Metrics for HairBSDF, Mp, lower

analyze599.0ms (4.6%)

Algorithm

1×

Search

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.4s (18.6%)

Results

2.4s	8256×	body	256	valid
31.0ms	124×	body	256	invalid

Bogosity

preprocess262.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Problems

87×	No Errors
83×	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
76×	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
10×	`(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	168	1613
1	467	1537
2	1378	1445
3	6222	1445

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 169 to 80 computations (52.7% saved)

eval1.0ms (0%)

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

prune3.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))))
▶	99.5%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (*.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000))))
▶	99.5%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 110 to 78 computations (29.1% saved)

localize350.0ms (2.7%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.9%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.5%	(exp.f32 (+.f32 (-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i)) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.3%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.2%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.8%	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.6%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.2%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.2%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series75.0ms (0.6%)

Counts

8 → 384

Calls

96 calls:

Time	Variable		Point	Expression
28.0ms	sinTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
6.0ms	cosTheta_i	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
5.0ms	v	@	-inf	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
2.0ms	v	@	-inf	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
2.0ms	v	@	0	(+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite175.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

346×	`frac-times`
301×	`log1p-expm1-u`
301×	`expm1-log1p-u`
295×	`add-exp-log`
294×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	393
1	690	353

Stop Event

1×	node limit

Counts

8 → 266

Calls

Call 1

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

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

simplify307.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

1068×	`times-frac`
910×	`associate-r`
844×	`fma-def`
760×	`associate-l`
330×	`*-commutative`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	823	42747
1	2430	40840

Stop Event

1×	node limit

Counts

650 → 451

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

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

eval248.0ms (1.9%)

Compiler: Compiled 16271 to 8785 computations (46% saved)

prune151.0ms (1.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	434	17	451
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	436	17	453

Accuracy

99.8%

Counts

453 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(pow.f32 (pow.f32 (.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000)) (/.f32 1/2 v)) 3) 1/3)
▶	99.5%	(pow.f32 (sqrt.f32 (.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000)) (/.f32 1/2 v))) 2)
	99.3%	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
▶	96.3%	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	99.5%	(.f32 (/.f32 1/2 v) (+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
▶	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	99.0%	(exp.f32 (/.f32 (-.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 2) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
	96.0%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
	99.5%	(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	13.6%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
	97.4%	(pow.f32 (pow.f32 (.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000)) (/.f32 1/2 v)) 3) 1/3)
▶	99.5%	(pow.f32 (sqrt.f32 (.f32 (exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000)) (/.f32 1/2 v))) 2)
	99.3%	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
▶	96.3%	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	99.5%	(.f32 (/.f32 1/2 v) (+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
▶	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	99.0%	(exp.f32 (/.f32 (-.f32 (pow.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 2) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2)) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (+.f32 (/.f32 1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))
	96.0%	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (+.f32 (.f32 sinTheta_O sinTheta_i) 1)) v))
	99.5%	(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	13.6%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))

Compiler

Compiled 1900 to 1344 computations (29.3% saved)

localize794.0ms (6%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.8%	(-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.6%	(exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	98.0%	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
✓	91.4%	(pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v))
✓	99.9%	(+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000)
✓	99.8%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.5%	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000))
✓	88.3%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.7%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	99.5%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	74.7%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.1%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
✓	99.9%	(.f32 (/.f32 1/2 v) (+.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_O sinTheta_i) v)))) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))))) v)))
✓	99.9%	(-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)))
✓	99.5%	(exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v))))
✓	78.2%	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)

Compiler

Compiled 499 to 237 computations (52.5% saved)

series181.0ms (1.4%)

Counts

17 → 525

Calls

180 calls:

Time	Variable		Point	Expression
29.0ms	cosTheta_i	@	-inf	(pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v))
21.0ms	cosTheta_i	@	inf	(pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v))
18.0ms	cosTheta_i	@	inf	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
16.0ms	sinTheta_i	@	inf	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
13.0ms	sinTheta_O	@	inf	(/.f32 (*.f32 sinTheta_O sinTheta_i) v)

rewrite167.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

467×	`log1p-expm1-u`
467×	`expm1-log1p-u`
461×	`add-exp-log`
460×	`add-log-exp`
442×	`pow1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	52	831
1	973	823

Stop Event

1×	node limit

Counts

17 → 397

Calls

Call 1

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

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

simplify425.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

1534×	`times-frac`
662×	`sqr-pow`
612×	`*-commutative`
530×	`+-commutative`
512×	`fma-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1455	66831
1	4241	62893

Stop Event

1×	node limit

Counts

922 → 756

Calls

Call 1

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

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

eval625.0ms (4.7%)

Compiler: Compiled 35946 to 22530 computations (37.3% saved)

prune241.0ms (1.8%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	849	14	863
Fresh	4	8	12
Picked	3	2	5
Done	0	0	0
Total	856	24	880

Accuracy

99.8%

Counts

880 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 3) 1/3) (/.f32 1/2 v))) 2)
▶	99.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) (/.f32 1/2 v))) 2)
	99.5%	(pow.f32 (sqrt.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
▶	4.7%	(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
	96.3%	(/.f32 (log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	97.4%	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))) 3) 1/3))
	99.3%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
	99.4%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
	94.0%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v))))
▶	99.5%	(.f32 (/.f32 1/2 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)))
	99.5%	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 6931/10000) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
	96.4%	(.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
✓	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
▶	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
▶	99.5%	(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	13.6%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))
	97.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 3) 1/3) (/.f32 1/2 v))) 2)
▶	99.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) (/.f32 1/2 v))) 2)
	99.5%	(pow.f32 (sqrt.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
▶	4.7%	(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
	96.3%	(/.f32 (log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	97.4%	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))) 3) 1/3))
	99.3%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
	99.4%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
	94.0%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v))))
▶	99.5%	(.f32 (/.f32 1/2 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)))
	99.5%	(.f32 (/.f32 1/2 v) (.f32 (exp.f32 6931/10000) (exp.f32 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
	96.4%	(.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
✓	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
▶	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
▶	99.5%	(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	13.6%	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_O sinTheta_i) v)))

Compiler

Compiled 2220 to 1680 computations (24.3% saved)

localize680.0ms (5.2%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) (/.f32 1/2 v))
✓	99.9%	(+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 1) v))
	99.8%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.4%	(pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 1) v)))
✓	99.6%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
✓	99.5%	(exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)))
	99.0%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	88.3%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	99.8%	(+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
✓	99.8%	(-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v))
✓	99.6%	(exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 1 v)))
✓	99.3%	(*.f32 cosTheta_O (/.f32 cosTheta_i v))
✓	99.0%	(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
✓	100.0%	(*.f32 cosTheta_i (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
✓	99.9%	(.f32 (/.f32 1/2 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)))
✓	99.9%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.5%	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))

Compiler

Compiled 423 to 227 computations (46.3% saved)

series53.0ms (0.4%)

Counts

14 → 511

Calls

135 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta_O	@	0	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
1.0ms	sinTheta_O	@	0	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
1.0ms	cosTheta_O	@	inf	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
1.0ms	sinTheta_O	@	inf	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
1.0ms	sinTheta_i	@	inf	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))

rewrite133.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

428×	`log1p-expm1-u`
428×	`expm1-log1p-u`
421×	`add-exp-log`
418×	`add-log-exp`
413×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	677
1	940	637

Stop Event

1×	node limit

Counts

14 → 287

Calls

Call 1

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

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

simplify332.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1280×	`associate-r`
1246×	`fma-def`
794×	`times-frac`
530×	`sqr-pow`
518×	`associate-+r+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	971	55891
1	2626	51687

Stop Event

1×	node limit

Counts

798 → 568

Calls

Call 1

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

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

eval440.0ms (3.3%)

Compiler: Compiled 25047 to 16244 computations (35.1% saved)

prune225.0ms (1.7%)

Pruning

27 alts after pruning (23 fresh and 4 done)

	Pruned	Kept	Total
New	793	10	803
Fresh	4	13	17
Picked	3	2	5
Done	0	2	2
Total	800	27	827

Accuracy

99.8%

Counts

827 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 3) 1/3) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (sqrt.f32 (.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2))) (/.f32 1/2 v))) 2)
	99.3%	(pow.f32 (sqrt.f32 (*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
▶	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
✓	4.7%	(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
	96.3%	(/.f32 (log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	97.4%	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))) 3) 1/3))
	99.3%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
	99.4%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
▶	94.0%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v))))
✓	99.5%	(.f32 (/.f32 1/2 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)))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
✓	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))) (/.f32 1 v)))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
▶	99.1%	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.3%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	96.0%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	97.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 3) 1/3) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (sqrt.f32 (.f32 (.f32 (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2))) (/.f32 1/2 v))) 2)
	99.3%	(pow.f32 (sqrt.f32 (*.f32 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (E.f32) (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
▶	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
✓	4.7%	(/.f32 (*.f32 1/2 (exp.f32 6931/10000)) v)
	96.3%	(/.f32 (log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	97.4%	(.f32 (/.f32 1/2 v) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))) 3) 1/3))
	99.3%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (*.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v))))))
	99.4%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (/.f32 1 v)))))
▶	94.0%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v))))
✓	99.5%	(.f32 (/.f32 1/2 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)))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
▶	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
✓	4.7%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))) (/.f32 1 v)))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
▶	99.1%	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.3%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	96.0%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))

Compiler

Compiled 2474 to 1876 computations (24.2% saved)

localize651.0ms (4.9%)

Localize:

Found 18 expressions with local error:

New	Accuracy	Program
✓	99.8%	(+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))
✓	99.5%	(pow.f32 (E.f32) (+.f32 6931/10000 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
✓	96.7%	(E.f32)
✓	88.3%	(/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v)
✓	99.6%	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.5%	(exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)))
✓	90.8%	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
	88.3%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	99.7%	(+.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))
✓	99.5%	(exp.f32 (/.f32 1 v))
✓	99.2%	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
✓	98.1%	(/.f32 (exp.f32 (+.f32 6931/10000 (*.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v)))
✓	99.8%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
✓	99.3%	(*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))
✓	100.0%	(*.f32 cosTheta_O cosTheta_i)
✓	99.9%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
✓	99.9%	(-.f32 6931/10000 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) v))
✓	99.5%	(exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) v)))

Compiler

Compiled 369 to 160 computations (56.6% saved)

series140.0ms (1.1%)

Counts

16 → 548

Calls

144 calls:

Time	Variable		Point	Expression
45.0ms	v	@	-inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
27.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
9.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
9.0ms	v	@	inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
5.0ms	sinTheta_i	@	inf	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))

rewrite146.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

449×	`log1p-expm1-u`
449×	`expm1-log1p-u`
444×	`add-exp-log`
442×	`add-log-exp`
437×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	605
1	1015	589

Stop Event

1×	node limit

Counts

16 → 294

Calls

Call 1

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

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

simplify626.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

1270×	`times-frac`
1158×	`fma-def`
666×	`sqr-pow`
614×	`associate-+r+`
428×	`unswap-sqr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1061	49868
1	2985	44907

Stop Event

1×	node limit

Counts

842 → 548

Calls

Call 1

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

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

eval358.0ms (2.7%)

Compiler: Compiled 20702 to 12771 computations (38.3% saved)

prune184.0ms (1.4%)

Pruning

30 alts after pruning (25 fresh and 5 done)

	Pruned	Kept	Total
New	663	15	678
Fresh	8	10	18
Picked	2	3	5
Done	2	2	4
Total	675	30	705

Accuracy

99.9%

Counts

705 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
	97.4%	(pow.f32 (pow.f32 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))) (/.f32 1/2 v)) 3) 1/3)
	97.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 3) 1/3) (/.f32 1/2 v))) 2)
	99.4%	(pow.f32 (sqrt.f32 (.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))) (/.f32 1/2 v))) 2)
	99.5%	(pow.f32 (sqrt.f32 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))) (/.f32 1/2 v))) 2)
	99.3%	(pow.f32 (sqrt.f32 (E.f32)) (.f32 2 (+.f32 6931/10000 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))
	99.4%	(pow.f32 (E.f32) (+.f32 6931/10000 (-.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	96.3%	(/.f32 (log.f32 (exp.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)))) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.4%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_O sinTheta_i) v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	6.3%	(-.f32 1 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))
	99.4%	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (+.f32 (/.f32 -1 v) (log.f32 (/.f32 1/2 v))))) 2)) (pow.f32 (E.f32) (/.f32 (+.f32 6931/10000 (+.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O (neg.f32 sinTheta_i))) v) (+.f32 (/.f32 -1 v) (log.f32 (/.f32 1/2 v))))) 2)))
	99.1%	(.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))))
	99.3%	(.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))) 2)) (cbrt.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (*.f32 cosTheta_O cosTheta_i)) v)))))
	99.4%	(.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
	93.9%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (pow.f32 (E.f32) (/.f32 1 v))))
✓	94.0%	(.f32 (/.f32 1/2 v) (/.f32 (exp.f32 (+.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))) (exp.f32 (/.f32 1 v))))
	99.3%	(*.f32 (/.f32 1/2 v) (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))))
✓	99.5%	(.f32 (/.f32 1/2 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)))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
✓	99.5%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 (-.f32 1 (.f32 cosTheta_O cosTheta_i)) v))))
	99.3%	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
	99.0%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (exp.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))) (/.f32 1 v)))
	99.1%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (*.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
	97.0%	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (pow.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 3) 1/3))
	99.1%	(.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (-.f32 (/.f32 (.f32 cosTheta_O cosTheta_i) v) (/.f32 1 v))))
	99.4%	(exp.f32 (fma.f32 (pow.f32 (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) 2) (cbrt.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.3%	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	96.0%	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
✓	13.6%	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
	6.5%	1

Compiler

Compiled 1915 to 1268 computations (33.8% saved)

regimes223.0ms (1.7%)

Counts

59 → 1

Calls

Call 1

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

Outputs
(.f32 (/.f32 1/2 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)))

Calls

9 calls:

30.0ms	cosTheta_i
29.0ms	sinTheta_i
28.0ms	cosTheta_O
28.0ms	sinTheta_O
21.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

Accuracy	Segments	Branch
99.5%	1	`cosTheta_i`
99.5%	1	`cosTheta_O`
99.5%	1	`sinTheta_i`
99.5%	1	`sinTheta_O`
99.5%	1	`v`
99.5%	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)))))`
99.5%	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))))`
99.5%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.5%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 1306 to 801 computations (38.7% saved)

regimes155.0ms (1.2%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

5 calls:

90.0ms	cosTheta_O
18.0ms	v
13.0ms	sinTheta_O
12.0ms	cosTheta_i
12.0ms	sinTheta_i

Results

Accuracy	Segments	Branch
99.5%	1	`cosTheta_i`
99.5%	1	`cosTheta_O`
99.5%	1	`sinTheta_i`
99.5%	1	`sinTheta_O`
99.5%	1	`v`

Compiler

Compiled 360 to 239 computations (33.6% saved)

regimes61.0ms (0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

5 calls:

13.0ms	sinTheta_i
12.0ms	cosTheta_i
10.0ms	sinTheta_O
10.0ms	cosTheta_O
8.0ms	v

Results

Accuracy	Segments	Branch
99.5%	1	`cosTheta_i`
99.5%	1	`cosTheta_O`
99.5%	1	`sinTheta_i`
99.5%	1	`sinTheta_O`
99.5%	1	`v`

Compiler

Compiled 245 to 168 computations (31.4% saved)

regimes41.0ms (0.3%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	sinTheta_O
8.0ms	cosTheta_O
7.0ms	sinTheta_i
7.0ms	cosTheta_i
6.0ms	v

Results

Accuracy	Segments	Branch
99.5%	1	`cosTheta_O`
99.5%	1	`cosTheta_i`
99.5%	1	`sinTheta_i`
99.5%	1	`sinTheta_O`
99.5%	1	`v`

Compiler

Compiled 136 to 95 computations (30.1% saved)

regimes92.0ms (0.7%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

5 calls:

62.0ms	sinTheta_O
8.0ms	cosTheta_i
7.0ms	sinTheta_i
7.0ms	cosTheta_O
6.0ms	v

Results

Accuracy	Segments	Branch
99.3%	1	`cosTheta_i`
99.3%	1	`cosTheta_O`
99.3%	1	`sinTheta_i`
99.3%	1	`sinTheta_O`
99.3%	1	`v`

Compiler

Compiled 122 to 86 computations (29.5% saved)

regimes67.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

8.0ms	sinTheta_O
6.0ms	cosTheta_i
6.0ms	sinTheta_i
6.0ms	cosTheta_O
5.0ms	v

Results

Accuracy	Segments	Branch
99.3%	1	`cosTheta_i`
99.3%	1	`cosTheta_O`
99.3%	1	`sinTheta_i`
99.3%	1	`sinTheta_O`
99.3%	1	`v`

Compiler

Compiled 88 to 66 computations (25% saved)

regimes32.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

Outputs
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
96.0%	1	`cosTheta_O`
96.0%	1	`sinTheta_O`
96.0%	1	`v`
96.0%	1	`cosTheta_i`
96.0%	1	`sinTheta_i`

Compiler

Compiled 78 to 58 computations (25.6% saved)

regimes27.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
13.6%	1	`cosTheta_i`
13.6%	1	`cosTheta_O`
13.6%	1	`sinTheta_i`
13.6%	1	`sinTheta_O`
13.6%	1	`v`

Compiler

Compiled 70 to 53 computations (24.3% saved)

regimes21.0ms (0.2%)

Accuracy

Total -0.6b remaining (-2%)

Threshold costs -0.6b (-2%)

Counts

4 → 1

Calls

Call 1

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

Outputs
1

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
6.5%	1	`cosTheta_O`
6.5%	1	`sinTheta_i`
6.5%	1	`v`
6.5%	1	`cosTheta_i`
6.5%	1	`sinTheta_O`

Compiler

Compiled 55 to 45 computations (18.2% saved)

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

290×	`distribute-lft-neg-in`
272×	`unsub-neg`
224×	`neg-mul-1`
154×	`neg-sub0`
150×	`cancel-sign-sub`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	401
1	88	401
2	120	401
3	149	401
4	214	401
5	310	401
6	358	401
7	462	401
8	559	401
9	608	401
10	660	401
11	710	401
12	751	401
13	797	401
14	847	401
15	891	401
16	944	401
17	993	401
18	1036	401
19	1065	401
20	1076	401
21	1078	401

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 151 to 121 computations (19.9% saved)

soundness1.2s (9.5%)

Rules

1534×	`times-frac`
1068×	`times-frac`
1068×	`times-frac`
910×	`associate-r`
910×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	168	1613
1	467	1537
2	1378	1445
3	6222	1445
0	168	1613
1	467	1537
2	1378	1445
3	6222	1445
0	823	42747
1	2430	40840
0	823	42747
1	2430	40840
0	1455	66831
1	4241	62893
0	52	831
1	973	823

Stop Event

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

Compiler

Compiled 701 to 421 computations (39.9% saved)

end0.0ms (0%)

preprocess114.0ms (0.9%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 394 to 290 computations (26.4% saved)

analyze599.0ms (4.6%)

sample2.4s (18.6%)

preprocess262.0ms (2%)

eval1.0ms (0%)

prune3.0ms (0%)

localize350.0ms (2.7%)

series75.0ms (0.6%)

rewrite175.0ms (1.3%)

simplify307.0ms (2.3%)

eval248.0ms (1.9%)

prune151.0ms (1.1%)

localize794.0ms (6%)

series181.0ms (1.4%)

rewrite167.0ms (1.3%)

simplify425.0ms (3.2%)

eval625.0ms (4.7%)

prune241.0ms (1.8%)

localize680.0ms (5.2%)

series53.0ms (0.4%)

rewrite133.0ms (1%)

simplify332.0ms (2.5%)

eval440.0ms (3.3%)

prune225.0ms (1.7%)

localize651.0ms (4.9%)

series140.0ms (1.1%)

rewrite146.0ms (1.1%)

simplify626.0ms (4.8%)

eval358.0ms (2.7%)

prune184.0ms (1.4%)

regimes223.0ms (1.7%)

regimes155.0ms (1.2%)

regimes61.0ms (0.5%)

regimes41.0ms (0.3%)

regimes92.0ms (0.7%)

regimes67.0ms (0.5%)

regimes32.0ms (0.2%)

regimes27.0ms (0.2%)

regimes21.0ms (0.2%)

simplify62.0ms (0.5%)

soundness1.2s (9.5%)

end0.0ms (0%)

preprocess114.0ms (0.9%)

Profiling