Metrics for HairBSDF, Mp, lower

analyze647.0ms (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)

sample3.1s (19.2%)

Results

3.1s	8256×	body	256	valid
33.0ms	103×	body	256	invalid

Bogosity

preprocess279.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Problems

98×	No Errors
82×	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
74×	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
2×	`(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	162	1205
1	461	1129
2	1373	1037
3	6228	1037

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 169 to 80 computations (52.7% saved)

eval1.0ms (0%)

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

prune4.0ms (0%)

Alt Table

Click to see full alt table

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

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize388.0ms (2.4%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.7%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.4%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.3%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.9%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.8%	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.3%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.2%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series149.0ms (0.9%)

Counts

8 → 384

Calls

96 calls:

Time	Variable		Point	Expression
24.0ms	cosTheta_O	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
17.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
8.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
7.0ms	sinTheta_O	@	0	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
5.0ms	cosTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite256.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	270
1	803	262

Stop Event

1×	node limit

Counts

8 → 192

Calls

Call 1

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

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

simplify532.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

1664×	`fma-neg`
774×	`log-prod`
590×	`associate-r`
574×	`fma-def`
536×	`exp-prod`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	545	24882
1	1481	23158
2	5974	23158

Stop Event

1×	node limit

Counts

576 → 321

Calls

Call 1

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

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

eval312.0ms (1.9%)

Compiler: Compiled 11412 to 6127 computations (46.3% saved)

prune130.0ms (0.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	312	9	321
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	314	9	323

Accuracy

99.9%

Counts

323 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	98.4%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	10.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	10.9%	(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.8%	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	4.7%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	98.4%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
▶	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	10.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	10.9%	(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))

Compiler

Compiled 708 to 536 computations (24.3% saved)

localize1.1s (6.6%)

Localize:

Found 15 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.5%	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))
✓	99.4%	(*.f32 sinTheta_i (/.f32 sinTheta_O v))
✓	99.4%	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	75.7%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
✓	99.5%	(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))
✓	98.9%	(*.f32 (exp.f32 6931/10000) (/.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 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	75.7%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 338 to 151 computations (55.3% saved)

series72.0ms (0.4%)

Counts

15 → 391

Calls

147 calls:

Time	Variable		Point	Expression
6.0ms	v	@	-inf	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
6.0ms	sinTheta_O	@	0	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
5.0ms	sinTheta_O	@	-inf	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
4.0ms	cosTheta_i	@	inf	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
4.0ms	sinTheta_i	@	0	(pow.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)

rewrite114.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

948×	`add-sqr-sqrt`
924×	`pow1`
920×	`*-un-lft-identity`
888×	`add-exp-log`
886×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	427
1	971	427

Stop Event

1×	node limit

Counts

15 → 150

Calls

Call 1

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

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

simplify383.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1534×	`fma-def`
792×	`times-frac`
612×	`distribute-lft-in`
598×	`distribute-rgt-in`
552×	`associate-*r/`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	842	27951
1	2590	25155

Stop Event

1×	node limit

Counts

541 → 363

Calls

Call 1

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

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

eval1.2s (7.4%)

Compiler: Compiled 19771 to 12709 computations (35.7% saved)

prune187.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	365	8	373
Fresh	2	2	4
Picked	4	1	5
Done	0	0	0
Total	371	11	382

Accuracy

99.9%

Counts

382 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	6.3%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
	6.3%	(+.f32 1 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
▶	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	98.4%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	10.9%	(exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v))
▶	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	10.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	6.4%	1
	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	6.3%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
	6.3%	(+.f32 1 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
▶	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
▶	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	98.4%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
▶	10.9%	(exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v))
▶	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	10.9%	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
	6.4%	1

Compiler

Compiled 684 to 534 computations (21.9% saved)

localize1.2s (7.4%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
✓	99.9%	(exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v))))
✓	99.8%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.4%	(pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
✓	88.6%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	100.0%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.9%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
✓	100.0%	(*.f32 sinTheta_i (neg.f32 sinTheta_O))
✓	99.9%	(exp.f32 (/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v))
✓	78.5%	(/.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)
✓	99.9%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
✓	99.5%	(*.f32 sinTheta_O (/.f32 sinTheta_i v))
✓	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))

Compiler

Compiled 255 to 130 computations (49% saved)

series291.0ms (1.8%)

Counts

16 → 451

Calls

120 calls:

Time	Variable		Point	Expression
100.0ms	v	@	-inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
88.0ms	v	@	0	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
26.0ms	cosTheta_O	@	-inf	(pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)
13.0ms	v	@	inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
6.0ms	cosTheta_i	@	inf	(pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3)

rewrite135.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

880×	`add-sqr-sqrt`
856×	`pow1`
852×	`*-un-lft-identity`
826×	`add-exp-log`
824×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	368
1	913	368

Stop Event

1×	node limit

Counts

16 → 221

Calls

Call 1

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

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

simplify267.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1596×	`fma-def`
726×	`times-frac`
626×	`distribute-lft-in`
622×	`distribute-rgt-in`
568×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	984	31130
1	2785	28774

Stop Event

1×	node limit

Counts

672 → 450

Calls

Call 1

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

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

eval610.0ms (3.8%)

Compiler: Compiled 21009 to 13444 computations (36% saved)

prune123.0ms (0.8%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	445	5	450
Fresh	2	3	5
Picked	2	3	5
Done	1	0	1
Total	450	11	461

Accuracy

99.9%

Counts

461 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	6.3%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	6.3%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
✓	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	21.7%	(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
▶	38.8%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
▶	98.4%	(exp.f32 (/.f32 -1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1
▶	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
▶	6.3%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	6.3%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
✓	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	21.7%	(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
▶	38.8%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
▶	98.4%	(exp.f32 (/.f32 -1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1

Compiler

Compiled 578 to 452 computations (21.8% saved)

localize498.0ms (3.1%)

Localize:

Found 11 expressions with local error:

New	Accuracy	Program
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	100.0%	(*.f32 sinTheta_O sinTheta_i)
✓	99.9%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	78.5%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
✓	100.0%	(*.f32 sinTheta_O sinTheta_i)
✓	78.5%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)
✓	99.5%	(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
✓	99.9%	(exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.8%	(+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.3%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	98.1%	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

Compiler

Compiled 218 to 96 computations (56% saved)

series55.0ms (0.3%)

Counts

11 → 296

Calls

105 calls:

Time	Variable		Point	Expression
10.0ms	cosTheta_i	@	-inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
5.0ms	sinTheta_i	@	0	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
3.0ms	sinTheta_i	@	inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
3.0ms	cosTheta_i	@	inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
2.0ms	v	@	-inf	(cbrt.f32 (exp.f32 (+.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

rewrite162.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

720×	`add-sqr-sqrt`
702×	`pow1`
702×	`*-un-lft-identity`
666×	`add-exp-log`
664×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	295
1	719	283

Stop Event

1×	node limit

Counts

11 → 244

Calls

Call 1

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

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

simplify247.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

1352×	`associate-r`
914×	`fma-def`
548×	`sqr-pow`
492×	`times-frac`
452×	`distribute-rgt-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	852	35778
1	2475	33402

Stop Event

1×	node limit

Counts

540 → 414

Calls

Call 1

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

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

eval490.0ms (3%)

Compiler: Compiled 21002 to 13340 computations (36.5% saved)

prune187.0ms (1.1%)

Pruning

19 alts after pruning (12 fresh and 7 done)

	Pruned	Kept	Total
New	467	9	476
Fresh	0	3	3
Picked	1	4	5
Done	0	3	3
Total	468	19	487

Accuracy

100.0%

Counts

487 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.9%	(pow.f32 (.f32 (cbrt.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))))) (cbrt.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v)))))))) 3)
	99.9%	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))) 3)
	99.8%	(/.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) (/.f32 1 v))))
✓	6.3%	(-.f32 1 (/.f32 (*.f32 sinTheta_O sinTheta_i) v))
✓	6.3%	(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
	99.3%	(.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (+.f32 6931/10000 (/.f32 -1 v)))) 3) 1/3) (/.f32 1/2 v))
✓	99.8%	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	21.7%	(*.f32 sinTheta_i (/.f32 sinTheta_O v))
	21.7%	(*.f32 sinTheta_O (/.f32 sinTheta_i v))
✓	21.7%	(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
✓	38.8%	(.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v))
	38.8%	(.f32 -1 (/.f32 1 (/.f32 v (.f32 sinTheta_O sinTheta_i))))
	71.7%	(*.f32 -1 (-.f32 (+.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i))) 1))
	72.1%	(.f32 -1 (+.f32 1 (-.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 1)))
	38.8%	(.f32 -1 (.f32 (*.f32 sinTheta_i sinTheta_O) (/.f32 1 v)))
	21.7%	(.f32 -1 (.f32 1 (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
✓	98.4%	(exp.f32 (/.f32 -1 v))
✓	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	6.4%	1

Compiler

Compiled 768 to 508 computations (33.9% saved)

regimes145.0ms (0.9%)

Counts

34 → 1

Calls

Call 1

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

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

Calls

9 calls:

24.0ms	cosTheta_O
18.0ms	cosTheta_i
18.0ms	sinTheta_i
16.0ms	sinTheta_O
16.0ms	v

Results

Accuracy	Segments	Branch
99.9%	1	`cosTheta_i`
99.9%	1	`cosTheta_O`
99.9%	1	`sinTheta_i`
99.9%	1	`sinTheta_O`
99.9%	1	`v`
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 561 to 348 computations (38% saved)

regimes81.0ms (0.5%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

6 calls:

15.0ms	sinTheta_i
14.0ms	cosTheta_i
13.0ms	v
12.0ms	cosTheta_O
11.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
99.8%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 238 to 141 computations (40.8% saved)

regimes69.0ms (0.4%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

6 calls:

13.0ms	cosTheta_O
13.0ms	v
10.0ms	sinTheta_i
10.0ms	cosTheta_i
9.0ms	sinTheta_O

Results

Accuracy	Segments	Branch
98.4%	1	`cosTheta_i`
98.4%	1	`cosTheta_O`
98.4%	1	`sinTheta_i`
98.4%	1	`sinTheta_O`
98.4%	1	`v`
98.4%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 178 to 105 computations (41% saved)

regimes73.0ms (0.4%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

6 calls:

24.0ms	sinTheta_i
12.0ms	sinTheta_O
9.0ms	(*.f32 sinTheta_i sinTheta_O)
8.0ms	cosTheta_i
8.0ms	cosTheta_O

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`
72.1%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 139 to 84 computations (39.6% saved)

regimes54.0ms (0.3%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

6 calls:

11.0ms	v
11.0ms	cosTheta_i
10.0ms	sinTheta_i
8.0ms	sinTheta_O
6.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
38.8%	1	`cosTheta_O`
38.8%	1	`cosTheta_i`
38.8%	1	`sinTheta_i`
38.8%	1	`sinTheta_O`
38.8%	1	`(*.f32 sinTheta_i sinTheta_O)`
38.8%	1	`v`

Compiler

Compiled 117 to 72 computations (38.5% saved)

regimes56.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

24.0ms	sinTheta_i
11.0ms	cosTheta_O
9.0ms	sinTheta_O
5.0ms	cosTheta_i
5.0ms	v

Results

Accuracy	Segments	Branch
38.8%	1	`sinTheta_O`
38.8%	1	`cosTheta_i`
38.8%	1	`cosTheta_O`
38.8%	1	`v`
38.8%	1	`sinTheta_i`

Compiler

Compiled 82 to 51 computations (37.8% saved)

regimes26.0ms (0.2%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	v
5.0ms	cosTheta_O
4.0ms	sinTheta_O
4.0ms	cosTheta_i
4.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
21.7%	1	`cosTheta_i`
21.7%	1	`sinTheta_O`
21.7%	1	`cosTheta_O`
21.7%	1	`v`
21.7%	1	`sinTheta_i`

Compiler

Compiled 52 to 37 computations (28.8% saved)

regimes18.0ms (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:

5.0ms	cosTheta_O
4.0ms	v
3.0ms	sinTheta_i
3.0ms	sinTheta_O
3.0ms	cosTheta_i

Results

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

Compiler

Compiled 36 to 31 computations (13.9% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

34×	`+-commutative`
30×	`sub-neg`
30×	`*-commutative`
24×	`neg-sub0`
18×	`neg-mul-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	156
1	51	156
2	71	148
3	103	148
4	126	148
5	138	148
6	144	148
7	145	148

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 93 to 76 computations (18.3% saved)

soundness2.5s (15.6%)

Rules

1664×	`fma-neg`
1596×	`fma-def`
1534×	`fma-def`
1534×	`fma-def`
1352×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037
0	842	27951
1	2590	25155
0	545	24882
1	1481	23158
2	5974	23158
0	842	27951
1	2590	25155
0	984	31130
1	2785	28774
0	33	295
1	719	283
0	852	35778
1	2475	33402
0	33	295
1	719	283
0	33	295
1	719	283
0	852	35778
1	2475	33402
0	162	1205
1	461	1129
2	1373	1037
3	6228	1037

Stop Event

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

Compiler

Compiled 505 to 298 computations (41% saved)

end0.0ms (0%)

preprocess71.0ms (0.4%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 240 to 178 computations (25.8% saved)

analyze647.0ms (4%)

sample3.1s (19.2%)

preprocess279.0ms (1.7%)

eval1.0ms (0%)

prune4.0ms (0%)

localize388.0ms (2.4%)

series149.0ms (0.9%)

rewrite256.0ms (1.6%)

simplify532.0ms (3.3%)

eval312.0ms (1.9%)

prune130.0ms (0.8%)

localize1.1s (6.6%)

series72.0ms (0.4%)

rewrite114.0ms (0.7%)

simplify383.0ms (2.4%)

eval1.2s (7.4%)

prune187.0ms (1.2%)

localize1.2s (7.4%)

series291.0ms (1.8%)

rewrite135.0ms (0.8%)

simplify267.0ms (1.6%)

eval610.0ms (3.8%)

prune123.0ms (0.8%)

localize498.0ms (3.1%)

series55.0ms (0.3%)

rewrite162.0ms (1%)

simplify247.0ms (1.5%)

eval490.0ms (3%)

prune187.0ms (1.1%)

regimes145.0ms (0.9%)

regimes81.0ms (0.5%)

regimes69.0ms (0.4%)

regimes73.0ms (0.4%)

regimes54.0ms (0.3%)

regimes56.0ms (0.3%)

regimes26.0ms (0.2%)

regimes18.0ms (0.1%)

simplify11.0ms (0.1%)

soundness2.5s (15.6%)

end0.0ms (0%)

preprocess71.0ms (0.4%)

Profiling