Metrics for HairBSDF, Mp, lower

analyze630.0ms (4.4%)

Algorithm

1×

Search

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.7s (18.9%)

Results

2.6s	8256×	body	256	valid
45.0ms	145×	body	256	invalid

Bogosity

preprocess274.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

798×	`times-frac`
782×	`associate-+l-`
664×	`associate-+l+`
622×	`associate-+r-`
588×	`sub-neg`

Problems

106×	No Errors
75×	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
71×	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
4×	`(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)))))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2130
1	482	2026
2	1419	1870
3	6386	1870

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 169 to 80 computations (52.7% saved)

eval1.0ms (0%)

Compiler: Compiled 92 to 54 computations (41.3% saved)

prune4.0ms (0%)

Alt Table

Click to see full alt table

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

localize354.0ms (2.5%)

Localize:

Found 8 expressions with local error:

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

Compiler

Compiled 218 to 87 computations (60.1% saved)

series50.0ms (0.3%)

Counts

8 → 336

Calls

84 calls:

Time	Variable		Point	Expression
9.0ms	cosTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.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_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
4.0ms	sinTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	sinTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite197.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

284×	`frac-times`
263×	`log1p-expm1-u`
263×	`expm1-log1p-u`
259×	`add-exp-log`
259×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	335
1	574	323

Stop Event

1×	node limit

Counts

8 → 297

Calls

Call 1

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

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

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def`
890×	`associate-r`
826×	`associate-l`
452×	`times-frac`
428×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	818	41649
1	2432	37666

Stop Event

1×	node limit

Counts

633 → 438

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

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

eval269.0ms (1.9%)

Compiler: Compiled 17574 to 9156 computations (47.9% saved)

prune114.0ms (0.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	473	8	481
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	475	8	483

Accuracy

99.9%

Counts

483 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)))))
	99.8%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
▶	99.1%	(exp.f32 (/.f32 (fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	98.7%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	9.0%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
▶	99.9%	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)))))
	99.8%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))
▶	99.1%	(exp.f32 (/.f32 (fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	98.7%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	9.0%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))

Compiler

Compiled 832 to 568 computations (31.7% saved)

localize795.0ms (5.6%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.3%	(fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
✓	98.3%	(pow.f32 (log.f32 (/.f32 1/2 v)) 2)
✓	89.8%	(/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v)
✓	55.6%	(/.f32 (fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.9%	(+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
✓	76.9%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	100.0%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
✓	99.7%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
✓	99.3%	(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))))
✓	99.8%	(pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)))))
✓	99.8%	(+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)))
✓	89.8%	(/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v)

Compiler

Compiled 532 to 224 computations (57.9% saved)

series140.0ms (1%)

Counts

17 → 678

Calls

198 calls:

Time	Variable		Point	Expression
26.0ms	v	@	0	(pow.f32 (log.f32 (/.f32 1/2 v)) 2)
8.0ms	v	@	-inf	(pow.f32 (log.f32 (/.f32 1/2 v)) 2)
7.0ms	cosTheta_i	@	-inf	(fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
5.0ms	v	@	inf	(pow.f32 (log.f32 (/.f32 1/2 v)) 2)
3.0ms	sinTheta_i	@	-inf	(/.f32 (fma.f32 (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (+.f32 6931/10000 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v))) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (-.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 1 v)) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite141.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`log1p-expm1-u`
431×	`expm1-log1p-u`
421×	`add-exp-log`
420×	`add-log-exp`
419×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	975
1	899	849

Stop Event

1×	node limit

Counts

17 → 352

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))) 1)
(.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (/.f32 1 v))
(.f32 1 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v))
(.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 2) (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))
(.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))
(pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 3)
(pow.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 2)
(pow.f32 (/.f32 v (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) -1)
(log.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(cbrt.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 3))
(cbrt.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(exp.f32 (log.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(exp.f32 (.f32 (log.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)) 1))
(log1p.f32 (expm1.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) (/.f32 1 v))
(-.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))) 1)
(.f32 1 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2)) (cbrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) 2) (.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) 2)) (-.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 1)
(pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) 3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) 2)
(log.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3))
(expm1.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(exp.f32 (log.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(exp.f32 (.f32 (log.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) 1))
(log1p.f32 (expm1.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(fma.f32 1 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 6931/10000)
(fma.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 6931/10000)
(-.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))) 1)
(.f32 1 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (/.f32 1/2 v))
(.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))) (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 2)))
(.f32 (pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(.f32 (pow.f32 1 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(.f32 (pow.f32 (sqrt.f32 (E.f32)) (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) (pow.f32 (sqrt.f32 (E.f32)) (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))))
(cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))) 3))
(expm1.f32 (log1p.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))))
(log1p.f32 (expm1.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))))) 1)
(.f32 1 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))))
(.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 1)
(.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) 2) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(.f32 (sqrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(/.f32 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2)) (-.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))
(/.f32 (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3)) (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (-.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(pow.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 1)
(pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) 3)
(pow.f32 (pow.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) 2)
(log.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))))))
(cbrt.f32 (pow.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v))) 3))
(expm1.f32 (log1p.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(exp.f32 (log.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(exp.f32 (.f32 (log.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))) 1))
(log1p.f32 (expm1.f32 (+.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))))
(fma.f32 1 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))
(fma.f32 1 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(fma.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2)) (cbrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (cbrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(fma.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(+.f32 0 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
(+.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 (neg.f32 sinTheta_i) v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 (neg.f32 sinTheta_i) v)))))
(+.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 (neg.f32 sinTheta_i) v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 (neg.f32 sinTheta_i) v)))))
(-.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))) 1)
(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
(pow.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)) 1)
(pow.f32 (cbrt.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) 3)
(pow.f32 (pow.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))) 2)
(log.f32 (pow.f32 (exp.f32 sinTheta_O) (/.f32 (neg.f32 sinTheta_i) v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))))
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(cbrt.f32 (/.f32 (pow.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) 3) (pow.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))
(expm1.f32 (log1p.f32 (/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(exp.f32 (log.f32 (/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(exp.f32 (.f32 (log.f32 (/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 1))
(log1p.f32 (expm1.f32 (/.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))) 1)
(.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) (/.f32 1 v))
(.f32 1 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v))
(.f32 (pow.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 2) (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))
(.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)))
(pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 3)
(pow.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)) 2)
(pow.f32 (/.f32 v (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) -1)
(log.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v))))
(cbrt.f32 (pow.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) 3))
(cbrt.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(exp.f32 (log.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(exp.f32 (.f32 (log.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v)) 1))
(log1p.f32 (expm1.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)))
(-.f32 (exp.f32 (log1p.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) 1)
(*.f32 1 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))
(*.f32 (log.f32 (/.f32 1/2 v)) (log.f32 (/.f32 1/2 v)))
(*.f32 (cbrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 4)) (cbrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(*.f32 (sqrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) (sqrt.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(log.f32 (exp.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(log.f32 (+.f32 1 (expm1.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))))
(cbrt.f32 (pow.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) 3))
(cbrt.f32 (*.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 3) (pow.f32 (log.f32 (/.f32 1/2 v)) 3)))
(expm1.f32 (log1p.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(exp.f32 (*.f32 2 (log.f32 (log.f32 (/.f32 1/2 v)))))
(exp.f32 (.f32 (.f32 2 (log.f32 (log.f32 (/.f32 1/2 v)))) 1))
(log1p.f32 (expm1.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))
(-.f32 (exp.f32 (log1p.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))))) 1)
(.f32 1 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))))
(.f32 (pow.f32 (cbrt.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))) 2) (cbrt.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))
(.f32 (hypot.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (sqrt.f32 (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))) (hypot.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (sqrt.f32 (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))
(pow.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) 1)
(pow.f32 (cbrt.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))) 3)
(pow.f32 (pow.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) 3) 1/3)
(pow.f32 (hypot.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (sqrt.f32 (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))) 2)
(log.f32 (exp.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))))))
(cbrt.f32 (pow.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) 3))
(expm1.f32 (log1p.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))
(exp.f32 (log.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))
(exp.f32 (.f32 (log.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))) 1))
(log1p.f32 (expm1.f32 (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2) (neg.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)))))

simplify519.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1152×	`times-frac`
626×	`sqr-pow`
564×	`sub-neg`
528×	`+-commutative`
506×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1357	92813
1	4028	86971

Stop Event

1×	node limit

Counts

1030 → 706

Calls

Call 1

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

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

eval877.0ms (6.2%)

Compiler: Compiled 50390 to 29428 computations (41.6% saved)

prune192.0ms (1.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	866	10	876
Fresh	2	1	3
Picked	4	1	5
Done	0	0	0
Total	872	12	884

Accuracy

99.9%

Counts

884 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	6.2%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	6.2%	(+.f32 1 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
▶	99.8%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
	99.0%	(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
▶	99.8%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
	98.7%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	9.0%	(exp.f32 (/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
✓	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	6.4%	1
▶	99.9%	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	6.2%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	6.2%	(+.f32 1 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
▶	99.8%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000))))
	99.0%	(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
▶	99.8%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
	98.7%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	9.0%	(exp.f32 (/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))))
✓	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	6.4%	1

Compiler

Compiled 768 to 598 computations (22.1% saved)

localize602.0ms (4.2%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)
✓	100.0%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
✓	100.0%	(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
✓	99.8%	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
✓	99.9%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.8%	(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 -1 v) 6931/10000)))
	99.8%	(+.f32 (/.f32 -1 v) 6931/10000)
✓	89.8%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	99.7%	(exp.f32 (/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
✓	79.2%	(/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v)
✓	100.0%	(-.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
✓	99.3%	(/.f32 sinTheta_O (/.f32 v sinTheta_i))
	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	99.8%	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
	76.9%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 273 to 124 computations (54.6% saved)

series54.0ms (0.4%)

Counts

12 → 460

Calls

123 calls:

Time	Variable		Point	Expression
15.0ms	v	@	-inf	(exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
2.0ms	sinTheta_i	@	-inf	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
1.0ms	v	@	-inf	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
1.0ms	cosTheta_O	@	0	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
1.0ms	cosTheta_O	@	inf	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))

rewrite99.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

401×	`log1p-expm1-u`
401×	`expm1-log1p-u`
394×	`add-exp-log`
391×	`add-log-exp`
388×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	49	460
1	855	456

Stop Event

1×	node limit

Counts

12 → 246

Calls

Call 1

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

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

simplify253.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

1238×	`associate-r`
1038×	`associate-l`
846×	`fma-def`
708×	`times-frac`
504×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	819	34262
1	2210	32958

Stop Event

1×	node limit

Counts

706 → 465

Calls

Call 1

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

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

eval381.0ms (2.7%)

Compiler: Compiled 15706 to 9582 computations (39% saved)

prune182.0ms (1.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	599	9	608
Fresh	2	4	6
Picked	4	1	5
Done	0	1	1
Total	605	15	620

Accuracy

100.0%

Counts

620 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
	6.2%	(fma.f32 (/.f32 (neg.f32 sinTheta_O) v) sinTheta_i 1)
	41.2%	(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
▶	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	24.0%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
▶	99.9%	(.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))))
	99.0%	(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
	99.9%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i -1)) (/.f32 1 v))))
	99.8%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v))))
	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
▶	98.7%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	9.0%	(exp.f32 (/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
✓	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	6.4%	1
	6.2%	(fma.f32 (/.f32 (neg.f32 sinTheta_O) v) sinTheta_i 1)
	41.2%	(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
▶	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
▶	24.0%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
▶	99.9%	(.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))))
	99.0%	(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
	99.9%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i -1)) (/.f32 1 v))))
	99.8%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v))))
	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
▶	98.7%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	9.0%	(exp.f32 (/.f32 (*.f32 sinTheta_O (neg.f32 sinTheta_i)) v))
▶	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
✓	9.0%	(exp.f32 (*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v)))
	6.4%	1

Compiler

Compiled 844 to 672 computations (20.4% saved)

localize456.0ms (3.2%)

Localize:

Found 14 expressions with local error:

New	Accuracy	Program
✓	100.0%	(log.f32 (/.f32 1/2 v))
✓	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)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	100.0%	(/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)
✓	99.8%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	100.0%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	79.2%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
✓	99.2%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
	99.9%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.9%	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.8%	(+.f32 6931/10000 (/.f32 -1 v))
	89.8%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)

Compiler

Compiled 202 to 91 computations (55% saved)

series21.0ms (0.1%)

Counts

11 → 228

Calls

75 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
1.0ms	cosTheta_O	@	0	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
1.0ms	sinTheta_O	@	0	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
1.0ms	v	@	-inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
1.0ms	v	@	inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))

rewrite90.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`log1p-expm1-u`
329×	`expm1-log1p-u`
324×	`add-exp-log`
322×	`add-log-exp`
320×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	41	325
1	700	313

Stop Event

1×	node limit

Counts

11 → 280

Calls

Call 1

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

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

simplify195.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

796×	`associate-r`
680×	`fma-def`
664×	`associate-l`
574×	`times-frac`
514×	`associate-/l*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	786	24194
1	2103	20927

Stop Event

1×	node limit

Counts

508 → 476

Calls

Call 1

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

Outputs
(/.f32 -1 v)
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(+.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))) (log.f32 (E.f32))))) v))
(+.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))) v))
(+.f32 (/.f32 (*.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 v cosTheta_O)) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))
(+.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.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) (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (pow.f32 (log.f32 (E.f32)) 2)))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))) (log.f32 (E.f32))))) v)))
(+.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))) (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))))) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))) v)))
(+.f32 (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))) (/.f32 (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 v cosTheta_O))) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))
(+.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_O 3) (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (pow.f32 (log.f32 (E.f32)) 3)))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (pow.f32 (log.f32 (E.f32)) 2)))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))) (log.f32 (E.f32))))) v))))
(+.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v 3) (.f32 (pow.f32 cosTheta_i 3) (.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))))) (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))))) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))) v))))
(+.f32 (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_i 3)) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))) (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))) (/.f32 (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 v cosTheta_O)))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
(exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))))
(pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v))))
(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
(+.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))) (log.f32 (E.f32))))) v))
(+.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))) v))
(+.f32 (/.f32 (*.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 v cosTheta_O)) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))
(+.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.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) (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v))))) (pow.f32 (log.f32 (E.f32)) 2)))) (pow.f32 v 2))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (.f32 (exp.f32 (.f32 (log.f32 (E.f32)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))) (log.f32 (E.f32))))) v)))
(+.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))) (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))))) (/.f32 (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 1 (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))) v)))
(+.f32 (fma.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (/.f32 (pow.f32 v 2) (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))) (/.f32 (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))) (/.f32 v cosTheta_O))) (exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))
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eval243.0ms (1.7%)

Compiler: Compiled 13391 to 8339 computations (37.7% saved)

prune128.0ms (0.9%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	585	8	593
Fresh	2	6	8
Picked	2	3	5
Done	2	0	2
Total	591	17	608

Accuracy

100.0%

Counts

608 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	41.2%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
	24.0%	(/.f32 sinTheta_O (/.f32 v sinTheta_i))
	41.4%	(/.f32 1 (/.f32 v (*.f32 sinTheta_O sinTheta_i)))
	72.1%	(-.f32 (+.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 1)
✓	6.2%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
	6.2%	(+.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i)))
	71.3%	(+.f32 1 (-.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) 1))
✓	24.0%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
	99.9%	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (+.f32 (/.f32 sinTheta_O (/.f32 v sinTheta_i)) (/.f32 1 v)))))
	99.0%	(.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) 6931/10000)) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
	99.9%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (fma.f32 cosTheta_O cosTheta_i -1)) (/.f32 1 v))))
	99.8%	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v))))
	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
	98.7%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(exp.f32 (*.f32 (log.f32 (E.f32)) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))))
	6.4%	1

Compiler

Compiled 761 to 488 computations (35.9% saved)

regimes140.0ms (1%)

Counts

38 → 1

Calls

Call 1

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

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

Calls

9 calls:

20.0ms	(+.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))))
18.0ms	sinTheta_i
17.0ms	cosTheta_i
16.0ms	cosTheta_O
16.0ms	sinTheta_O

Results

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

Compiler

Compiled 623 to 373 computations (40.1% saved)

regimes65.0ms (0.5%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 257 to 150 computations (41.6% saved)

regimes59.0ms (0.4%)

Counts

22 → 1

Calls

Call 1

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

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

Calls

5 calls:

12.0ms	sinTheta_i
11.0ms	sinTheta_O
11.0ms	cosTheta_i
10.0ms	v
10.0ms	cosTheta_O

Results

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

Compiler

Compiled 218 to 121 computations (44.5% saved)

regimes49.0ms (0.3%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
98.7%	1	`cosTheta_i`
98.7%	1	`cosTheta_O`
98.7%	1	`sinTheta_i`
98.7%	1	`sinTheta_O`
98.7%	1	`v`

Compiler

Compiled 154 to 83 computations (46.1% saved)

regimes38.0ms (0.3%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
72.1%	1	`cosTheta_i`
72.1%	1	`cosTheta_O`
72.1%	1	`sinTheta_i`
72.1%	1	`sinTheta_O`
72.1%	1	`v`

Compiler

Compiled 113 to 63 computations (44.2% saved)

regimes36.0ms (0.3%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
71.3%	1	`cosTheta_O`
71.3%	1	`cosTheta_i`
71.3%	1	`v`
71.3%	1	`sinTheta_i`
71.3%	1	`sinTheta_O`

Compiler

Compiled 104 to 58 computations (44.2% saved)

regimes32.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
41.4%	1	`cosTheta_O`
41.4%	1	`v`
41.4%	1	`cosTheta_i`
41.4%	1	`sinTheta_i`
41.4%	1	`sinTheta_O`

Compiler

Compiled 95 to 54 computations (43.2% saved)

regimes29.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
41.2%	1	`cosTheta_i`
41.2%	1	`sinTheta_i`
41.2%	1	`v`
41.2%	1	`cosTheta_O`
41.2%	1	`sinTheta_O`

Compiler

Compiled 79 to 47 computations (40.5% saved)

regimes18.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
24.0%	1	`v`
24.0%	1	`cosTheta_i`
24.0%	1	`cosTheta_O`
24.0%	1	`sinTheta_i`
24.0%	1	`sinTheta_O`

Compiler

Compiled 41 to 33 computations (19.5% 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:

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

Results

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

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	295
1	62	295
2	76	295
3	95	295
4	102	295
5	105	295
6	106	295

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 128 to 103 computations (19.5% saved)

soundness3.4s (24.2%)

Rules

1238×	`associate-r`
1238×	`associate-r`
1152×	`times-frac`
1152×	`times-frac`
1038×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	173	2130
1	482	2026
2	1419	1870
3	6386	1870
0	49	460
1	855	456
0	786	24194
1	2103	20927
0	173	2130
1	482	2026
2	1419	1870
3	6386	1870
0	818	41649
1	2432	37666
0	1357	92813
1	4028	86971
0	819	34262
1	2210	32958
0	41	325
1	700	313
0	786	24194
1	2103	20927
0	41	325
1	700	313
0	41	325
1	700	313
0	41	325
1	700	313
0	786	24194
1	2103	20927
0	818	41649
1	2432	37666
0	35	335
1	574	323
0	818	41649
1	2432	37666
0	1357	92813
1	4028	86971
0	819	34262
1	2210	32958

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
1×	node limit

Compiler

Compiled 2085 to 1049 computations (49.7% saved)

end0.0ms (0%)

preprocess103.0ms (0.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 1194 to 898 computations (24.8% saved)

analyze630.0ms (4.4%)

sample2.7s (18.9%)

preprocess274.0ms (1.9%)

eval1.0ms (0%)

prune4.0ms (0%)

localize354.0ms (2.5%)

series50.0ms (0.3%)

rewrite197.0ms (1.4%)

simplify244.0ms (1.7%)

eval269.0ms (1.9%)

prune114.0ms (0.8%)

localize795.0ms (5.6%)

series140.0ms (1%)

rewrite141.0ms (1%)

simplify519.0ms (3.6%)

eval877.0ms (6.2%)

prune192.0ms (1.3%)

localize602.0ms (4.2%)

series54.0ms (0.4%)

rewrite99.0ms (0.7%)

simplify253.0ms (1.8%)

eval381.0ms (2.7%)

prune182.0ms (1.3%)

localize456.0ms (3.2%)

series21.0ms (0.1%)

rewrite90.0ms (0.6%)

simplify195.0ms (1.4%)

eval243.0ms (1.7%)

prune128.0ms (0.9%)

regimes140.0ms (1%)

regimes65.0ms (0.5%)

regimes59.0ms (0.4%)

regimes49.0ms (0.3%)

regimes38.0ms (0.3%)

regimes36.0ms (0.3%)

regimes32.0ms (0.2%)

regimes29.0ms (0.2%)

regimes18.0ms (0.1%)

regimes15.0ms (0.1%)

simplify11.0ms (0.1%)

soundness3.4s (24.2%)

end0.0ms (0%)

preprocess103.0ms (0.7%)

Profiling