Metrics for HairBSDF, Mp, lower

analyze886.0ms (4.8%)

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)

Precisions

Click to see histograms. Total time spent on operations: 286.0ms

Operation ival-exp, time spent: 59.0ms, 21.0% of total-time

Operation ival-log, time spent: 59.0ms, 21.0% of total-time

Operation ival-<=, time spent: 52.0ms, 18.0% of total-time

Operation ival-mult, time spent: 37.0ms, 13.0% of total-time

Operation ival-div, time spent: 23.0ms, 8.0% of total-time

Operation ival-add, time spent: 15.0ms, 5.0% of total-time

Operation ival-sub, time spent: 15.0ms, 5.0% of total-time

Operation ival-and, time spent: 15.0ms, 5.0% of total-time

Operation const, time spent: 11.0ms, 4.0% of total-time

sample4.0s (21.6%)

Results

3.4s	8255×	256	valid
41.0ms	135×	256	invalid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 1.5s

Operation ival-<=, time spent: 427.0ms, 28.0% of total-time

Operation ival-div, time spent: 278.0ms, 18.0% of total-time

Operation ival-log, time spent: 221.0ms, 14.0% of total-time

Operation ival-mult, time spent: 193.0ms, 13.0% of total-time

Operation ival-add, time spent: 103.0ms, 7.0% of total-time

Operation ival-sub, time spent: 93.0ms, 6.0% of total-time

Operation ival-and, time spent: 83.0ms, 5.0% of total-time

Operation ival-exp, time spent: 67.0ms, 4.0% of total-time

Operation const, time spent: 66.0ms, 4.0% of total-time

Bogosity

preprocess624.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg`
366×	`associate-+l-`
333×	`fma-define`
320×	`associate-+l+`
291×	`associate-+r-`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Underpredictions	Example	Subexpression
89	2	(-6.409625818156939e-28 6.279956887235662e-34 -1.6531764021956996e-12 1.054326778334759e-13 2.1210113957342527e-16)	30	(-3.1993024895982103e-10 1.472035759691249e-33 -1.0941195730451367e-13 -2.522691757027881e-16 5.845735019749e-17)	`(/.f32 (*.f32 cosTheta_i cosTheta_O) v)`
89	3	(-0.14423184096813202 7.233666790562587e-12 3.4287106784681827e-35 2.984464888763916e-12 0.005230874754488468)	30	(-5.947904729144224e-24 3.910875889800991e-8 5.873934362471395e-30 8.350356539045534e-13 6.876576763535443e-17)	`(/.f32 (*.f32 sinTheta_i sinTheta_O) v)`
2	12	(-1.47980117742863e-11 -9.977980997068697e-23 -1.7564291766194338e-24 0.06980067491531372 0.0052248211577534676)	2	(-3.664387196455898e-11 -4.842232720173067e-16 1.1725304754905963e-11 8.355730551912188e-10 0.010950800962746143)	`(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	0	-	0	-	`(log.f32 (/.f32 1 (*.f32 2 v)))`
0	0	-	0	-	`cosTheta_O`
0	0	-	0	-	`(*.f32 2 v)`
0	0	-	0	-	`(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))`
0	0	-	0	-	`(/.f32 1 v)`
0	0	-	0	-	`(*.f32 cosTheta_i cosTheta_O)`
0	0	-	0	-	`(*.f32 sinTheta_i sinTheta_O)`
0	0	-	0	-	`(+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000)`
0	0	-	0	-	`sinTheta_O`
0	0	-	0	-	`v`
0	0	-	0	-	`(+.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))))`
0	0	-	0	-	`cosTheta_i`
0	0	-	0	-	`sinTheta_i`
0	0	-	0	-	`(/.f32 1 (*.f32 2 v))`
0	0	-	0	-	`2`
0	0	-	0	-	`6931/10000`
0	0	-	0	-	`1`
0	0	-	0	-	`(-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	173	2130
1	492	1898
2	1530	1854
3	6648	1854

Stop Event

1×	node limit

Calls

Call 1

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 308 to 138 computations (55.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 145.0ms

Operation ival-div, time spent: 45.0ms, 31.0% of total-time

Operation ival-log, time spent: 35.0ms, 24.0% of total-time

Operation ival-mult, time spent: 25.0ms, 17.0% of total-time

Operation ival-sub, time spent: 15.0ms, 10.0% of total-time

Operation ival-add, time spent: 15.0ms, 10.0% of total-time

Operation const, time spent: 6.0ms, 4.0% of total-time

Operation ival-exp, time spent: 4.0ms, 3.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 70 to 40 computations (42.9% saved)

prune5.0ms (0%)

Alt Table

Click to see full alt table

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

Status

Accuracy

Program

▶

99.4%

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

▶

99.4%

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

Compiler

Compiled 54 to 38 computations (29.6% saved)

localize487.0ms (2.6%)

Localize:

Found 8 expressions with local error:

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

Compiler

Compiled 209 to 88 computations (57.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 130.0ms

Operation ival-div, time spent: 39.0ms, 30.0% of total-time

Operation ival-add, time spent: 23.0ms, 18.0% of total-time

Operation ival-log, time spent: 22.0ms, 17.0% of total-time

Operation composed, time spent: 15.0ms, 12.0% of total-time

Operation ival-mult, time spent: 13.0ms, 10.0% of total-time

Operation ival-sub, time spent: 7.0ms, 5.0% of total-time

Operation ival-exp, time spent: 6.0ms, 5.0% of total-time

Operation const, time spent: 4.0ms, 3.0% of total-time

series150.0ms (0.8%)

Counts

8 → 336

Calls

84 calls:

Time	Variable		Point	Expression
29.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
20.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))
8.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
6.0ms	v	@	inf	(exp.f32 (+.f32 (-.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 1 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
4.0ms	cosTheta_i	@	0	(*.f32 cosTheta_i (/.f32 cosTheta_O v))

rewrite236.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

243×	`log1p-expm1-u`
243×	`expm1-log1p-u`
239×	`add-exp-log`
238×	`add-log-exp`
238×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	35	352
1	532	325

Stop Event

1×	node limit

Counts

8 → 279

Calls

Call 1

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

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

simplify280.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

464×	`associate-r`
445×	`associate-l`
348×	`fma-define`
338×	`times-frac`
209×	`associate-/r*`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	734	41090
1	2085	38817

Stop Event

1×	node limit

Counts

615 → 410

Calls

Call 1

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

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

eval239.0ms (1.3%)

Compiler: Compiled 14977 to 8301 computations (44.6% saved)

prune95.0ms (0.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	425	13	438
Fresh	0	0	0
Picked	2	0	2
Done	0	0	0
Total	427	13	440

Accuracy

99.9%

Counts

440 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))))
	99.4%	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))))) 3)
	95.5%	(/.f32 (pow.f32 (exp.f32 cosTheta_i) (/.f32 cosTheta_O v)) (exp.f32 (-.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	99.8%	(/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) 1/2) v)
▶	99.8%	(/.f32 1 (/.f32 v (.f32 1/2 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))))))
	99.4%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	8.7%	(.f32 (/.f32 1/2 v) (exp.f32 (.f32 sinTheta_O (/.f32 sinTheta_i (neg.f32 v)))))
	4.6%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.4%	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))
	99.5%	(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))
▶	99.8%	(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v))
▶	4.6%	(*.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 594 to 450 computations (24.2% saved)

localize879.0ms (4.8%)

Localize:

Found 17 expressions with local error:

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

Compiler

Compiled 427 to 185 computations (56.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 309.0ms

Operation ival-div, time spent: 72.0ms, 23.0% of total-time

Operation ival-exp, time spent: 66.0ms, 21.0% of total-time

Operation ival-log, time spent: 60.0ms, 19.0% of total-time

Operation ival-mult, time spent: 34.0ms, 11.0% of total-time

Operation ival-add, time spent: 33.0ms, 11.0% of total-time

Operation ival-sub, time spent: 23.0ms, 7.0% of total-time

Operation ival-pow, time spent: 11.0ms, 4.0% of total-time

Operation const, time spent: 10.0ms, 3.0% of total-time

series222.0ms (1.2%)

Counts

16 → 558

Calls

186 calls:

Time	Variable		Point	Expression
39.0ms	sinTheta_O	@	inf	(/.f32 v (.f32 1/2 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v))))))
12.0ms	cosTheta_i	@	-inf	(/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))) v)
4.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
3.0ms	cosTheta_i	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_O cosTheta_i) v))) (/.f32 1 v))
3.0ms	v	@	inf	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v)

rewrite199.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

372×	`log1p-expm1-u`
372×	`expm1-log1p-u`
367×	`add-exp-log`
366×	`add-log-exp`
363×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	789
1	812	765

Stop Event

1×	node limit

Counts

16 → 348

Calls

Call 1

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

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

simplify561.0ms (3%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-define`
510×	`times-frac`
324×	`associate-+r+`
292×	`sqr-pow`
231×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1080	62098
1	3143	59604

Stop Event

1×	node limit

Counts

906 → 664

Calls

Call 1

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

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

eval561.0ms (3%)

Compiler: Compiled 26495 to 16892 computations (36.2% saved)

prune242.0ms (1.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	824	10	834
Fresh	5	3	8
Picked	4	1	5
Done	0	0	0
Total	833	14	847

Accuracy

99.9%

Counts

847 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(/.f32 1 (/.f32 v (.f32 1/2 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 sinTheta_i sinTheta_O))) 1) v))))))
▶	99.8%	(/.f32 1 (/.f32 v (.f32 1/2 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))))
	4.6%	(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 6931/10000))))
	99.8%	(/.f32 1 (exp.f32 (-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O))) 1) v)))))
▶	99.4%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
▶	4.6%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.5%	(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))
	99.4%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
▶	99.4%	(.f32 (exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.7%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 1 v))) v))
	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	99.8%	(*.f32 1/2 (exp.f32 (-.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 1 v)) (log.f32 v))))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 547 to 438 computations (19.9% saved)

localize1.0s (5.5%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	99.9%	(.f32 (exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	99.9%	(exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (.f32 sinTheta_O sinTheta_i)) -1) v))
✓	98.8%	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	27.9%	(E.f32)
✓	99.9%	(/.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 1 v))) v)
✓	99.8%	(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 1 v))
✓	99.8%	(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (/.f32 1 v)))
✓	27.9%	(E.f32)
✓	99.9%	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
	99.8%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
	99.2%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)
✓	99.8%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
✓	99.9%	(/.f32 v (.f32 1/2 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))))
	99.9%	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))
	99.8%	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))
	99.2%	(/.f32 (*.f32 cosTheta_O cosTheta_i) v)

Compiler

Compiled 348 to 171 computations (50.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 396.0ms

Operation ival-exp, time spent: 102.0ms, 26.0% of total-time

Operation ival-div, time spent: 98.0ms, 25.0% of total-time

Operation ival-pow, time spent: 57.0ms, 14.0% of total-time

Operation ival-add, time spent: 32.0ms, 8.0% of total-time

Operation ival-mult, time spent: 30.0ms, 8.0% of total-time

Operation composed, time spent: 26.0ms, 7.0% of total-time

Operation ival-log, time spent: 23.0ms, 6.0% of total-time

Operation ival-sub, time spent: 16.0ms, 4.0% of total-time

Operation const, time spent: 10.0ms, 3.0% of total-time

Operation ival-e, time spent: 3.0ms, 1.0% of total-time

series253.0ms (1.4%)

Counts

11 → 324

Calls

81 calls:

Time	Variable		Point	Expression
53.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
23.0ms	cosTheta_i	@	-inf	(.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v))))
23.0ms	cosTheta_i	@	inf	(/.f32 v (.f32 1/2 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))))
20.0ms	cosTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
17.0ms	cosTheta_i	@	inf	(.f32 (exp.f32 (/.f32 (+.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (*.f32 sinTheta_O sinTheta_i)) -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite125.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

336×	`log1p-expm1-u`
336×	`expm1-log1p-u`
319×	`add-exp-log`
315×	`add-log-exp`
315×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	437
1	784	388

Stop Event

1×	node limit

Counts

11 → 253

Calls

Call 1

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

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

simplify356.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

659×	`associate-l`
556×	`times-frac`
491×	`fma-define`
245×	`*-commutative`
236×	`sqr-pow`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	961	37454
1	2892	35085

Stop Event

1×	node limit

Counts

577 → 543

Calls

Call 1

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

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

eval619.0ms (3.4%)

Compiler: Compiled 29619 to 20434 computations (31% saved)

prune174.0ms (0.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	1004	11	1015
Fresh	4	4	8
Picked	4	1	5
Done	0	1	1
Total	1012	17	1029

Accuracy

99.9%

Counts

1029 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.8%	(/.f32 1 (/.f32 (.f32 (pow.f32 (cbrt.f32 v) 2) (cbrt.f32 (.f32 2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))
▶	4.6%	(/.f32 1 (/.f32 (*.f32 2 v) (exp.f32 6931/10000)))
	99.8%	(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
	99.8%	(/.f32 1 (.f32 (/.f32 (pow.f32 (cbrt.f32 v) 2) (sqrt.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))))) (/.f32 (cbrt.f32 v) (sqrt.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))))))))
▶	99.8%	(/.f32 1 (exp.f32 (-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))))
	99.4%	(.f32 (pow.f32 (exp.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))) (/.f32 1 v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
✓	4.6%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.5%	(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))
▶	99.4%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
	99.4%	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	99.7%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v))
	99.8%	(.f32 1/2 (/.f32 (.f32 (exp.f32 6931/10000) (pow.f32 (E.f32) (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))) v))
	99.8%	(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	99.8%	(.f32 1/2 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)) (log.f32 v))))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 694 to 570 computations (17.9% saved)

localize927.0ms (5%)

Localize:

Found 17 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f32 1 (exp.f32 (-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))))
✓	99.8%	(-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))
✓	99.8%	(exp.f32 (-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))))
✓	99.9%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 -1 v)))
✓	99.9%	(exp.f32 (/.f32 -1 v))
✓	99.8%	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
✓	99.9%	(/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v)
✓	99.8%	(-.f32 6931/10000 (/.f32 1 v))
✓	99.8%	(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
	27.9%	(E.f32)
✓	99.8%	(/.f32 (*.f32 2 v) (exp.f32 6931/10000))
✓	99.8%	(/.f32 1 (/.f32 (*.f32 2 v) (exp.f32 6931/10000)))
✓	99.8%	(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))
✓	99.6%	(pow.f32 (cbrt.f32 v) 2)
✓	97.0%	(cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
✓	96.9%	(cbrt.f32 (*.f32 2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))

Compiler

Compiled 390 to 273 computations (30% saved)

Precisions

Click to see histograms. Total time spent on operations: 429.0ms

Operation ival-div, time spent: 95.0ms, 22.0% of total-time

Operation ival-mult, time spent: 60.0ms, 14.0% of total-time

Operation composed, time spent: 57.0ms, 13.0% of total-time

Operation ival-exp, time spent: 50.0ms, 12.0% of total-time

Operation ival-pow, time spent: 47.0ms, 11.0% of total-time

Operation ival-add, time spent: 45.0ms, 10.0% of total-time

Operation ival-log, time spent: 23.0ms, 5.0% of total-time

Operation ival-sub, time spent: 20.0ms, 5.0% of total-time

Operation ival-cbrt, time spent: 16.0ms, 4.0% of total-time

Operation const, time spent: 14.0ms, 3.0% of total-time

Operation ival-e, time spent: 3.0ms, 1.0% of total-time

series158.0ms (0.9%)

Counts

16 → 323

Calls

90 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta_i	@	inf	(cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
8.0ms	v	@	0	(-.f32 (log.f32 (/.f32 v 1/2)) (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v)))
6.0ms	v	@	0	(cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
6.0ms	cosTheta_i	@	0	(cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
6.0ms	cosTheta_O	@	inf	(cbrt.f32 (*.f32 2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))

rewrite151.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

331×	`log1p-expm1-u`
331×	`expm1-log1p-u`
325×	`add-exp-log`
323×	`add-log-exp`
323×	`add-cube-cbrt`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	50	510
1	845	502

Stop Event

1×	node limit

Counts

16 → 398

Calls

Call 1

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

Outputs
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))) 1)
(.f32 1 (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(*.f32 (cbrt.f32 2) (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(*.f32 (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) (cbrt.f32 2))
(.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))) 2) (cbrt.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(.f32 (pow.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1/6) (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1/6))
(.f32 (pow.f32 1 1/3) (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(.f32 (pow.f32 (pow.f32 (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(.f32 (pow.f32 (sqrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 1/3) (pow.f32 (sqrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 1/3))
(/.f32 (cbrt.f32 (*.f32 2 v)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(pow.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 1)
(pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1/3)
(pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))) 3)
(pow.f32 (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1/6) 2)
(sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2))
(log.f32 (exp.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))))
(expm1.f32 (log1p.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(log1p.f32 (expm1.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(exp.f32 (.f32 1/3 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (.f32 (.f32 1/3 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1))
(exp.f32 (.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/3))
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)))) 1)
(.f32 1 (cbrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)))
(*.f32 (cbrt.f32 1/2) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(*.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) (cbrt.f32 1/2))
(.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))) 2) (cbrt.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))))
(.f32 (pow.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2) 1/6) (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2) 1/6))
(.f32 (pow.f32 1 1/3) (cbrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)))
(.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)) 2) 1/3) (cbrt.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))))
(.f32 (pow.f32 (sqrt.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)) 1/3) (pow.f32 (sqrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)) 1/3))
(pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2) 1/3)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)) 1)
(pow.f32 (cbrt.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))) 3)
(pow.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2) 1/6) 2)
(sqrt.f32 (pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)) 2))
(log.f32 (exp.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2)))))
(expm1.f32 (log1p.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))))
(log1p.f32 (expm1.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/2))))
(exp.f32 (*.f32 1/3 (+.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (log.f32 1/2))))
(exp.f32 (*.f32 (+.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (log.f32 1/2)) 1/3))
(exp.f32 (.f32 (.f32 1/3 (+.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (log.f32 1/2))) 1))
(-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (pow.f32 v 2)))) 1)
(*.f32 (cbrt.f32 v) (cbrt.f32 v))
(*.f32 1 (cbrt.f32 (pow.f32 v 2)))
(*.f32 (cbrt.f32 (pow.f32 (cbrt.f32 v) 4)) (cbrt.f32 (cbrt.f32 (pow.f32 v 2))))
(sqrt.f32 (pow.f32 (cbrt.f32 v) 4))
(log.f32 (exp.f32 (cbrt.f32 (pow.f32 v 2))))
(log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (pow.f32 v 2)))))
(cbrt.f32 (pow.f32 v 2))
(expm1.f32 (log1p.f32 (cbrt.f32 (pow.f32 v 2))))
(log1p.f32 (expm1.f32 (cbrt.f32 (pow.f32 v 2))))
(exp.f32 (log.f32 (cbrt.f32 (pow.f32 v 2))))
(exp.f32 (*.f32 (log.f32 (cbrt.f32 (pow.f32 v 2))) 1))
(-.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1)
(-.f32 (/.f32 48038761/100000000 (-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) (/.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2) (-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 1 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
(*.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2) (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(*.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(/.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 3)) (+.f32 48038761/100000000 (-.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2) (*.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(/.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2)) (-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))
(/.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 3))) (neg.f32 (+.f32 48038761/100000000 (-.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2) (*.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(/.f32 (neg.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 2))) (neg.f32 (-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 1)
(pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2)
(sqrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2))
(log.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3))
(expm1.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(log1p.f32 (expm1.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(exp.f32 (log.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1))
(fma.f32 1 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v) 6931/10000)
(fma.f32 (fma.f32 cosTheta_O cosTheta_i -1) (/.f32 -1 v) 6931/10000)
(fma.f32 (pow.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2) (cbrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 6931/10000)
(fma.f32 (sqrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) (sqrt.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 6931/10000)
(-.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))) 1)
(*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 6931/10000)) -1))
(.f32 1 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 -6931/10000) -1))
(.f32 (cbrt.f32 (pow.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000)) -2)) (cbrt.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(.f32 (sqrt.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v))) (sqrt.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))
(.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000))) 2) -1) (pow.f32 (cbrt.f32 (.f32 (*.f32 2 v) (exp.f32 -6931/10000))) -1))
(.f32 (pow.f32 (sqrt.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000))) -1) (pow.f32 (sqrt.f32 (.f32 (*.f32 2 v) (exp.f32 -6931/10000))) -1))
(*.f32 (/.f32 (exp.f32 6931/10000) (cbrt.f32 (pow.f32 v 2))) (/.f32 1/2 (cbrt.f32 v)))
(*.f32 (/.f32 (exp.f32 6931/10000) 1) (/.f32 1/2 v))
(*.f32 (/.f32 (exp.f32 6931/10000) (sqrt.f32 v)) (/.f32 1/2 (sqrt.f32 v)))
(pow.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000)) -1)
(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 (/.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000)) 1) -1)
(sqrt.f32 (pow.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000)) -2))
(log.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 6931/10000) (/.f32 1/2 v)))))
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(*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))
(.f32 1 (.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)))
(.f32 (cbrt.f32 (pow.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -2)) (/.f32 1 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(.f32 (pow.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2) (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2))
(*.f32 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1) 1/2)
(.f32 (pow.f32 (pow.f32 (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2) -1) (pow.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1))
(.f32 (pow.f32 (sqrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1) (pow.f32 (sqrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1))
(pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)
(pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 1)
(pow.f32 (/.f32 1 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 3) 1/3)
(pow.f32 (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2) 2)
(pow.f32 (/.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1) -1)
(sqrt.f32 (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -2))
(log.f32 (exp.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 3))
(expm1.f32 (log1p.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))))
(log1p.f32 (expm1.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))))
(exp.f32 (neg.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) -1))
(exp.f32 (.f32 (neg.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1))

simplify349.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-define`
573×	`times-frac`
359×	`sqr-pow`
320×	`*-commutative`
245×	`distribute-lft-in`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1300	45327
1	3698	42501

Stop Event

1×	node limit

Counts

721 → 693

Calls

Call 1

Inputs
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (.f32 (pow.f32 (/.f32 (*.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2)))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_O 2) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))))))) (.f32 (pow.f32 (/.f32 (*.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2))))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_O 2) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_O 3) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (.f32 cosTheta_i (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))) v)) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 v 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 -1/27 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/3) (pow.f32 cosTheta_i 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 v 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (.f32 2/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 5) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 4))) 1/9) (.f32 cosTheta_i (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_i 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_i 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))))))))))))))) (.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2)))))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (.f32 (pow.f32 (/.f32 (*.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2)))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_i 2) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))))))) (.f32 (pow.f32 (/.f32 (*.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2))))
(+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/9) (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 2))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_i 2) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))))))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/3) (.f32 (pow.f32 cosTheta_i 3) (.f32 (cbrt.f32 2) (+.f32 (.f32 -1 (/.f32 (.f32 cosTheta_O (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))))) v)) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 cosTheta_O 3) (.f32 (pow.f32 v 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 -1/27 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 2) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7))) 1/3) (pow.f32 cosTheta_O 3))) (+.f32 (.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (.f32 (pow.f32 v 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (.f32 2/3 (.f32 (pow.f32 (/.f32 1 (.f32 (pow.f32 v 5) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 4))) 1/9) (.f32 cosTheta_O (+.f32 (.f32 -1 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (.f32 v (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17))) 1/9) (pow.f32 cosTheta_O 2))) (.f32 1/2 (/.f32 (pow.f32 cosTheta_O 2) (.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))))))))))))))) (.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 2)))))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (/.f32 (.f32 1 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 2))
(.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 1/2))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) 1/9) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 1/2))) v))) (.f32 (pow.f32 (*.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 1/2)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) 1/9) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 1/2))) v))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_O 2) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 2))) (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2))))))))) (.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 1/2))))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) 1/9) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_i (cbrt.f32 1/2))) v))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_O 2) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 2))) (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2))))))))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_O 3) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (+.f32 (.f32 1/27 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) 1/3) (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)))) (.f32 2/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 4)) 1/9) (/.f32 (.f32 cosTheta_i (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 2))) (.f32 1/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2)))))) v))))))))) (.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (cbrt.f32 1/2)))))
(.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_O cosTheta_i) v)) (/.f32 1 v)))) 1/3) (cbrt.f32 1/2))
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(pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 3)
(pow.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3) 1/3)
(pow.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2)
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(+.f32 (log.f32 (sqrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))) (log.f32 (sqrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
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(.f32 (pow.f32 (cbrt.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2) (cbrt.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
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(/.f32 (-.f32 (pow.f32 (log.f32 (.f32 2 v)) 3) (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3)) (+.f32 (pow.f32 (log.f32 (.f32 2 v)) 2) (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2) (.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))
(/.f32 (-.f32 (pow.f32 (log.f32 (.f32 2 v)) 2) (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2)) (+.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (log.f32 (.f32 2 v)) 3) (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 3))) (neg.f32 (+.f32 (pow.f32 (log.f32 (.f32 2 v)) 2) (+.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2) (.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (log.f32 (.f32 2 v)) 2) (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)) 2))) (neg.f32 (+.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(pow.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1)
(pow.f32 (cbrt.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 3)
(pow.f32 (pow.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 3) 1/3)
(pow.f32 (sqrt.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 2)
(sqrt.f32 (pow.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 2))
(log.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
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(exp.f32 (log.f32 (-.f32 (log.f32 (*.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))
(exp.f32 (.f32 (log.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1))
(fma.f32 1 (log.f32 (*.f32 2 v)) (neg.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
(fma.f32 (pow.f32 (cbrt.f32 (log.f32 (.f32 2 v))) 2) (cbrt.f32 (log.f32 (.f32 2 v))) (neg.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
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(-.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)))) 1)
(*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))
(.f32 1 (.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)))
(.f32 (cbrt.f32 (pow.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -2)) (/.f32 1 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))))
(.f32 (pow.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2) (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2))
(*.f32 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1) 1/2)
(.f32 (pow.f32 (pow.f32 (cbrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2) -1) (pow.f32 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1))
(.f32 (pow.f32 (sqrt.f32 (/.f32 (.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1) (pow.f32 (sqrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) -1))
(pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)
(pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 1)
(pow.f32 (/.f32 1 (cbrt.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))))) 3)
(pow.f32 (pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 3) 1/3)
(pow.f32 (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1/2) 2)
(pow.f32 (/.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1) -1)
(sqrt.f32 (pow.f32 (/.f32 (*.f32 2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -2))
(log.f32 (exp.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))))
(log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)))))
(cbrt.f32 (pow.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1)) 3))
(expm1.f32 (log1p.f32 (*.f32 1/2 (pow.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) -1))))
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(exp.f32 (.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) -1))
(exp.f32 (.f32 (neg.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v)))) 1))

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

eval1.0s (5.7%)

Compiler: Compiled 28065 to 22371 computations (20.3% saved)

prune248.0ms (1.3%)

Pruning

22 alts after pruning (18 fresh and 4 done)

	Pruned	Kept	Total
New	739	10	749
Fresh	2	8	10
Picked	3	2	5
Done	0	2	2
Total	744	22	766

Accuracy

100.0%

Counts

766 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.8%	(/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)
	99.8%	(/.f32 1 (/.f32 (.f32 (pow.f32 (cbrt.f32 v) 2) (.f32 (cbrt.f32 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (cbrt.f32 2))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))
	99.8%	(/.f32 1 (/.f32 (.f32 (pow.f32 (cbrt.f32 v) 2) (exp.f32 (.f32 (-.f32 (log.f32 (.f32 2 v)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))) 1/3))) (pow.f32 (cbrt.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))
	99.8%	(/.f32 1 (/.f32 (.f32 (pow.f32 (cbrt.f32 v) 2) (cbrt.f32 (.f32 2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))
	27.2%	(/.f32 1 (/.f32 (.f32 (-.f32 (exp.f32 (log1p.f32 (cbrt.f32 (pow.f32 v 2)))) 1) (cbrt.f32 (.f32 2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))
	99.8%	(/.f32 1 (/.f32 (.f32 (.f32 2 v) (exp.f32 -6931/10000)) (exp.f32 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))
✓	4.6%	(/.f32 1 (/.f32 (*.f32 2 v) (exp.f32 6931/10000)))
	99.8%	(/.f32 1 (/.f32 v (*.f32 1/2 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
	99.8%	(/.f32 1 (.f32 (/.f32 (pow.f32 (cbrt.f32 v) 2) (sqrt.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)))))) (/.f32 (cbrt.f32 v) (sqrt.f32 (.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (*.f32 cosTheta_O cosTheta_i) 1) v))))))))
	99.8%	(/.f32 1 (exp.f32 (-.f32 (+.f32 (log.f32 (*.f32 2 v)) (/.f32 1 v)) 6931/10000)))
	99.4%	(.f32 (pow.f32 (exp.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) (fma.f32 sinTheta_O sinTheta_i 1))) (/.f32 1 v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.4%	(*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
✓	4.6%	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	99.5%	(.f32 (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))
	99.4%	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (pow.f32 (E.f32) (/.f32 -1 v)))
	99.4%	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	99.4%	(.f32 (exp.f32 6931/10000) (.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v)))
	98.3%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (/.f32 -1 v)) v))
✓	99.7%	(*.f32 1/2 (/.f32 (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))) v))
✓	4.6%	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	99.8%	(.f32 1/2 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_O cosTheta_i) 1) v)) (log.f32 v))))
	99.4%	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 1385 to 1017 computations (26.6% saved)

regimes207.0ms (1.1%)

Counts

47 → 1

Calls

Call 1

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

Outputs

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

Calls

9 calls:

36.0ms	cosTheta_O
30.0ms	sinTheta_O
28.0ms	cosTheta_i
26.0ms	sinTheta_i
21.0ms	(*.f32 cosTheta_i 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 105 to 80 computations (23.8% saved)

regimes179.0ms (1%)

Counts

45 → 1

Calls

Call 1

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

Outputs

(/.f32 1 (/.f32 (*.f32 (pow.f32 (cbrt.f32 v) 2) (*.f32 (cbrt.f32 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (cbrt.f32 2))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))

Calls

9 calls:

26.0ms	cosTheta_O
23.0ms	sinTheta_i
23.0ms	sinTheta_O
23.0ms	cosTheta_i
22.0ms	v

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
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 105 to 80 computations (23.8% saved)

regimes174.0ms (0.9%)

Counts

43 → 1

Calls

Call 1

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

Outputs

(/.f32 1 (/.f32 (*.f32 (pow.f32 (cbrt.f32 v) 2) (cbrt.f32 (*.f32 2 (/.f32 v (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))) (pow.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O cosTheta_i -1) v))))) 2)))

Calls

9 calls:

26.0ms	cosTheta_O
23.0ms	sinTheta_O
22.0ms	sinTheta_i
22.0ms	cosTheta_i
20.0ms	v

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
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 105 to 80 computations (23.8% saved)

regimes164.0ms (0.9%)

Counts

42 → 1

Calls

Call 1

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

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

Calls

9 calls:

24.0ms	cosTheta_i
22.0ms	cosTheta_O
22.0ms	sinTheta_O
22.0ms	sinTheta_i
19.0ms	v

Results

Accuracy	Segments	Branch
99.8%	1	`cosTheta_i`
99.8%	1	`cosTheta_O`
99.8%	1	`sinTheta_i`
99.8%	1	`sinTheta_O`
99.8%	1	`v`
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 105 to 80 computations (23.8% saved)

regimes37.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

5 calls:

10.0ms	cosTheta_O
8.0ms	sinTheta_O
6.0ms	sinTheta_i
6.0ms	cosTheta_i
5.0ms	v

Results

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

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes31.0ms (0.2%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

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

Compiler

Compiled 30 to 25 computations (16.7% saved)

regimes23.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

5 calls:

7.0ms	cosTheta_O
4.0ms	cosTheta_i
4.0ms	sinTheta_O
4.0ms	sinTheta_i
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 30 to 25 computations (16.7% saved)

regimes20.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

5 calls:

6.0ms	sinTheta_O
4.0ms	cosTheta_O
4.0ms	v
3.0ms	sinTheta_i
3.0ms	cosTheta_i

Results

Accuracy	Segments	Branch
4.6%	1	`cosTheta_i`
4.6%	1	`cosTheta_O`
4.6%	1	`sinTheta_i`
4.6%	1	`sinTheta_O`
4.6%	1	`v`

Compiler

Compiled 30 to 25 computations (16.7% saved)

simplify18.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

20×	`*-commutative`
10×	`+-commutative`
9×	`sub-neg`
7×	`neg-sub0`
7×	`neg-mul-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	545
1	91	545
2	105	545
3	122	545
4	137	545
5	142	545
6	143	545

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 192 to 163 computations (15.1% saved)

soundness2.3s (12.5%)

Rules

712×	`fma-define`
659×	`associate-l`
617×	`fma-define`
617×	`fma-define`
573×	`times-frac`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	173	2130
1	492	1898
2	1530	1854
3	6648	1854
0	35	352
1	532	325
0	46	437
1	784	388
0	961	37454
1	2892	35085
0	50	510
1	845	502
0	173	2130
1	492	1898
2	1530	1854
3	6648	1854
0	44	789
1	812	765
0	1080	62098
1	3143	59604
0	1300	45327
1	3698	42501
0	1300	45327
1	3698	42501

Stop Event

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

Compiler

Compiled 1607 to 1075 computations (33.1% saved)

end0.0ms (0%)

preprocess186.0ms (1%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 1922 to 1556 computations (19% saved)

analyze886.0ms (4.8%)

sample4.0s (21.6%)

preprocess624.0ms (3.4%)

eval1.0ms (0%)

prune5.0ms (0%)

localize487.0ms (2.6%)

series150.0ms (0.8%)

rewrite236.0ms (1.3%)

simplify280.0ms (1.5%)

eval239.0ms (1.3%)

prune95.0ms (0.5%)

localize879.0ms (4.8%)

series222.0ms (1.2%)

rewrite199.0ms (1.1%)

simplify561.0ms (3%)

eval561.0ms (3%)

prune242.0ms (1.3%)

localize1.0s (5.5%)

series253.0ms (1.4%)

rewrite125.0ms (0.7%)

simplify356.0ms (1.9%)

eval619.0ms (3.4%)

prune174.0ms (0.9%)

localize927.0ms (5%)

series158.0ms (0.9%)

rewrite151.0ms (0.8%)

simplify349.0ms (1.9%)

eval1.0s (5.7%)

prune248.0ms (1.3%)

regimes207.0ms (1.1%)

regimes179.0ms (1%)

regimes174.0ms (0.9%)

regimes164.0ms (0.9%)

regimes37.0ms (0.2%)

regimes31.0ms (0.2%)

regimes23.0ms (0.1%)

regimes20.0ms (0.1%)

simplify18.0ms (0.1%)

soundness2.3s (12.5%)

end0.0ms (0%)

preprocess186.0ms (1%)

Profiling