1/2 v)))
(fma.f32 (*.f32 cosTheta_O cosTheta_i) (/.f32 1 v) (log.f32 (/.f32 1/2 v)))
(fma.f32 (*.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) (cbrt.f32 (log.f32 (/.f32 1/2 v)))) (cbrt.f32 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
(fma.f32 (*.f32 (cbrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (cbrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (cbrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
(fma.f32 (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (log.f32 (/.f32 1/2 v)))
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))))) 1)
(*.f32 1 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))))
(.f32 (.f32 (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(*.f32 (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))) (sqrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))) 1/3)
(pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))) 1)
(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))
(exp.f32 (*.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))) 1/3))
(exp.f32 (.f32 (.f32 1/3 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))) 1))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))) 1)
(*.f32 1 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(.f32 (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))) (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(*.f32 (sqrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) (sqrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) 1/2)
(pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 1)
(log.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(log.f32 (+.f32 1 (expm1.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))))
(cbrt.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(hypot.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(hypot.f32 (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (sqrt.f32 (log.f32 (/.f32 1/2 v))))
(exp.f32 (log.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(exp.f32 (*.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 1/2))
(exp.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) 1))
(log1p.f32 (expm1.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))

Outputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))
(pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(cbrt.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (*.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 7)) 1/9) (/.f32 1 v))) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 1/2) (log.f32 (/.f32 1 v))))) 1/3))
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(fma.f32 -1/3 (/.f32 (.f32 (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 7) 1/18) (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 7) 1/18)) v) (cbrt.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
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(fma.f32 -1/3 (.f32 (/.f32 1 v) (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 7) 1/18) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 7) 1/18))) (fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (.f32 1/3 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 17) 1/18) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 17) 1/18)))) (*.f32 v v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(fma.f32 -1/3 (/.f32 (.f32 (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 7) 1/18) (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 7) 1/18)) v) (fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 2))) (/.f32 (fma.f32 1/2 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (.f32 -1/3 (.f32 (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 17) 1/18) (pow.f32 (pow.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) 17) 1/18)))) (.f32 v v))) (cbrt.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
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(log.f32 (exp.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(expm1.f32 (log1p.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (*.f32 1/3 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (*.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v))) 1/3))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (.f32 (.f32 1/3 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))) 1))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(log1p.f32 (expm1.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (/.f32 1 v)))))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(-.f32 (exp.f32 (log1p.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))) 1)
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(*.f32 1 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(.f32 (.f32 (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))) (cbrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(*.f32 (sqrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) (sqrt.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(pow.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) 1/2)
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(pow.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 1)
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(log.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(log.f32 (+.f32 1 (expm1.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(cbrt.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(cbrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))) 3/2))
(expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(hypot.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(hypot.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i)))
(hypot.f32 (sqrt.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (sqrt.f32 (log.f32 (/.f32 1/2 v))))
(hypot.f32 (sqrt.f32 (*.f32 (/.f32 cosTheta_O v) cosTheta_i)) (sqrt.f32 (log.f32 (/.f32 1/2 v))))
(exp.f32 (log.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (log.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) 1/2))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(exp.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))) 1))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))
(log1p.f32 (expm1.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))))
(sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
(sqrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (log.f32 (/.f32 1/2 v))))

eval1.5s (7.7%)

Compiler: Compiled 20759 to 15946 computations (23.2% saved)

prune446.0ms (2.3%)

Pruning

16 alts after pruning (10 fresh and 6 done)

	Pruned	Kept	Total
New	545	5	550
Fresh	0	5	5
Picked	1	4	5
Done	0	2	2
Total	546	16	562

Accuracy

100.0%

Counts

562 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))))) 3)
	100.0%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (pow.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) 2)) (/.f32 1 v)))) 3)
✓	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)
	43.4%	(/.f32 (neg.f32 (*.f32 sinTheta_O sinTheta_i)) v)
✓	21.9%	(/.f32 (neg.f32 sinTheta_O) (/.f32 v sinTheta_i))
	44.1%	(/.f32 1 (/.f32 v (*.f32 (neg.f32 sinTheta_O) sinTheta_i)))
✓	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	6.2%	(-.f32 1 (-.f32 (+.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) 1))
	99.9%	(*.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	21.9%	(*.f32 (/.f32 (neg.f32 sinTheta_O) v) sinTheta_i)
	21.9%	(*.f32 (neg.f32 sinTheta_O) (/.f32 1 (/.f32 v sinTheta_i)))
✓	99.9%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	99.1%	(exp.f32 (/.f32 -1 v))
	99.9%	(exp.f32 (+.f32 (*.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v)))) (-.f32 6931/10000 (/.f32 1 v))))
✓	99.9%	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 682 to 486 computations (28.7% saved)

regimes477.0ms (2.5%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

9 calls:

171.0ms	(*.f32 sinTheta_i sinTheta_O)
136.0ms	cosTheta_O
37.0ms	sinTheta_i
35.0ms	sinTheta_O
26.0ms	v

Results

Accuracy	Segments	Branch
100.0%	1	`cosTheta_i`
100.0%	1	`cosTheta_O`
100.0%	1	`sinTheta_i`
100.0%	1	`sinTheta_O`
100.0%	1	`v`
100.0%	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)))))`
100.0%	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))))`
100.0%	1	`(*.f32 cosTheta_i cosTheta_O)`
100.0%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 525 to 351 computations (33.1% saved)

regimes189.0ms (1%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

9 calls:

65.0ms	cosTheta_O
25.0ms	sinTheta_O
12.0ms	cosTheta_i
12.0ms	sinTheta_i
10.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.9%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 441 to 290 computations (34.2% saved)

regimes106.0ms (0.6%)

Counts

25 → 1

Calls

Call 1

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

Outputs
(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)

Calls

9 calls:

14.0ms	v
14.0ms	sinTheta_i
13.0ms	cosTheta_i
11.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
11.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.9%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 398 to 261 computations (34.4% saved)

regimes264.0ms (1.4%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

9 calls:

35.0ms	sinTheta_i
35.0ms	cosTheta_i
34.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
33.0ms	sinTheta_O
33.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
99.9%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.9%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.9%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.9%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 364 to 236 computations (35.2% saved)

regimes183.0ms (1%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

5 calls:

58.0ms	sinTheta_O
29.0ms	cosTheta_i
29.0ms	cosTheta_O
29.0ms	sinTheta_i
24.0ms	v

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`

Compiler

Compiled 192 to 119 computations (38% saved)

regimes109.0ms (0.6%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

5 calls:

28.0ms	sinTheta_i
27.0ms	sinTheta_O
24.0ms	v
11.0ms	cosTheta_O
9.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`

Compiler

Compiled 181 to 110 computations (39.2% saved)

regimes39.0ms (0.2%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
99.1%	1	`cosTheta_i`
99.1%	1	`cosTheta_O`
99.1%	1	`sinTheta_i`
99.1%	1	`sinTheta_O`
99.1%	1	`v`

Compiler

Compiled 121 to 73 computations (39.7% saved)

regimes33.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	cosTheta_O
7.0ms	v
6.0ms	sinTheta_O
6.0ms	cosTheta_i
5.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
44.1%	1	`cosTheta_i`
44.1%	1	`cosTheta_O`
44.1%	1	`sinTheta_i`
44.1%	1	`sinTheta_O`
44.1%	1	`v`

Compiler

Compiled 96 to 59 computations (38.5% saved)

regimes27.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
43.4%	1	`v`
43.4%	1	`cosTheta_i`
43.4%	1	`cosTheta_O`
43.4%	1	`sinTheta_O`
43.4%	1	`sinTheta_i`

Compiler

Compiled 77 to 49 computations (36.4% saved)

regimes19.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
21.9%	1	`cosTheta_O`
21.9%	1	`sinTheta_i`
21.9%	1	`v`
21.9%	1	`sinTheta_O`
21.9%	1	`cosTheta_i`

Compiler

Compiled 48 to 36 computations (25% saved)

regimes15.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
1

Outputs
1

Calls

5 calls:

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

Results

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

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`+-commutative`
28×	`*-commutative`
22×	`sub-neg`
18×	`neg-mul-1`
18×	`neg-sub0`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	317
1	77	317
2	100	317
3	118	317
4	128	317
5	129	317

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 161 to 138 computations (14.3% saved)

soundness3.4s (18.1%)

Rules

1924×	`fma-neg`
1924×	`fma-neg`
1518×	`fma-def`
1518×	`fma-def`
1370×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	33	270
1	803	262
0	34	279
1	766	275
0	929	25067
1	2670	21645
0	545	24910
1	1475	23130
2	6088	23130
0	901	39410
1	2552	34466
0	796	19570
1	2049	17682
0	38	355
1	871	343
0	796	19570
1	2049	17682
0	38	355
1	871	343
0	929	25067
1	2670	21645
0	545	24910
1	1475	23130
2	6088	23130
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	34	279
1	766	275
0	34	279
1	766	275
0	796	19570
1	2049	17682
0	38	355
1	871	343

Stop Event

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

Compiler

Compiled 900 to 601 computations (33.2% saved)

end0.0ms (0%)

preprocess239.0ms (1.3%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 370 to 296 computations (20% saved)

analyze709.0ms (3.7%)

sample4.4s (23.1%)

preprocess71.0ms (0.4%)

eval1.0ms (0%)

prune3.0ms (0%)

localize330.0ms (1.7%)

series50.0ms (0.3%)

rewrite88.0ms (0.5%)

simplify235.0ms (1.2%)

eval367.0ms (1.9%)

prune258.0ms (1.4%)

localize1.4s (7.6%)

series177.0ms (0.9%)

rewrite178.0ms (0.9%)

simplify807.0ms (4.2%)

eval385.0ms (2%)

prune98.0ms (0.5%)

localize426.0ms (2.2%)

series41.0ms (0.2%)

rewrite107.0ms (0.6%)

simplify150.0ms (0.8%)

eval308.0ms (1.6%)

prune103.0ms (0.5%)

localize786.0ms (4.1%)

series104.0ms (0.5%)

rewrite107.0ms (0.6%)

simplify253.0ms (1.3%)

eval1.5s (7.7%)

prune446.0ms (2.3%)

regimes477.0ms (2.5%)

regimes189.0ms (1%)

regimes106.0ms (0.6%)

regimes264.0ms (1.4%)

regimes183.0ms (1%)

regimes109.0ms (0.6%)

regimes39.0ms (0.2%)

regimes33.0ms (0.2%)

regimes27.0ms (0.1%)

regimes19.0ms (0.1%)

regimes15.0ms (0.1%)

simplify13.0ms (0.1%)

soundness3.4s (18.1%)

end0.0ms (0%)

preprocess239.0ms (1.3%)

Profiling