Metrics for HairBSDF, Mp, lower

analyze590.0ms (5%)

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)

sample2.5s (20.7%)

Results

2.4s	8256×	body	256	valid
29.0ms	122×	body	256	invalid

Bogosity

preprocess269.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

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

Problems

89×	No Errors
88×	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
74×	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
4×	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
1×	`(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
▶	99.4%	(.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))))
▶	99.4%	(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)))))
▶	99.4%	(.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))))
▶	99.4%	(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)

localize353.0ms (3%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	99.7%	(-.f32 (.f32 (/.f32 cosTheta_O v) cosTheta_i) (.f32 (/.f32 sinTheta_O v) sinTheta_i))
✓	99.6%	(.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))))
✓	99.3%	(*.f32 (/.f32 cosTheta_O v) cosTheta_i)
✓	99.2%	(*.f32 (/.f32 sinTheta_O v) sinTheta_i)
✓	99.8%	(exp.f32 (+.f32 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.4%	(/.f32 sinTheta_i (/.f32 v sinTheta_O))
✓	99.3%	(/.f32 cosTheta_i (/.f32 v cosTheta_O))

Compiler

Compiled 218 to 89 computations (59.2% saved)

series89.0ms (0.7%)

Counts

8 → 336

Calls

84 calls:

Time	Variable		Point	Expression
26.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
17.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))
6.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
5.0ms	cosTheta_i	@	inf	(.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))))
2.0ms	v	@	0	(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)))))

rewrite133.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

348×	`frac-times`
311×	`log1p-expm1-u`
311×	`expm1-log1p-u`
305×	`add-exp-log`
304×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	40	333
1	712	302

Stop Event

1×	node limit

Counts

8 → 207

Calls

Call 1

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

simplify273.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

848×	`times-frac`
776×	`associate-r`
764×	`fma-def`
696×	`log-prod`
684×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	622	31465
1	1808	30065
2	7966	30065

Stop Event

1×	node limit

Counts

543 → 337

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

eval175.0ms (1.5%)

Compiler: Compiled 11637 to 6387 computations (45.1% saved)

prune69.0ms (0.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	332	5	337
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	334	5	339

Accuracy

99.9%

Counts

339 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.4%	(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)
▶	99.4%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (.f32 (neg.f32 sinTheta_O) sinTheta_i) v) (+.f32 (/.f32 -1 v) 6931/10000))))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
▶	99.4%	(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)
▶	99.4%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (.f32 (neg.f32 sinTheta_O) sinTheta_i) v) (+.f32 (/.f32 -1 v) 6931/10000))))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))

Compiler

Compiled 416 to 324 computations (22.1% saved)

localize610.0ms (5.1%)

Localize:

Found 18 expressions with local error:

New	Accuracy	Program
✓	99.8%	(exp.f32 (+.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v) (/.f32 1 v)) 6931/10000))
✓	99.6%	(.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))
✓	99.3%	(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)))
✓	88.3%	(/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) v)
✓	99.8%	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v)))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	76.0%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.9%	(+.f32 (/.f32 -1 v) 6931/10000)
✓	99.8%	(exp.f32 (+.f32 (/.f32 (*.f32 (neg.f32 sinTheta_O) sinTheta_i) v) (+.f32 (/.f32 -1 v) 6931/10000)))
✓	99.6%	(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (.f32 (neg.f32 sinTheta_O) sinTheta_i) v) (+.f32 (/.f32 -1 v) 6931/10000))))
✓	73.1%	(/.f32 (*.f32 (neg.f32 sinTheta_O) sinTheta_i) v)
✓	99.8%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
✓	99.0%	(/.f32 (exp.f32 6931/10000) v)
✓	99.9%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v))
✓	76.0%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 393 to 183 computations (53.4% saved)

series63.0ms (0.5%)

Counts

17 → 407

Calls

159 calls:

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

rewrite151.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

421×	`log1p-expm1-u`
421×	`expm1-log1p-u`
416×	`add-exp-log`
415×	`add-log-exp`
413×	`add-cube-cbrt`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	725
1	889	725

Stop Event

1×	node limit

Counts

17 → 342

Calls

Call 1

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

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

simplify343.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

1644×	`fma-def`
1234×	`times-frac`
602×	`sqr-pow`
514×	`*-commutative`
442×	`unswap-sqr`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1174	51322
1	3185	49752

Stop Event

1×	node limit

Counts

749 → 686

Calls

Call 1

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

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

eval501.0ms (4.2%)

Compiler: Compiled 24418 to 16266 computations (33.4% saved)

prune165.0ms (1.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	727	11	738
Fresh	0	0	0
Picked	4	1	5
Done	0	0	0
Total	731	12	743

Accuracy

99.9%

Counts

743 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(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 (exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 1/2)) 2)
▶	99.8%	(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
▶	89.6%	(/.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (exp.f32 (/.f32 1 v)))
	99.4%	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))))))
	99.3%	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))))
▶	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	91.2%	(*.f32 1/2 (/.f32 (/.f32 (exp.f32 (+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 6931/10000)) (exp.f32 (/.f32 1 v))) v))
✓	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	4.5%	(*.f32 1/2 (/.f32 1 (/.f32 v (exp.f32 6931/10000))))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.4%	(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 (exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 1/2)) 2)
▶	99.8%	(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
▶	89.6%	(/.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (exp.f32 (/.f32 1 v)))
	99.4%	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))) 2))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))))))
	99.3%	(*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))))
▶	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))))
▶	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	91.2%	(*.f32 1/2 (/.f32 (/.f32 (exp.f32 (+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 6931/10000)) (exp.f32 (/.f32 1 v))) v))
✓	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	4.5%	(*.f32 1/2 (/.f32 1 (/.f32 v (exp.f32 6931/10000))))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 950 to 756 computations (20.4% saved)

localize613.0ms (5.2%)

Localize:

Found 16 expressions with local error:

New	Accuracy	Program
	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.3%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
✓	94.3%	(/.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (exp.f32 (/.f32 1 v)))
✓	92.0%	(exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 cosTheta_O (/.f32 v cosTheta_i))))
✓	99.8%	(exp.f32 (+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 6931/10000))
✓	99.8%	(+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 6931/10000)
✓	99.3%	(/.f32 cosTheta_O (/.f32 v cosTheta_i))
✓	95.4%	(/.f32 (exp.f32 (+.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)) 6931/10000)) (exp.f32 (/.f32 1 v)))
✓	99.9%	(+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))
✓	99.8%	(exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i)))))
✓	99.6%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 -1 v) (/.f32 sinTheta_O (/.f32 v sinTheta_i))))))
✓	99.3%	(/.f32 sinTheta_O (/.f32 v sinTheta_i))
✓	98.9%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	100.0%	(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
✓	99.9%	(+.f32 6931/10000 (/.f32 -1 v))
✓	99.8%	(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))

Compiler

Compiled 282 to 160 computations (43.3% saved)

series44.0ms (0.4%)

Counts

15 → 444

Calls

111 calls:

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

rewrite114.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

354×	`add-exp-log`
354×	`log1p-expm1-u`
354×	`expm1-log1p-u`
353×	`add-log-exp`
348×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	533
1	748	513

Stop Event

1×	node limit

Counts

15 → 304

Calls

Call 1

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

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

simplify245.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def`
1154×	`times-frac`
594×	`associate-+r+`
546×	`sqr-pow`
520×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	970	37168
1	2686	34062

Stop Event

1×	node limit

Counts

748 → 542

Calls

Call 1

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

Outputs
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(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 (exp.f32 6931/10000) (-.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) (pow.f32 v 2)) (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))))
(+.f32 (exp.f32 6931/10000) (fma.f32 -1 (/.f32 (exp.f32 6931/10000) v) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (*.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))))
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(exp.f32 6931/10000)
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(+.f32 (-.f32 (exp.f32 6931/10000) (/.f32 (exp.f32 6931/10000) v)) (fma.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)) (/.f32 (*.f32 (exp.f32 6931/10000) -1/6) (pow.f32 v 3))))
(/.f32 -1 v)
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6931/10000
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6931/10000
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(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
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(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)
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(fma.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)) -1/2 (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (/.f32 (*.f32 1/4 (exp.f32 6931/10000)) (pow.f32 v 3))))
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(fma.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)) (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3)) (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
(fma.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)) -1/2 (fma.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4)) (fma.f32 (exp.f32 6931/10000) (/.f32 1/2 v) (/.f32 (*.f32 1/4 (exp.f32 6931/10000)) (pow.f32 v 3)))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
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eval419.0ms (3.5%)

Compiler: Compiled 16851 to 12330 computations (26.8% saved)

prune149.0ms (1.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	589	9	598
Fresh	4	2	6
Picked	4	1	5
Done	0	1	1
Total	597	13	610

Accuracy

99.9%

Counts

610 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(pow.f32 (sqrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))) 2)
▶	99.4%	(pow.f32 (exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 1/2)) 2)
	89.7%	(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (exp.f32 (/.f32 1 v)))
	89.7%	(/.f32 (pow.f32 (E.f32) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (exp.f32 (/.f32 1 v)))
	99.7%	(/.f32 (*.f32 1/2 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))) v)
▶	98.3%	(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
	89.6%	(/.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 3)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (exp.f32 (/.f32 1 v)))
▶	99.4%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
✓	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.8%	(*.f32 1/2 (/.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) v))
✓	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.8%	(pow.f32 (sqrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))) 2)
▶	99.4%	(pow.f32 (exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 1/2)) 2)
	89.7%	(/.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (exp.f32 (/.f32 1 v)))
	89.7%	(/.f32 (pow.f32 (E.f32) (fma.f32 (/.f32 cosTheta_O v) cosTheta_i (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (exp.f32 (/.f32 1 v)))
	99.7%	(/.f32 (*.f32 1/2 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))) v)
▶	98.3%	(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
	89.6%	(/.f32 (exp.f32 (+.f32 (+.f32 6931/10000 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 3)) (/.f32 cosTheta_O (/.f32 v cosTheta_i)))) (exp.f32 (/.f32 1 v)))
▶	99.4%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
✓	4.5%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
▶	99.8%	(*.f32 1/2 (/.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) v))
✓	4.5%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 952 to 788 computations (17.2% saved)

localize617.0ms (5.2%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.9%	(-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))
✓	99.8%	(+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 1) v)))
✓	99.7%	(exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) 1) v))) 1/2))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	99.8%	(exp.f32 (/.f32 1 v))
✓	99.6%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	90.2%	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	99.9%	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	99.8%	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))
✓	99.8%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	99.6%	(log.f32 (/.f32 1/2 v))
✓	100.0%	(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
✓	99.8%	(exp.f32 (/.f32 -1 v))
✓	100.0%	(/.f32 (/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v))) v)
✓	100.0%	(/.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 1 v)))
✓	99.8%	(exp.f32 (/.f32 1 v))

Compiler

Compiled 298 to 190 computations (36.2% saved)

series22.0ms (0.2%)

Counts

14 → 280

Calls

75 calls:

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

rewrite118.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

328×	`log1p-expm1-u`
328×	`expm1-log1p-u`
324×	`add-exp-log`
323×	`add-log-exp`
322×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	456
1	709	442

Stop Event

1×	node limit

Counts

14 → 402

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2) (cbrt.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) 2)
(pow.f32 (exp.f32 1) (/.f32 1 v))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 v -2))) (cbrt.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (pow.f32 v -1/2)) (pow.f32 v -1/2))
(pow.f32 (exp.f32 -1) (/.f32 1 v))
(sqrt.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2))
(log.f32 (exp.f32 (exp.f32 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 1 v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (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 (/.f32 1 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2)) (/.f32 (exp.f32 6931/10000) (cbrt.f32 (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 1 (sqrt.f32 (exp.f32 (/.f32 1 v)))) (/.f32 (exp.f32 6931/10000) (sqrt.f32 (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) 1) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2)) (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (sqrt.f32 (exp.f32 (/.f32 1 v)))) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) (sqrt.f32 (exp.f32 (/.f32 1 v)))))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) 1) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2)) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (cbrt.f32 (exp.f32 (/.f32 1 v)))))
(pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 1)
(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 (-.f32 (/.f32 1 v) 6931/10000)) -1)
(sqrt.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2))
(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))
(cbrt.f32 (/.f32 (pow.f32 (exp.f32 6931/10000) 3) (pow.f32 (exp.f32 (/.f32 1 v)) 3)))
(expm1.f32 (log1p.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (*.f32 (-.f32 6931/10000 (/.f32 1 v)) 1))
(log1p.f32 (expm1.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(-.f32 (exp.f32 (log1p.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))) 1)
(*.f32 1 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 (/.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1 v))
(*.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) 2) (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (pow.f32 v -1/2) (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (sqrt.f32 v)))
(*.f32 (sqrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) (sqrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 6931/10000) 1) (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) v))
(*.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) v) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) v) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v))))
(*.f32 (/.f32 (exp.f32 6931/10000) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 6931/10000) (sqrt.f32 v)) (/.f32 (exp.f32 (neg.f32 (/.f32 1 v))) (sqrt.f32 v)))
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) 1) (/.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) v))
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(*.f32 (/.f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 2) (sqrt.f32 v)) (/.f32 (cbrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (sqrt.f32 v)))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1) (/.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) v))
(*.f32 (/.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (cbrt.f32 v)))
(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1)
(pow.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) 3)
(pow.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 3) 1/3)
(pow.f32 (sqrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) 2)
(pow.f32 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) -1)
(sqrt.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 2))
(log.f32 (exp.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(log.f32 (+.f32 1 (expm1.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))))
(cbrt.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 3))
(cbrt.f32 (*.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 3) (pow.f32 v -3)))
(cbrt.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 3) (pow.f32 v 3)))
(expm1.f32 (log1p.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v)))
(exp.f32 (*.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v)) 1))
(log1p.f32 (expm1.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)))
(-.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 1 v)))) 1)
(*.f32 1 (exp.f32 (/.f32 1 v)))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 2) (cbrt.f32 (exp.f32 (/.f32 1 v))))
(*.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) (sqrt.f32 (exp.f32 (/.f32 1 v))))
(pow.f32 (exp.f32 (/.f32 1 v)) 1)
(pow.f32 (cbrt.f32 (exp.f32 (/.f32 1 v))) 3)
(pow.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 3) 1/3)
(pow.f32 (sqrt.f32 (exp.f32 (/.f32 1 v))) 2)
(pow.f32 (exp.f32 1) (/.f32 1 v))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 v -2))) (cbrt.f32 (/.f32 1 v)))
(pow.f32 (exp.f32 (pow.f32 v -1/2)) (pow.f32 v -1/2))
(pow.f32 (exp.f32 -1) (/.f32 1 v))
(sqrt.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 2))
(log.f32 (exp.f32 (exp.f32 (/.f32 1 v))))
(log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 1 v)))))
(cbrt.f32 (pow.f32 (exp.f32 (/.f32 1 v)) 3))
(expm1.f32 (log1p.f32 (exp.f32 (/.f32 1 v))))
(log1p.f32 (expm1.f32 (exp.f32 (/.f32 1 v))))
(-.f32 (exp.f32 (log1p.f32 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v)))))) 1)
(*.f32 1 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v)))))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 1 v)) v))
(.f32 (.f32 (exp.f32 (/.f32 1 v)) 1/2) (/.f32 1 v))
(*.f32 (pow.f32 (cbrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v))))) 2) (cbrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v))))))
(.f32 (pow.f32 v -1/2) (/.f32 (.f32 (exp.f32 (/.f32 1 v)) 1/2) (sqrt.f32 v)))
(*.f32 (sqrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v))))) (sqrt.f32 (/.f32 1/2 (/.f32 v (exp.f32 (/.f32 1 v))))))
(.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (.f32 (exp.f32 (/.f32 1 v)) 1/2) (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 (/.f32 1 v)) 1) (/.f32 1/2 v))
(*.f32 (/.f32 (exp.f32 (/.f32 1 v)) (pow.f32 (cbrt.f32 v) 2)) (/.f32 1/2 (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 (/.f32 1 v)) (sqrt.f32 v)) (/.f32 1/2 (sqrt.f32 v)))
(*.f32 (/.f32 1/2 (sqrt.f32 v)) (/.f32 (exp.f32 (/.f32 1 v)) (sqrt.f32 v)))
(*.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (/.f32 1 v)) (cbrt.f32 v)))
(.f32 (/.f32 (pow.f32 (cbrt.f32 (.f32 (exp.f32 (/.f32 1 v)) 1/2)) 2) 1) (/.f32 (cbrt.f32 (*.f32 (exp.f32 (/.f32 1 v)) 1/2)) v))
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(/.f32 (+.f32 (.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) (neg.f32 v)) (.f32 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (neg.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))))) (.f32 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (neg.f32 v)))
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(/.f32 (neg.f32 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (pow.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) 2))) (neg.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)))))
(pow.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)
(pow.f32 (cbrt.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)))) 3)
(pow.f32 (pow.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))) 3) 1/3)
(pow.f32 (sqrt.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)))) 2)
(sqrt.f32 (pow.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))) 2))
(log.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))))))
(cbrt.f32 (pow.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))) 3))
(expm1.f32 (log1p.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 (log.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 (log.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 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))))
(fma.f32 1 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(fma.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))
(fma.f32 1 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)) (log.f32 (/.f32 1/2 v)))
(fma.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))
(fma.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) 2) (cbrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) (cbrt.f32 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(fma.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))
(fma.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v))) (log.f32 (/.f32 1/2 v)))
(fma.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1)) v)))
(+.f32 (.f32 cosTheta_O cosTheta_i) (neg.f32 (.f32 sinTheta_O sinTheta_i)))
(+.f32 (.f32 cosTheta_O cosTheta_i) (.f32 (neg.f32 sinTheta_O) sinTheta_i))
(+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_O) sinTheta_i (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 (sqrt.f32 (.f32 sinTheta_O sinTheta_i))) (sqrt.f32 (.f32 sinTheta_O sinTheta_i)) (*.f32 sinTheta_O sinTheta_i)))
(+.f32 (fma.f32 1 (.f32 cosTheta_O cosTheta_i) (neg.f32 (.f32 (.f32 sinTheta_O sinTheta_i) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_O sinTheta_i)) 1 (.f32 (.f32 sinTheta_O sinTheta_i) 1)))
(+.f32 (fma.f32 1 (.f32 cosTheta_O cosTheta_i) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i))) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (*.f32 sinTheta_O sinTheta_i)) 2))))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (.f32 (.f32 sinTheta_O sinTheta_i) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_O sinTheta_i)) 1 (.f32 (*.f32 sinTheta_O sinTheta_i) 1)))
(+.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i))) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2))))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 (.f32 sinTheta_O sinTheta_i) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_O sinTheta_i)) 1 (.f32 (*.f32 sinTheta_O sinTheta_i) 1)))
(+.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i))) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2))))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) 2) (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (.f32 (.f32 sinTheta_O sinTheta_i) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_O sinTheta_i)) 1 (.f32 (*.f32 sinTheta_O sinTheta_i) 1)))
(+.f32 (fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) 2) (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i))) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2))))
(+.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (.f32 (.f32 sinTheta_O sinTheta_i) 1))) (fma.f32 (neg.f32 (.f32 sinTheta_O sinTheta_i)) 1 (.f32 (*.f32 sinTheta_O sinTheta_i) 1)))
(+.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2)))) (fma.f32 (neg.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i))) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) (pow.f32 (cbrt.f32 (.f32 sinTheta_O sinTheta_i)) 2))))
(.f32 1 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)))
(.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) 2) (cbrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))))
(.f32 (sqrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) (sqrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))))
(/.f32 (-.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 3) (pow.f32 (.f32 sinTheta_O sinTheta_i) 3)) (+.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 2) (+.f32 (pow.f32 (.f32 sinTheta_O sinTheta_i) 2) (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)))))
(/.f32 (-.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 2) (pow.f32 (.f32 sinTheta_O sinTheta_i) 2)) (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O sinTheta_i)))
(/.f32 (neg.f32 (-.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 3) (pow.f32 (.f32 sinTheta_O sinTheta_i) 3))) (neg.f32 (+.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 2) (+.f32 (pow.f32 (.f32 sinTheta_O sinTheta_i) 2) (.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (.f32 cosTheta_O cosTheta_i) 2) (pow.f32 (.f32 sinTheta_O sinTheta_i) 2))) (neg.f32 (fma.f32 cosTheta_O cosTheta_i (*.f32 sinTheta_O sinTheta_i))))
(pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 1)
(pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) 3)
(pow.f32 (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) 2)
(sqrt.f32 (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 2))
(log.f32 (exp.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))))
(log.f32 (+.f32 1 (expm1.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)))))
(cbrt.f32 (pow.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) 3))
(expm1.f32 (log1p.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))))
(exp.f32 (log.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))))
(exp.f32 (.f32 (log.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i))) 1))
(log1p.f32 (expm1.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))))
(fma.f32 1 (.f32 cosTheta_O cosTheta_i) (neg.f32 (.f32 sinTheta_O sinTheta_i)))
(fma.f32 1 (.f32 cosTheta_O cosTheta_i) (.f32 (neg.f32 sinTheta_O) sinTheta_i))
(fma.f32 1 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 cosTheta_O cosTheta_i (neg.f32 (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 cosTheta_O cosTheta_i (*.f32 (neg.f32 sinTheta_O) sinTheta_i))
(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 cosTheta_i cosTheta_O (*.f32 (neg.f32 sinTheta_O) sinTheta_i))
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) 2) (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) 2) (cbrt.f32 (.f32 cosTheta_O cosTheta_i)) (*.f32 (neg.f32 sinTheta_O) sinTheta_i))
(fma.f32 (pow.f32 (cbrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) 2) (cbrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (neg.f32 (*.f32 sinTheta_O sinTheta_i)))
(fma.f32 (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (sqrt.f32 (.f32 cosTheta_O cosTheta_i)) (*.f32 (neg.f32 sinTheta_O) sinTheta_i))
(fma.f32 (sqrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) (sqrt.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i))) (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (*.f32 sinTheta_O sinTheta_i)))

simplify290.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1098×	`times-frac`
974×	`fma-def`
494×	`sqr-pow`
482×	`associate-+r+`
474×	`associate-+l+`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1049	40301
1	2820	37491

Stop Event

1×	node limit

Counts

682 → 623

Calls

Call 1

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

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

eval550.0ms (4.6%)

Compiler: Compiled 23070 to 17474 computations (24.3% saved)

prune281.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	964	7	971
Fresh	4	2	6
Picked	2	3	5
Done	2	0	2
Total	972	12	984

Accuracy

100.0%

Counts

984 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.4%	(pow.f32 (exp.f32 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v))) 1/2)) 2)
	99.4%	(/.f32 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	99.7%	(/.f32 (*.f32 1/2 (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))) v)
✓	98.3%	(/.f32 (*.f32 1/2 (exp.f32 (/.f32 -1 v))) v)
	99.4%	(/.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)) (exp.f32 (/.f32 1 v)))
✓	99.4%	(/.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (exp.f32 (/.f32 1 v)))
	4.5%	(/.f32 1/2 v)
	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	99.8%	(*.f32 1/2 (/.f32 (/.f32 1 (exp.f32 (+.f32 (/.f32 1 v) -6931/10000))) v))
	99.8%	(*.f32 1/2 (exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (log.f32 v))))
	98.1%	(exp.f32 (/.f32 -1 v))
✓	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 738 to 553 computations (25.1% saved)

regimes185.0ms (1.6%)

Counts

35 → 1

Calls

Call 1

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

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

Calls

9 calls:

38.0ms	v
16.0ms	sinTheta_O
16.0ms	sinTheta_i
15.0ms	cosTheta_i
14.0ms	cosTheta_O

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
99.8%	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
99.8%	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
99.8%	1	`(*.f32 cosTheta_i cosTheta_O)`
99.8%	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 652 to 466 computations (28.5% saved)

regimes45.0ms (0.4%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	sinTheta_i
8.0ms	v
8.0ms	sinTheta_O
7.0ms	cosTheta_i
7.0ms	cosTheta_O

Results

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

Compiler

Compiled 195 to 150 computations (23.1% saved)

regimes54.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

5 calls:

27.0ms	cosTheta_i
9.0ms	v
5.0ms	sinTheta_i
5.0ms	sinTheta_O
5.0ms	cosTheta_O

Results

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

Compiler

Compiled 90 to 74 computations (17.8% saved)

regimes30.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Accuracy	Segments	Branch
99.4%	1	`cosTheta_i`
99.4%	1	`cosTheta_O`
99.4%	1	`sinTheta_i`
99.4%	1	`sinTheta_O`
99.4%	1	`v`

Compiler

Compiled 80 to 66 computations (17.5% saved)

regimes29.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

5 calls:

9.0ms	sinTheta_i
5.0ms	cosTheta_O
5.0ms	cosTheta_i
5.0ms	sinTheta_O
4.0ms	v

Results

Accuracy	Segments	Branch
98.3%	1	`cosTheta_i`
98.3%	1	`cosTheta_O`
98.3%	1	`sinTheta_i`
98.3%	1	`sinTheta_O`
98.3%	1	`v`

Compiler

Compiled 70 to 58 computations (17.1% saved)

regimes33.0ms (0.3%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

15.0ms	sinTheta_i
4.0ms	v
4.0ms	cosTheta_O
4.0ms	sinTheta_O
4.0ms	cosTheta_i

Results

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

Compiler

Compiled 62 to 52 computations (16.1% saved)

regimes37.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f32 1/2 v)

Outputs
(/.f32 1/2 v)

Calls

5 calls:

26.0ms	cosTheta_O
3.0ms	sinTheta_i
3.0ms	cosTheta_i
3.0ms	sinTheta_O
3.0ms	v

Results

Accuracy	Segments	Branch
4.5%	1	`cosTheta_i`
4.5%	1	`cosTheta_O`
4.5%	1	`sinTheta_i`
4.5%	1	`sinTheta_O`
4.5%	1	`v`

Compiler

Compiled 38 to 32 computations (15.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative`
4×	`+-commutative`
2×	`1-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	203
1	41	203

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 93 to 81 computations (12.9% saved)

soundness1.7s (14%)

Rules

1644×	`fma-def`
1234×	`times-frac`
1186×	`fma-def`
1154×	`times-frac`
1098×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	168	1613
1	467	1537
2	1378	1445
3	6222	1445
0	49	725
1	889	725
0	622	31465
1	1808	30065
2	7966	30065
0	1174	51322
1	3185	49752
0	168	1613
1	467	1537
2	1378	1445
3	6222	1445
0	44	533
1	748	513
0	970	37168
1	2686	34062
0	43	456
1	709	442
0	1049	40301
1	2820	37491

Stop Event

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

Compiler

Compiled 712 to 474 computations (33.4% saved)

end0.0ms (0%)

preprocess83.0ms (0.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 250 to 202 computations (19.2% saved)

analyze590.0ms (5%)

sample2.5s (20.7%)

preprocess269.0ms (2.3%)

eval1.0ms (0%)

prune3.0ms (0%)

localize353.0ms (3%)

series89.0ms (0.7%)

rewrite133.0ms (1.1%)

simplify273.0ms (2.3%)

eval175.0ms (1.5%)

prune69.0ms (0.6%)

localize610.0ms (5.1%)

series63.0ms (0.5%)

rewrite151.0ms (1.3%)

simplify343.0ms (2.9%)

eval501.0ms (4.2%)

prune165.0ms (1.4%)

localize613.0ms (5.2%)

series44.0ms (0.4%)

rewrite114.0ms (1%)

simplify245.0ms (2.1%)

eval419.0ms (3.5%)

prune149.0ms (1.3%)

localize617.0ms (5.2%)

series22.0ms (0.2%)

rewrite118.0ms (1%)

simplify290.0ms (2.4%)

eval550.0ms (4.6%)

prune281.0ms (2.4%)

regimes185.0ms (1.6%)

regimes45.0ms (0.4%)

regimes54.0ms (0.5%)

regimes30.0ms (0.2%)

regimes29.0ms (0.2%)

regimes33.0ms (0.3%)

regimes37.0ms (0.3%)

simplify5.0ms (0%)

soundness1.7s (14%)

end0.0ms (0%)

preprocess83.0ms (0.7%)

Profiling