Details

analyze902.0ms (4.4%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	3%	97%	0%	0%	0%	0
0%	0%	3%	97%	0%	0%	0%	1
0%	0%	3%	97%	0%	0%	0%	2
0%	0%	3%	97%	0%	0%	0%	3
0%	0%	3%	97%	0%	0%	0%	4
0%	0%	3%	97%	0%	0%	0%	5
0%	0%	1.5%	97%	0%	1.5%	0%	6
0%	0%	1.5%	97%	0%	1.5%	0%	7
0%	0%	1.5%	97%	0%	1.5%	0%	8
0%	0%	1.5%	97%	0%	1.5%	0%	9
0%	0%	1.5%	97%	0%	1.5%	0%	10
38.3%	0.6%	0.9%	97%	0%	1.5%	0%	11
38.3%	0.6%	0.9%	97%	0%	1.5%	0%	12

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample2.8s (13.3%)

Results

2.7s	8256×	body	256	valid
50.0ms	129×	body	256	invalid

Bogosity

preprocess56.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

880×	`fma-neg_binary32`
856×	`exp-diff_binary32`
339×	`cancel-sign-sub-inv_binary32`
307×	`distribute-neg-in_binary32`
278×	`associate-+l-_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	116	385
1	327	363
2	978	341
3	4387	330
0	5	5
1	5	5

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
0
2
3
2
4

Call 2

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

688×	`fma-def_binary32`
507×	`exp-sum_binary32`
492×	`fma-neg_binary32`
429×	`exp-diff_binary32`
428×	`sub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	147	31
3	583	29
4	2984	29

Stop Event

1×	node limit

Counts

1 → 2

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)))))

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

eval1.0ms (0%)

Compiler: Compiled 50 to 34 computations (32% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
▶	0.1b	(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)))))

Status

Error

Program

▶

0.1b

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

▶

0.1b

(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)))))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize134.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	0.1b	(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)))))
✓	7.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	7.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series39.0ms (0.2%)

Counts

4 → 120

Calls

48 calls:

Time	Variable		Point	Expression
6.0ms	cosTheta_i	@	0	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	cosTheta_i	@	0	(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)))))
3.0ms	sinTheta_O	@	inf	(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)))))
1.0ms	v	@	-inf	(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)))))
1.0ms	v	@	inf	(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)))))

rewrite119.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

453×	`log1p-udef_binary32`
261×	`add-sqr-sqrt_binary32`
253×	`*-un-lft-identity_binary32`
253×	`pow1_binary32`
244×	`add-log-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	506	54
2	7921	54

Stop Event

1×	node limit

Counts

4 → 185

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_i (/.f32 1 (/.f32 v sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_i (.f32 sinTheta_O (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 sinTheta_O (.f32 sinTheta_i (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 sinTheta_i sinTheta_O) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 sinTheta_i v) sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 v) (.f32 sinTheta_i sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (pow.f32 (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) 2) (cbrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 sinTheta_i sinTheta_O)) 2) (.f32 (cbrt.f32 (.f32 sinTheta_i sinTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (sqrt.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 v -1/2) (/.f32 (.f32 sinTheta_i sinTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (.f32 (sqrt.f32 (.f32 sinTheta_i sinTheta_O)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 sinTheta_i (neg.f32 sinTheta_O)) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i 1) (/.f32 sinTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_O 1) (/.f32 sinTheta_i v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 sinTheta_i v) 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(.f32 (/.f32 sinTheta_i v) sinTheta_O)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (/.f32 v sinTheta_i) sinTheta_O) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change 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(#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))) (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 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simplify118.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

946×	`associate-/l*_binary32`
694×	`associate-l_binary32`
590×	`associate-/r*_binary32`
364×	`fma-def_binary32`
265×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	4231
1	423	3930
2	1621	3576

Stop Event

1×	node limit

Counts

305 → 225

Calls

Call 1

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

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

localize75.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
✓	0.0b	(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
✓	0.1b	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)

Compiler

Compiled 90 to 42 computations (53.3% saved)

series42.0ms (0.2%)

Counts

4 → 180

Calls

54 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta_O	@	-inf	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
3.0ms	v	@	-inf	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
2.0ms	cosTheta_O	@	inf	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
2.0ms	v	@	-inf	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	0	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

rewrite121.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`prod-diff_binary32`
337×	`expm1-udef_binary32`
337×	`log1p-udef_binary32`
294×	`fma-def_binary32`
282×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	81
1	382	81
2	4977	81

Stop Event

1×	node limit

Counts

4 → 196

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 1) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .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)))))) (#(struct:change #<rule egg-rr> (2) ((x .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)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) -48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (/.f32 1 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (exp.f32 (fma.f32 sinTheta_i 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simplify109.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

863×	`associate-/r*_binary32`
742×	`associate-l_binary32`
592×	`fma-def_binary32`
450×	`associate-*r/_binary32`
406×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	5800
1	602	5291
2	2264	4778

Stop Event

1×	node limit

Counts

376 → 276

Calls

Call 1

Inputs
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
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Outputs
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
6931/10000
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
6931/10000
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
6931/10000
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(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v))))
(fma.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) (.f32 sinTheta_O (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))) (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (.f32 -1/2 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)))))
(fma.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) (fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (.f32 sinTheta_O sinTheta_O))) (.f32 (/.f32 -1/2 (.f32 v v)) (.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))
(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (+.f32 (.f32 -1/12 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 4))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))))
(fma.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) (.f32 sinTheta_O (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (pow.f32 sinTheta_O 3)))) (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (/.f32 (.f32 (.f32 -1/12 (pow.f32 sinTheta_i 3)) (*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (pow.f32 sinTheta_O 3))) (pow.f32 v 4)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) (.f32 (/.f32 -1/12 (pow.f32 v 4)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) (.f32 sinTheta_O (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))) (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v)))
(fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (.f32 -1/2 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v))))
(fma.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) (.f32 (/.f32 -1/2 (.f32 v v)) (.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))
(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v))))
(fma.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) (.f32 sinTheta_O (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))) (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (.f32 -1/2 (.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)))))
(fma.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) (fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (.f32 sinTheta_O sinTheta_O))) (.f32 (/.f32 -1/2 (.f32 v v)) (.f32 (.f32 sinTheta_i sinTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))
(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (+.f32 (.f32 -1/12 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 4))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))))
(fma.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) (.f32 sinTheta_O (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (pow.f32 sinTheta_O 3)))) (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) v)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (/.f32 (.f32 (.f32 -1/12 (pow.f32 sinTheta_i 3)) (*.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (pow.f32 sinTheta_O 3))) (pow.f32 v 4)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) (.f32 (/.f32 -1/12 (pow.f32 v 4)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)))))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v))))

eval268.0ms (1.3%)

Compiler: Compiled 16612 to 9263 computations (44.2% saved)

prune95.0ms (0.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	489	12	501
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	491	12	503

Error

0.1b

Counts

503 → 12

Alt Table

Click to see full alt table

Status	Error	Program
	30.5b	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	30.5b	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
	0.1b	(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
	0.1b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))) 3)
	0.4b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))) 3) 1/3)
	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	27.7b	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
	0.2b	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
▶	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))

Compiler

Compiled 556 to 420 computations (24.5% saved)

localize116.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
✓	0.0b	(+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)
✓	0.1b	(exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))
✓	0.5b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))

Compiler

Compiled 135 to 61 computations (54.8% saved)

series143.0ms (0.7%)

Counts

4 → 216

Calls

57 calls:

Time	Variable		Point	Expression
23.0ms	sinTheta_O	@	0	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))
21.0ms	sinTheta_i	@	0	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))
12.0ms	cosTheta_i	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))
6.0ms	cosTheta_O	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))
6.0ms	sinTheta_i	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))))

rewrite208.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

475×	`prod-diff_binary32`
336×	`expm1-udef_binary32`
336×	`log1p-udef_binary32`
295×	`fma-def_binary32`
274×	`fma-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	19	79
1	408	71
2	5310	65

Stop Event

1×	node limit

Counts

4 → 253

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (cbrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (pow.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) 2) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/6) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 1 1/3) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/3) (pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cbrt.f32 (.f32 1/2 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 6931/10000) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2) (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (sqrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2)) (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) v) (-.f32 (/.f32 1 v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) -6931/10000)) (/.f32 48038761/100000000 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) -6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) v)) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) 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cosTheta_i (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i) (pow.f32 (cbrt.f32 sinTheta_O) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i)) (pow.f32 (cbrt.f32 sinTheta_O) 2) (.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i) (pow.f32 (cbrt.f32 sinTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (sqrt.f32 cosTheta_O)) (sqrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i) (pow.f32 (cbrt.f32 sinTheta_O) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i)) (pow.f32 (cbrt.f32 sinTheta_O) 2) (.f32 (.f32 (cbrt.f32 sinTheta_O) sinTheta_i) (pow.f32 (cbrt.f32 sinTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (.f32 cosTheta_i cosTheta_O) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (pow.f32 (cbrt.f32 cosTheta_i) 2) (.f32 (cbrt.f32 cosTheta_i) cosTheta_O) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 cosTheta_i) (.f32 (sqrt.f32 cosTheta_i) cosTheta_O) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (cbrt.f32 (.f32 cosTheta_i cosTheta_O))) (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (neg.f32 (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2)))) (fma.f32 (neg.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O)) (pow.f32 (cbrt.f32 sinTheta_i) 2) (.f32 (.f32 (cbrt.f32 sinTheta_i) sinTheta_O) (pow.f32 (cbrt.f32 sinTheta_i) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O) (neg.f32 (.f32 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sinTheta_i)) (sqrt.f32 sinTheta_O) (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i)) (sqrt.f32 sinTheta_O) (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i)) (sqrt.f32 sinTheta_O) (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (sqrt.f32 cosTheta_O)) (sqrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i)) (sqrt.f32 sinTheta_O) (.f32 (.f32 (sqrt.f32 sinTheta_O) sinTheta_i) (sqrt.f32 sinTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (.f32 cosTheta_i cosTheta_O) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 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(.f32 cosTheta_i cosTheta_O))) (cbrt.f32 (.f32 cosTheta_i cosTheta_O)) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (sqrt.f32 cosTheta_O)) (sqrt.f32 cosTheta_O) (neg.f32 (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i)))) (fma.f32 (neg.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O)) (sqrt.f32 sinTheta_i) (.f32 (.f32 (sqrt.f32 sinTheta_i) sinTheta_O) (sqrt.f32 sinTheta_i))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_i cosTheta_O (neg.f32 (.f32 (.f32 sinTheta_i sinTheta_O) -1))) (fma.f32 (.f32 sinTheta_i sinTheta_O) -1 (.f32 (.f32 sinTheta_i sinTheta_O) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_O cosTheta_i (neg.f32 (.f32 (.f32 sinTheta_i sinTheta_O) -1))) (fma.f32 (.f32 sinTheta_i sinTheta_O) -1 (.f32 (.f32 sinTheta_i sinTheta_O) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (.f32 cosTheta_i cosTheta_O) (neg.f32 (.f32 (.f32 sinTheta_i sinTheta_O) -1))) (fma.f32 (.f32 sinTheta_i sinTheta_O) -1 (.f32 (.f32 sinTheta_i sinTheta_O) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (pow.f32 (cbrt.f32 cosTheta_i) 2) (.f32 (cbrt.f32 cosTheta_i) cosTheta_O) (neg.f32 (.f32 (.f32 sinTheta_i sinTheta_O) -1))) (fma.f32 (.f32 sinTheta_i sinTheta_O) -1 (.f32 (.f32 sinTheta_i sinTheta_O) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 cosTheta_i) (.f32 (sqrt.f32 cosTheta_i) cosTheta_O) (neg.f32 (.f32 (.f32 sinTheta_i sinTheta_O) -1))) (fma.f32 (.f32 sinTheta_i sinTheta_O) -1 (.f32 (.f32 sinTheta_i sinTheta_O) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 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(#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (sqrt.f32 (.f32 cosTheta_i cosTheta_O)) (neg.f32 (.f32 (sqrt.f32 sinTheta_i) (.f32 sinTheta_O (sqrt.f32 sinTheta_i))))) (fma.f32 (neg.f32 (sqrt.f32 sinTheta_i)) (.f32 sinTheta_O (sqrt.f32 sinTheta_i)) (.f32 (sqrt.f32 sinTheta_i) (.f32 sinTheta_O (sqrt.f32 sinTheta_i)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (.f32 (sqrt.f32 cosTheta_i) (sqrt.f32 cosTheta_O)) (neg.f32 (.f32 (sqrt.f32 sinTheta_i) (.f32 sinTheta_O (sqrt.f32 sinTheta_i))))) (fma.f32 (neg.f32 (sqrt.f32 sinTheta_i)) (.f32 sinTheta_O (sqrt.f32 sinTheta_i)) (.f32 (sqrt.f32 sinTheta_i) (.f32 sinTheta_O (sqrt.f32 sinTheta_i)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (.f32 cosTheta_i (pow.f32 (cbrt.f32 cosTheta_O) 2)) (cbrt.f32 cosTheta_O) (neg.f32 (.f32 (sqrt.f32 sinTheta_i) (.f32 sinTheta_O (sqrt.f32 sinTheta_i))))) (fma.f32 (neg.f32 (sqrt.f32 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sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 2) (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 2) (.f32 (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) (sqrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) (.f32 (sqrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (.f32 cosTheta_i cosTheta_O) 3) (pow.f32 (.f32 sinTheta_i sinTheta_O) 3)) (fma.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i cosTheta_O) (-.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 2) (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (.f32 cosTheta_i cosTheta_O) (.f32 cosTheta_i cosTheta_O) (pow.f32 (.f32 sinTheta_i sinTheta_O) 2)) (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (/.f32 (exp.f32 (.f32 cosTheta_i cosTheta_O)) (pow.f32 (exp.f32 sinTheta_O) sinTheta_i)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (/.f32 (exp.f32 (.f32 cosTheta_i cosTheta_O)) (+.f32 1 (expm1.f32 (.f32 sinTheta_i sinTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (.f32 (pow.f32 (exp.f32 sinTheta_O) sinTheta_i) (exp.f32 (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (.f32 (+.f32 1 (expm1.f32 (.f32 sinTheta_i sinTheta_O))) (exp.f32 (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (.f32 (exp.f32 (.f32 cosTheta_i cosTheta_O)) (+.f32 1 (expm1.f32 (.f32 sinTheta_i sinTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (fma.f32 sinTheta_i sinTheta_O (*.f32 cosTheta_i cosTheta_O))) 1))))))

simplify290.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

529×	`distribute-rgt-in_binary32`
521×	`distribute-lft-in_binary32`
411×	`associate-r_binary32`
292×	`associate-l_binary32`
238×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	8936
1	933	8553
2	3969	7808

Stop Event

1×	node limit

Counts

469 → 322

Calls

Call 1

Inputs
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/9) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)))) (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/9) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2)) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_i 2) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 17) 1) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))) (cbrt.f32 1/2)))))))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/9) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_i 3) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/6 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) (pow.f32 cosTheta_O 3)) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 4) 1) (pow.f32 v 13)) 1/9) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 17) 1) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))) cosTheta_O))) (.f32 1/27 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/3) (pow.f32 cosTheta_O 3))))))))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2)) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_i 2) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 17) 1) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))) (cbrt.f32 1/2))))))))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 -1 (.f32 sinTheta_i sinTheta_O))) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
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(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(/.f32 (-.f32 (+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O)) 1) v)
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
6931/10000
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
6931/10000
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(*.f32 cosTheta_i cosTheta_O)
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(.f32 -1 (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))

Outputs
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2))
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) v)) (cbrt.f32 1/2))
(.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) v)) (cbrt.f32 1/2))
(.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O))) v)) (cbrt.f32 1/2))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/9) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)))) (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18)) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O))) (*.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) v)) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18)) (.f32 (cbrt.f32 1/2) (.f32 cosTheta_i cosTheta_O))) (.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) v)) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O))) 7) (pow.f32 v 16)) 1/18)) (.f32 (cbrt.f32 1/2) (.f32 cosTheta_i cosTheta_O))) (.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O))) v)) (cbrt.f32 1/2)))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 7) 1) (pow.f32 v 16)) 1/9) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 1) v) 1/3) (cbrt.f32 1/2)) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 2)) 1/3) (.f32 (pow.f32 cosTheta_i 2) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 6931/10000) (/.f32 1 v))) 17) 1) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))) (cbrt.f32 1/2)))))))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18)) (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O))) (fma.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) v)) (cbrt.f32 1/2) (.f32 (.f32 1/3 (cbrt.f32 (/.f32 (.f32 v v) (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 2)))) (.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (+.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) (/.f32 (pow.f32 v 3) (.f32 cosTheta_O cosTheta_O)))) (.f32 -1/3 (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) 6931/10000) (/.f32 1 v))) 17) (pow.f32 v 35)) 1/18)))))) (cbrt.f32 1/2)))))
(fma.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18)) (.f32 (cbrt.f32 1/2) (.f32 cosTheta_i cosTheta_O))) (fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 (.f32 v v) (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 2))) (.f32 (cbrt.f32 1/2) (.f32 (.f32 cosTheta_i cosTheta_i) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) (pow.f32 v 3)) (.f32 cosTheta_O cosTheta_O)) (.f32 (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18))) -1/3))))) (.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 (-.f32 6931/10000 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 -1 v))) v)) (cbrt.f32 1/2))))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
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(+.f32 6931/10000 (/.f32 (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))
6931/10000
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(+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (+.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (/.f32 -1 v)))
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(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
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(+.f32 6931/10000 (/.f32 (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))
6931/10000
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
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(+.f32 6931/10000 (/.f32 (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(+.f32 6931/10000 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v)))
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(+.f32 6931/10000 (-.f32 (fma.f32 -1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v)))
(+.f32 (-.f32 6931/10000 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (+.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (/.f32 -1 v)))
(+.f32 6931/10000 (/.f32 (fma.f32 (neg.f32 sinTheta_i) sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))
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(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
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(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
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(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
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(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O)))
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(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O)))
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(neg.f32 (*.f32 sinTheta_i sinTheta_O))
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(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O)))
(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O)))
(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
(+.f32 (.f32 -1 (.f32 sinTheta_i sinTheta_O)) (*.f32 cosTheta_i cosTheta_O))
(fma.f32 cosTheta_i cosTheta_O (neg.f32 (*.f32 sinTheta_i sinTheta_O)))
(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))

localize42.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (exp.f32 6931/10000) v)

Compiler

Compiled 20 to 17 computations (15% saved)

series3.0ms (0%)

Counts

1 → 0

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	v	@	0	(/.f32 (exp.f32 6931/10000) v)
1.0ms	v	@	inf	(/.f32 (exp.f32 6931/10000) v)
1.0ms	v	@	-inf	(/.f32 (exp.f32 6931/10000) v)

rewrite64.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

511×	`pow1_binary32`
496×	`add-sqr-sqrt_binary32`
478×	`add-log-exp_binary32`
478×	`log1p-expm1-u_binary32`
478×	`expm1-log1p-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	102	6
2	1267	6

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

Inputs
(/.f32 (exp.f32 6931/10000) v)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (/.f32 (exp.f32 6931/10000) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (exp.f32 6931/10000) v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (exp.f32 6931/10000) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 6931/5000)) (*.f32 (cbrt.f32 (exp.f32 6931/10000)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) (pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 6931/10000)) (*.f32 (sqrt.f32 (exp.f32 6931/10000)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)) (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (exp.f32 6931/10000)) (/.f32 1 (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 v) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) 1) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) 1) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 6931/10000) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (pow.f32 (cbrt.f32 v) 2)) (/.f32 (sqrt.f32 (exp.f32 6931/10000)) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 (exp.f32 6931/10000) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (cbrt.f32 (exp.f32 6931/5000)) (sqrt.f32 v)) (/.f32 (cbrt.f32 (exp.f32 6931/10000)) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (exp.f32 6931/10000) v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) v) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) v)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (exp.f32 6931/10000)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (exp.f32 6931/10000) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (/.f32 (exp.f32 6931/5000) (*.f32 v v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) v) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 6931/10000 (log.f32 v)))))))

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize88.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v))))
✓	0.2b	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
✓	0.2b	(*.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))

Compiler

Compiled 43 to 15 computations (65.1% saved)

series21.0ms (0.1%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_O	@	-inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	-inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	0	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))

rewrite767.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

547×	`log-prod_binary32`
330×	`pow-prod-down_binary32`
316×	`pow-unpow_binary32`
271×	`pow2_binary32`
193×	`pow1/3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	234	31
2	3066	31

Stop Event

1×	node limit

Counts

3 → 211

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 2 (*.f32 1/3 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) (*.f32 1/3 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 1/3 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) (*.f32 2 (*.f32 1/3 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 sinTheta_O v) 2) sinTheta_i) (*.f32 (/.f32 (/.f32 sinTheta_O v) 2) sinTheta_i))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 sinTheta_i (/.f32 v sinTheta_O))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (neg.f32 sinTheta_O) sinTheta_i) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 sinTheta_i sinTheta_O) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 sinTheta_i (neg.f32 sinTheta_O)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cbrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sqrt.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (/.f32 1/2 v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (/.f32 1/2 v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/2 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (log.f32 (/.f32 1/2 v))) 1) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2) (*.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))) 2)) (log.f32 (cbrt.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 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pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 sinTheta_O)) (sqrt.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 (sqrt.f32 (/.f32 sinTheta_O v)))) (sqrt.f32 (sqrt.f32 (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2))) (sqrt.f32 (cbrt.f32 (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 -1)) (sqrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) sinTheta_O) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) sinTheta_O) (neg.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) 1) (/.f32 sinTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (cbrt.f32 (/.f32 sinTheta_O v))) (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2)) (cbrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2)) (neg.f32 (cbrt.f32 (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (pow.f32 (cbrt.f32 sinTheta_O) 2)) (*.f32 (cbrt.f32 sinTheta_O) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (sqrt.f32 (/.f32 sinTheta_O v))) (sqrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (sqrt.f32 (/.f32 sinTheta_O v))) (neg.f32 (sqrt.f32 (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (sqrt.f32 sinTheta_O)) (*.f32 (sqrt.f32 sinTheta_O) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (neg.f32 sinTheta_O)) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (neg.f32 sinTheta_O)) (/.f32 1 (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 1 v)) sinTheta_O)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) -1) (/.f32 sinTheta_O v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 (pow.f32 (cbrt.f32 sinTheta_O) 2) 1)) (/.f32 (cbrt.f32 sinTheta_O) v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 (sqrt.f32 sinTheta_O) 1)) (/.f32 (sqrt.f32 sinTheta_O) v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (pow.f32 (cbrt.f32 v) -2)) (/.f32 sinTheta_O (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 (pow.f32 (cbrt.f32 sinTheta_O) 2) (pow.f32 (cbrt.f32 v) 2))) (cbrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 (sqrt.f32 sinTheta_O) (pow.f32 (cbrt.f32 v) 2))) (/.f32 (sqrt.f32 sinTheta_O) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (pow.f32 v -1/2)) (/.f32 sinTheta_O (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (/.f32 (pow.f32 (cbrt.f32 sinTheta_O) 2) (sqrt.f32 v))) (/.f32 (cbrt.f32 sinTheta_O) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (neg.f32 (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2))) (cbrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (neg.f32 (sqrt.f32 (/.f32 sinTheta_O v)))) (sqrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (*.f32 -1 (pow.f32 (cbrt.f32 (/.f32 sinTheta_O v)) 2))) (cbrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) -1) (*.f32 -1 (sqrt.f32 (/.f32 sinTheta_O v)))) (sqrt.f32 (/.f32 sinTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (pow.f32 (exp.f32 sinTheta_i) (/.f32 sinTheta_O v))))))))

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

639×	`times-frac_binary32`
374×	`cancel-sign-sub-inv_binary32`
355×	`unswap-sqr_binary32`
349×	`associate-/l*_binary32`
332×	`neg-mul-1_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1728
1	155	1700
2	526	1632
3	3631	1600
4	4966	1600
5	7187	1600

Stop Event

1×	node limit

Counts

319 → 231

Calls

Call 1

Inputs
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 1/4 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3)))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3))) (.f32 -1/12 (/.f32 (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4))))))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 1/4 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3)))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3))) (.f32 -1/12 (/.f32 (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4))))))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 1/4 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3)))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3))) (.f32 -1/12 (/.f32 (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4))))))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 1/4 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3)))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3))) (.f32 -1/12 (/.f32 (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4))))))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))))))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))))))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))))))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))))))

Outputs
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
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(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
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(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
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(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
(neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))
(*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O)
(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v))
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(*.f32 sinTheta_O (neg.f32 (/.f32 sinTheta_i v)))
(*.f32 sinTheta_O (/.f32 (neg.f32 sinTheta_i) v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (.f32 v v)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 1/4 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3)))))
(+.f32 (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (.f32 v v)) (/.f32 1/2 v)) (.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (*.f32 sinTheta_O sinTheta_O)))))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (*.f32 sinTheta_O sinTheta_O)) (/.f32 1/2 v)))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 sinTheta_i (/.f32 (pow.f32 v 3) sinTheta_i))) (/.f32 1/2 v)))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (/.f32 sinTheta_O (/.f32 (/.f32 (pow.f32 v 3) (*.f32 sinTheta_i sinTheta_i)) sinTheta_O)) (/.f32 1/2 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (+.f32 (.f32 1/2 (/.f32 1 v)) (+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 3))) (.f32 -1/12 (/.f32 (*.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4))))))
(+.f32 (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (.f32 v v)) (/.f32 1/2 v)) (fma.f32 1/4 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (pow.f32 v 3) (.f32 sinTheta_O sinTheta_O))) (.f32 -1/12 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 4)))))
(+.f32 (fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v)) (fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 sinTheta_O sinTheta_O)) (/.f32 -1/12 (/.f32 (pow.f32 v 4) (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 sinTheta_i (/.f32 (pow.f32 v 3) sinTheta_i))) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3))) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 sinTheta_i (/.f32 (pow.f32 v 3) sinTheta_i))) (fma.f32 -1/12 (/.f32 (pow.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) v) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (/.f32 sinTheta_O (/.f32 (/.f32 (pow.f32 v 3) (.f32 sinTheta_i sinTheta_i)) sinTheta_O)) (fma.f32 -1/12 (/.f32 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) v) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (/.f32 sinTheta_O (/.f32 (/.f32 (pow.f32 v 3) (.f32 sinTheta_i sinTheta_i)) sinTheta_O)) (fma.f32 -1/12 (/.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 3) (pow.f32 v 4)) (/.f32 1/2 v))))
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))) v))
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(/.f32 1/2 (*.f32 v (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))))
(/.f32 1/2 (*.f32 v (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)))
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(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))) v))
(/.f32 (/.f32 1/2 (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)) v)
(/.f32 1/2 (*.f32 v (pow.f32 (exp.f32 sinTheta_O) (/.f32 sinTheta_i v))))
(/.f32 1/2 (*.f32 v (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)))
(.f32 1/2 (/.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) v))
(.f32 1/2 (/.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O))) v))
(/.f32 (/.f32 1/2 (pow.f32 (exp.f32 (/.f32 sinTheta_i v)) sinTheta_O)) v)
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(+.f32 (fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v)) (fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 sinTheta_O sinTheta_O)) (/.f32 -1/12 (/.f32 (pow.f32 v 4) (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3))))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 sinTheta_i (/.f32 (pow.f32 v 3) sinTheta_i))) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3))) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 sinTheta_i (/.f32 (pow.f32 v 3) sinTheta_i))) (fma.f32 -1/12 (/.f32 (pow.f32 (*.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) v) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (/.f32 sinTheta_O (/.f32 (/.f32 (pow.f32 v 3) (.f32 sinTheta_i sinTheta_i)) sinTheta_O)) (fma.f32 -1/12 (/.f32 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) v) (/.f32 1/2 v))))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (fma.f32 1/4 (/.f32 sinTheta_O (/.f32 (/.f32 (pow.f32 v 3) (.f32 sinTheta_i sinTheta_i)) sinTheta_O)) (fma.f32 -1/12 (/.f32 (pow.f32 (.f32 sinTheta_i sinTheta_O) 3) (pow.f32 v 4)) (/.f32 1/2 v))))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(fma.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) 1)
(-.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) -1))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (fma.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v) 1) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (*.f32 sinTheta_O sinTheta_O)))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (.f32 sinTheta_O sinTheta_O)) 1) (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) 1) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 1 (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
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(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) 1)) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 (fma.f32 -1/6 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) 1) (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(fma.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) 1)
(-.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) -1))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
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(-.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (.f32 sinTheta_O sinTheta_O)) 1) (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) 1) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 1 (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
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(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) 1)) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 (fma.f32 -1/6 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) 1) (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
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(exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
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(exp.f32 (/.f32 (neg.f32 sinTheta_i) (/.f32 v sinTheta_O)))
(exp.f32 (*.f32 (neg.f32 (/.f32 sinTheta_i v)) sinTheta_O))
(pow.f32 (exp.f32 (/.f32 sinTheta_i v)) (neg.f32 sinTheta_O))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(fma.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) 1)
(-.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) -1))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (fma.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v) 1) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (*.f32 sinTheta_O sinTheta_O)))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (.f32 sinTheta_O sinTheta_O)) 1) (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) 1) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
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(+.f32 (fma.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v) 1) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (*.f32 sinTheta_O sinTheta_O))))))
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(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) 1)) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 (fma.f32 -1/6 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) 1) (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
1
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(fma.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v) 1)
(-.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 1 (*.f32 sinTheta_O (/.f32 sinTheta_i v)))
(neg.f32 (fma.f32 sinTheta_O (/.f32 sinTheta_i v) -1))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 (fma.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v) 1) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (*.f32 sinTheta_O sinTheta_O)))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (.f32 sinTheta_O sinTheta_O)) 1) (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) 1) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 1 (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (+.f32 1 (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2))))))
(+.f32 (fma.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v) 1) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (*.f32 sinTheta_O sinTheta_O))))))
(+.f32 (-.f32 1 (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (.f32 sinTheta_O sinTheta_O)) (.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))))))
(-.f32 (fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 -1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) 1)) (.f32 sinTheta_O (/.f32 sinTheta_i v)))
(+.f32 (fma.f32 -1/6 (pow.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) 3) 1) (.f32 sinTheta_O (-.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 sinTheta_i v))))

localize74.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	7.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series63.0ms (0.3%)

Counts

3 → 52

Calls

27 calls:

Time	Variable		Point	Expression
29.0ms	v	@	inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
6.0ms	cosTheta_i	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
5.0ms	v	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
5.0ms	v	@	-inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
5.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))

rewrite196.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

710×	`fma-def_binary32`
367×	`fma-neg_binary32`
317×	`expm1-udef_binary32`
317×	`log1p-udef_binary32`
259×	`log-pow_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	65
1	360	65
2	5231	59

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs

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

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

(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))))) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))))) (/.f32 1 (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))) (*.f32 (/.f32 -1 v) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) 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(#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 2 (*.f32 1/3 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) (*.f32 1/3 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 1/2 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))) (*.f32 1/2 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 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cosTheta_i cosTheta_O)) (sqrt.f32 v)) (log.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 (*.f32 cosTheta_i cosTheta_O) (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)) (log.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 (*.f32 cosTheta_i cosTheta_O) (pow.f32 v -1/2)) (pow.f32 v -1/2) (log.f32 (/.f32 1/2 v)))))))

simplify271.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-/l*_binary32`
542×	`associate-r_binary32`
446×	`associate-l_binary32`
389×	`associate-/r*_binary32`
236×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1627
1	313	1469
2	1174	1324
3	6831	1289

Stop Event

1×	node limit

Counts

280 → 273

Calls

Call 1

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

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

localize184.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O)))
✓	0.1b	(exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v))
✓	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	3.1b	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 98 to 47 computations (52% saved)

series183.0ms (0.9%)

Counts

3 → 132

Calls

33 calls:

Time	Variable		Point	Expression
61.0ms	v	@	-inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
52.0ms	cosTheta_i	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
17.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
11.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
9.0ms	cosTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite88.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

633×	`prod-diff_binary32`
349×	`expm1-udef_binary32`
349×	`log1p-udef_binary32`
275×	`fma-neg_binary32`
211×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	56
1	423	52
2	5472	52

Stop Event

1×	node limit

Counts

3 → 65

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) (pow.f32 (cbrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) 2) (cbrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) (sqrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 6931/10000) 1/2) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 6931/10000) 1) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 6931/10000) (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2)) (cbrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 6931/10000) (sqrt.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 6931/10000) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) 1) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x 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)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 3) (pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3) (pow.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v) (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (+.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 2) (cbrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) (sqrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i sinTheta_O)) v)) (exp.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1))) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 2)) (cbrt.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))) (sqrt.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))

simplify185.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

504×	`fma-def_binary32`
411×	`associate-/r/_binary32`
391×	`associate-*l/_binary32`
385×	`fma-neg_binary32`
348×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	4922
1	654	4520
2	2752	4264
3	7803	4264

Stop Event

1×	node limit

Counts

197 → 132

Calls

Call 1

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

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

eval1.1s (5.2%)

Compiler: Compiled 37979 to 21907 computations (42.3% saved)

prune341.0ms (1.6%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	1165	18	1183
Fresh	4	3	7
Picked	1	0	1
Done	4	0	4
Total	1174	21	1195

Error

0.0b

Counts

1195 → 21

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))))
▶	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
	0.9b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
▶	0.1b	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))
	28.0b	(exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
	0.4b	(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))) 3) 1/3)
	28.0b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
▶	0.2b	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	30.6b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
	0.1b	(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)))) 3)
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	30.5b	(/.f32 1/2 v)
	0.1b	(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
▶	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 3)
	0.2b	(.f32 (pow.f32 (exp.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1))) (/.f32 1 v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2)

Compiler

Compiled 992 to 760 computations (23.4% saved)

localize216.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))
✓	0.2b	(cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))
✓	0.5b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))
✓	0.5b	(pow.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3)

Compiler

Compiled 235 to 154 computations (34.5% saved)

series697.0ms (3.4%)

Counts

4 → 212

Calls

60 calls:

Time	Variable		Point	Expression
154.0ms	cosTheta_i	@	-inf	(cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))
60.0ms	v	@	-inf	(pow.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3)
59.0ms	v	@	0	(cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))
56.0ms	sinTheta_O	@	inf	(cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))
46.0ms	cosTheta_O	@	-inf	(cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))

rewrite153.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

374×	`expm1-udef_binary32`
374×	`log1p-udef_binary32`
315×	`log-pow_binary32`
220×	`add-sqr-sqrt_binary32`
215×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	99
1	464	99
2	5365	97

Stop Event

1×	node limit

Counts

4 → 104

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule 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((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 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1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 1 1/3) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/3) (pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) (cbrt.f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))) (cbrt.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 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(#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (*.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (cbrt.f32 (exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/6) (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (cbrt.f32 (/.f32 1/2 v))) (cbrt.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (cbrt.f32 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(exp.f32 (.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 1/3) (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/6) 1/3) (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/6) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/12) (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) 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(cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 2/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 6931/10000) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2) (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (sqrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2)) (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))

simplify468.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

803×	`fma-def_binary32`
639×	`times-frac_binary32`
397×	`*-commutative_binary32`
366×	`associate-/r*_binary32`
349×	`associate-/l*_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	845	27853
1	3042	24374

Stop Event

1×	node limit

Counts

316 → 236

Calls

Call 1

Inputs
(.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/9) (pow.f32 (pow.f32 (cbrt.f32 1/2) 2) 1/3))
(+.f32 (.f32 2/9 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 26)) (pow.f32 v 53)) 1/27) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/9)))) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/9) (pow.f32 (pow.f32 (cbrt.f32 1/2) 2) 1/3)))
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(+.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))
(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))))
(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000)))
(+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))))

Outputs
(.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/9) (pow.f32 (pow.f32 (cbrt.f32 1/2) 2) 1/3))
(.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2)))
(.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2)))
(+.f32 (.f32 2/9 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 26)) (pow.f32 v 53)) 1/27) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/9)))) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/9) (pow.f32 (pow.f32 (cbrt.f32 1/2) 2) 1/3)))
(fma.f32 2/9 (.f32 cosTheta_i (.f32 cosTheta_O (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 26) (pow.f32 v 53)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 26) (pow.f32 v 53)) 1/54)) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18))))) (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (*.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2))))
(fma.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2)) (.f32 2/9 (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 26) (pow.f32 v 53)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 26) (pow.f32 v 53)) 1/54))) (*.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18)))))
(+.f32 (.f32 2/9 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 26)) (pow.f32 v 53)) 1/27) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/9)))) (+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (+.f32 (.f32 1/9 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 14)) (pow.f32 v 32)) 1/9) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (pow.f32 cosTheta_O 2)))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 v 1) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) 1/3) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))))))) (.f32 4/27 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 58)) (pow.f32 v 112)) 1/27) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 34) 1/9) (pow.f32 cosTheta_O 2)))))) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 4) (pow.f32 1 4)) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 4)) 1/9) (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 1/2) 4)) 1/3)))) (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) (pow.f32 v 2)) 1/9) (pow.f32 (pow.f32 (cbrt.f32 1/2) 2) 1/3))))
(fma.f32 2/9 (.f32 cosTheta_i (.f32 cosTheta_O (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 26) (pow.f32 v 53)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 26) (pow.f32 v 53)) 1/54)) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18))))) (fma.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (+.f32 (fma.f32 1/9 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 14) (pow.f32 v 32)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 14) (pow.f32 v 32)) 1/18)) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (.f32 cosTheta_O cosTheta_O))) (.f32 2/3 (.f32 (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))))) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (+.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) (/.f32 (pow.f32 v 3) (.f32 cosTheta_O cosTheta_O)))) (.f32 -1/3 (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 17) (pow.f32 v 35)) 1/18))))))))) (.f32 -4/27 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 58) (pow.f32 v 112)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 58) (pow.f32 v 112)) 1/54)) (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 34) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 34) 1/18)))))) (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 v 4) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 4)) 1/18) (pow.f32 (/.f32 (pow.f32 v 4) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 4)) 1/18)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 1/2) 4)))))) (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 1 v)))) 2) (*.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2)))))
(fma.f32 2/9 (.f32 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 26) (pow.f32 v 53)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 26) (pow.f32 v 53)) 1/54))) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 14) 1/18))) (fma.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 2) (.f32 v v)) 1/18)) (cbrt.f32 (pow.f32 (cbrt.f32 1/2) 2)) (.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_i) (fma.f32 1/9 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 14) (pow.f32 v 32)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 14) (pow.f32 v 32)) 1/18)) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (.f32 cosTheta_O cosTheta_O))) (fma.f32 2/3 (.f32 (.f32 (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))))) (pow.f32 (cbrt.f32 1/2) 2)) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) (pow.f32 v 3)) (.f32 cosTheta_O cosTheta_O)) (.f32 (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18))) -1/3))) (.f32 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 58) (pow.f32 v 112)) 1/54) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 58) (pow.f32 v 112)) 1/54)) (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (pow.f32 (cbrt.f32 1/2) 34) 1/18) (pow.f32 (pow.f32 (cbrt.f32 1/2) 34) 1/18)))) -4/27))))) (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 v 4) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 4)) 1/18) (pow.f32 (/.f32 (pow.f32 v 4) (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 -1 v)))) 4)) 1/18)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 1/2) 4)))))))
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(+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))))
(fma.f32 1/6 (/.f32 (pow.f32 (+.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) -1) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (fma.f32 1/2 (/.f32 (pow.f32 (+.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) -1) 2) (/.f32 (.f32 v v) (exp.f32 6931/10000))) (+.f32 (exp.f32 6931/10000) (/.f32 (+.f32 (fma.f32 sinTheta_i sinTheta_O (.f32 cosTheta_i cosTheta_O)) -1) (/.f32 v (exp.f32 6931/10000))))))
(fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (fma.f32 1/2 (*.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) 2) v)) (+.f32 (exp.f32 6931/10000) (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) (/.f32 v (exp.f32 6931/10000))))))

localize10.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

localize81.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
✓	0.0b	(+.f32 6931/10000 (/.f32 -1 v))
✓	0.1b	(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))

Compiler

Compiled 36 to 29 computations (19.4% saved)

series9.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
5.0ms	v	@	0	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
1.0ms	v	@	inf	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
0.0ms	v	@	inf	(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
0.0ms	v	@	-inf	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
0.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))

rewrite110.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

461×	`log-prod_binary32`
365×	`exp-prod_binary32`
269×	`prod-exp_binary32`
266×	`pow2_binary32`
251×	`pow-prod-down_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	217	31
2	2670	31

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (/.f32 -1 v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 (exp.f32 1) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) 6931/10000) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (pow.f32 (exp.f32 1) (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) (*.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (exp.f32 1) (*.f32 1/2 (+.f32 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#<rule egg-rr> (2) ((x pow.f32 (exp.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1) (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (cbrt.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (sqrt.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (sqrt.f32 (cbrt.f32 (pow.f32 (+.f32 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(#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))) (sqrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (exp.f32 (*.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 6931/10000 (/.f32 -1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)) (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 3 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) 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(#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (log.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 -1 (/.f32 1 v) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 -1 v) 1 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (/.f32 -1 v) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 -1 (cbrt.f32 v)) (cbrt.f32 (pow.f32 v -2)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (pow.f32 v -2)) (/.f32 -1 (cbrt.f32 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (neg.f32 v) -1/2) (pow.f32 (neg.f32 v) -1/2) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1 v) -1 6931/10000)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v))))) (sqrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 1/2) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/2 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 1/2)) (*.f32 (log.f32 v) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (*.f32 (log.f32 (/.f32 1/2 v)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (/.f32 1/2 v)) 1) (+.f32 6931/10000 (/.f32 -1 v))))))))

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

737×	`cancel-sign-sub-inv_binary32`
690×	`fma-neg_binary32`
489×	`associate-l_binary32`
395×	`fma-def_binary32`
352×	`associate-/r/_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	531
1	119	525
2	282	475
3	781	449
4	2948	449
5	6577	445

Stop Event

1×	node limit

Counts

169 → 156

Calls

Call 1

Inputs
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 6931/10000)
(+.f32 (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (*.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (exp.f32 6931/10000))))
(exp.f32 6931/10000)
(+.f32 (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (*.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (exp.f32 6931/10000))))
(/.f32 -1 v)
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (*.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (*.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))))))

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

localize84.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 6931/10000 (/.f32 1 v))
✓	0.1b	(+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))
✓	0.1b	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
✓	0.2b	(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))

Compiler

Compiled 71 to 44 computations (38% saved)

series27.0ms (0.1%)

Counts

4 → 111

Calls

30 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta_O	@	0	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
2.0ms	v	@	-inf	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
1.0ms	cosTheta_i	@	0	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
1.0ms	cosTheta_i	@	0	(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))
1.0ms	v	@	-inf	(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))

rewrite133.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary32`
365×	`fma-def_binary32`
302×	`expm1-udef_binary32`
302×	`log1p-udef_binary32`
256×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	66
1	357	66
2	4663	66

Stop Event

1×	node limit

Counts

4 → 167

Calls

Call 1

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

Outputs
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simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

997×	`times-frac_binary32`
620×	`associate-/l*_binary32`
532×	`associate-r_binary32`
441×	`associate-l_binary32`
385×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2791
1	342	2465
2	1219	2353

Stop Event

1×	node limit

Counts

278 → 221

Calls

Call 1

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

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

localize145.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
✓	0.1b	(pow.f32 (E.f32) (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))
✓	0.1b	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	3.1b	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 91 to 52 computations (42.9% saved)

series30.0ms (0.1%)

Counts

3 → 132

Calls

33 calls:

Time	Variable		Point	Expression
8.0ms	cosTheta_i	@	0	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
2.0ms	v	@	0	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	cosTheta_O	@	0	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	v	@	-inf	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	v	@	inf	(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite85.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

425×	`fma-def_binary32`
373×	`expm1-udef_binary32`
373×	`log1p-udef_binary32`
312×	`log-pow_binary32`
245×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	52
1	426	48
2	5472	48

Stop Event

1×	node limit

Counts

3 → 77

Calls

Call 1

Inputs

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

(pow.f32 (E.f32) (/.f32 (+.f32 (*.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3) (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (cbrt.f32 (pow.f32 (exp.f32 2) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (exp.f32 2) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (cbrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (sqrt.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 2/3) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (pow.f32 (exp.f32 1/3) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1/2) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (pow.f32 (exp.f32 1/2) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 2) (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 6931/10000 (log.f32 (*.f32 v 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 1/2) (-.f32 (log.f32 v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 48038761/100000000 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (/.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (*.f32 (exp.f32 6931/10000) 1/2)) (log.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (*.f32 (exp.f32 6931/10000) 1)) (log.f32 (*.f32 v 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (*.f32 (exp.f32 6931/10000) -1/2)) (log.f32 (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 3 (*.f32 1/3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) (/.f32 1 (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) (/.f32 1 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (*.f32 1/2 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/3 (*.f32 3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000) (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3)) (+.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (-.f32 48038761/100000000 (*.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2)) (-.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3))) (neg.f32 (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (neg.f32 (-.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) 48038761/100000000) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (fma.f32 (/.f32 1/2 v) (exp.f32 6931/10000) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (fma.f32 (/.f32 1/2 v) (exp.f32 6931/10000) -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (log.f32 (/.f32 1/2 v)) 1 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (log.f32 (/.f32 1/2 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (log.f32 1/2) (neg.f32 (-.f32 (log.f32 v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (log.f32 (/.f32 1/2 v))) 2) (cbrt.f32 (log.f32 (/.f32 1/2 v))) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (log.f32 (/.f32 1/2 v))) (sqrt.f32 (log.f32 (/.f32 1/2 v))) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 (cbrt.f32 (log.f32 1/2)) (cbrt.f32 (log.f32 1/2))) (cbrt.f32 (log.f32 1/2)) (neg.f32 (-.f32 (log.f32 v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (log.f32 1/2)) (sqrt.f32 (log.f32 1/2)) (neg.f32 (-.f32 (log.f32 v) 6931/10000)))))))

simplify135.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-def_binary32`
410×	`associate-/r/_binary32`
398×	`distribute-lft-in_binary32`
398×	`distribute-rgt-in_binary32`
396×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	216	4566
1	693	4240
2	2846	3955

Stop Event

1×	node limit

Counts

209 → 150

Calls

Call 1

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

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

eval1.7s (8.2%)

Compiler: Compiled 54464 to 37976 computations (30.3% saved)

prune283.0ms (1.4%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	887	13	900
Fresh	7	9	16
Picked	1	0	1
Done	2	2	4
Total	897	24	921

Error

0.0b

Counts

921 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 3)
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))))
✓	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
▶	0.1b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
▶	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
	0.1b	(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))
	28.0b	(exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
	28.0b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	0.8b	(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
▶	30.6b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
▶	0.1b	(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 1) (.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (exp.f32 1) (.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v))))))
▶	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 1) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (pow.f32 (exp.f32 1) (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))))
	0.1b	(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2)
	0.4b	(.f32 (/.f32 1/2 v) (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3))))
✓	30.5b	(/.f32 1/2 v)
	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2))
	0.2b	(.f32 (pow.f32 (exp.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1))) (/.f32 1 v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.2b	(pow.f32 (E.f32) (fma.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 1 (+.f32 6931/10000 (/.f32 1 v))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (exp.f32 (.f32 (.f32 2/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1/6))) 3)

Compiler

Compiled 1169 to 944 computations (19.2% saved)

localize157.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))
	0.5b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))
	0.5b	(pow.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3)
✓	0.7b	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)

Compiler

Compiled 236 to 155 computations (34.3% saved)

series408.0ms (2%)

Counts

1 → 60

Calls

15 calls:

Time	Variable		Point	Expression
193.0ms	cosTheta_i	@	-inf	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)
27.0ms	cosTheta_i	@	inf	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)
26.0ms	sinTheta_i	@	-inf	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)
24.0ms	sinTheta_O	@	-inf	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)
23.0ms	sinTheta_i	@	inf	(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)

rewrite84.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

864×	`log-prod_binary32`
338×	`expm1-udef_binary32`
338×	`log1p-udef_binary32`
279×	`log-pow_binary32`
203×	`prod-diff_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	30
1	386	28
2	4741	28

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))) (cbrt.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (log.f32 (cbrt.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (exp.f32 (*.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (*.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))) (cbrt.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (*.f32 1/9 (log.f32 (/.f32 1/2 v)))) (exp.f32 (*.f32 1/9 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (*.f32 1/9 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (exp.f32 (*.f32 1/9 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/18))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 1/9) (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))) 2) 1/9) (pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))) 1/9) (pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))) 1/9))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (exp.f32 (*.f32 2/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/9 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1))))))

simplify102.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

908×	`times-frac_binary32`
725×	`associate-/l*_binary32`
465×	`associate-/r*_binary32`
285×	`distribute-rgt-out_binary32`
278×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5739
1	1000	4906
2	4129	4339

Stop Event

1×	node limit

Counts

82 → 68

Calls

Call 1

Inputs
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))
(+.f32 (.f32 1/9 (/.f32 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) v)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000)))))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 1/18 (+.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (.f32 -1 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2)))) (.f32 1/162 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2))) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) (pow.f32 v 2)) (+.f32 (.f32 1/9 (/.f32 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) v)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))))
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(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(pow.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)) 1/9)
(+.f32 (.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) (pow.f32 v 10)) 1/9))) (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)) 1/9))
(+.f32 (.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) (pow.f32 v 10)) 1/9))) (+.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)) 1/9) (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) v) 1/9) (.f32 (+.f32 (.f32 1/18 (+.f32 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)) (.f32 -1 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))))) (.f32 1/162 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2)))))
(+.f32 (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) v) 1/9) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/4374 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 1/54 (+.f32 (.f32 2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))))) (.f32 1/162 (/.f32 (.f32 sinTheta_i (+.f32 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)) (.f32 -1 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))))) v)))))) (+.f32 (.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) (pow.f32 v 10)) 1/9))) (+.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)) 1/9) (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) v) 1/9) (.f32 (+.f32 (.f32 1/18 (+.f32 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)) (.f32 -1 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))))) (*.f32 1/162 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2))))))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)

Outputs
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(pow.f32 (exp.f32 1/9) (fma.f32 -1 (log.f32 v) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))
(pow.f32 (exp.f32 1/9) (-.f32 (+.f32 (log.f32 1/2) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (log.f32 v)))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (log.f32 v))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(pow.f32 (exp.f32 1/9) (fma.f32 -1 (log.f32 v) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))
(pow.f32 (exp.f32 1/9) (-.f32 (+.f32 (log.f32 1/2) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (log.f32 v)))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (log.f32 v))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(pow.f32 (exp.f32 1/9) (fma.f32 -1 (log.f32 v) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))
(pow.f32 (exp.f32 1/9) (-.f32 (+.f32 (log.f32 1/2) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (log.f32 v)))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (log.f32 v))))
(exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))))))))
(pow.f32 (exp.f32 1/9) (fma.f32 -1 (log.f32 v) (log.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))))
(pow.f32 (exp.f32 1/9) (-.f32 (+.f32 (log.f32 1/2) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (log.f32 v)))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (log.f32 v))))
(exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))
(pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 6931/10000)))))
(pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v))))
(+.f32 (.f32 1/9 (/.f32 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) v)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000)))))))
(fma.f32 1/9 (/.f32 (.f32 (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))) (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1)) v) (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))
(fma.f32 1/9 (*.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v))))
(fma.f32 1/9 (*.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v))))) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v)))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 1/18 (+.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (.f32 -1 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2)))) (.f32 1/162 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2))) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) (pow.f32 v 2)) (+.f32 (.f32 1/9 (/.f32 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) v)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))))
(+.f32 (fma.f32 1/9 (/.f32 (.f32 (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))) (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1)) v) (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000)))))) (/.f32 (fma.f32 1/18 (.f32 0 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 2)) (.f32 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 2) 1/162)) (/.f32 (.f32 v v) (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))))
(+.f32 (fma.f32 1/9 (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))) (.f32 (/.f32 (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v))) v) (/.f32 (fma.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 2) 1/162 0) v)))
(+.f32 (.f32 (/.f32 1/9 v) (.f32 (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v)))) (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)))) (.f32 (+.f32 (/.f32 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 2) 1/162) (*.f32 v v)) 1) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v))))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 1/18 (+.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (.f32 -1 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2)))) (.f32 1/162 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2))) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) (pow.f32 v 2)) (+.f32 (.f32 1/9 (/.f32 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) v)) (+.f32 (/.f32 (.f32 (+.f32 (.f32 1/162 (.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) (+.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (.f32 -1 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 2))))) (+.f32 (.f32 1/54 (+.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 3) (+.f32 (.f32 2 (pow.f32 (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) 3)) (.f32 -3 (.f32 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 2) (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1)))))) (.f32 1/4374 (pow.f32 (-.f32 (+.f32 (.f32 sinTheta_i sinTheta_O) (.f32 cosTheta_i cosTheta_O)) 1) 3)))) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) (pow.f32 v 3)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 1 v)) (log.f32 (*.f32 1/2 (exp.f32 6931/10000)))))))))
(+.f32 (/.f32 (fma.f32 1/18 (.f32 0 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 2)) (.f32 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 2) 1/162)) (/.f32 (.f32 v v) (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))))) (fma.f32 1/9 (/.f32 (.f32 (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))) (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1)) v) (+.f32 (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (.f32 1/2 (exp.f32 6931/10000))))) (/.f32 (fma.f32 1/162 (.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) (.f32 0 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 2))) (fma.f32 1/54 (+.f32 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 3) (fma.f32 2 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 3) (.f32 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 3) -3))) (.f32 (pow.f32 (+.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i sinTheta_O)) -1) 3) 1/4374))) (/.f32 (pow.f32 v 3) (pow.f32 (exp.f32 1/9) (+.f32 (neg.f32 (log.f32 v)) (log.f32 (*.f32 1/2 (exp.f32 6931/10000))))))))))
(+.f32 (.f32 (/.f32 (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v))) v) (/.f32 (fma.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 2) 1/162 0) v)) (+.f32 (fma.f32 1/9 (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v)))) (.f32 (/.f32 (+.f32 (.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 0) (fma.f32 (.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 0) 1/54 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 3) 1/4374))) (pow.f32 v 3)) (pow.f32 (exp.f32 1/9) (-.f32 (+.f32 6931/10000 (log.f32 1/2)) (log.f32 v))))))
(+.f32 (fma.f32 1/9 (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v))))) (.f32 (/.f32 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 3) 1/4374) (pow.f32 v 3)) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v)))))) (.f32 (+.f32 (/.f32 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) 2) 1/162) (.f32 v v)) 1) (pow.f32 (exp.f32 1/9) (+.f32 (log.f32 1/2) (-.f32 6931/10000 (log.f32 v))))))
(exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 (.f32 -1/2 (exp.f32 6931/10000))))))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 (*.f32 (exp.f32 6931/10000) -1/2))))
(pow.f32 (exp.f32 1/9) (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))
(+.f32 (.f32 1/9 (/.f32 (.f32 (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 (.f32 -1/2 (exp.f32 6931/10000)))))) (-.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1)) v)) (exp.f32 (.f32 1/9 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 (.f32 -1/2 (exp.f32 6931/10000)))))))
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(+.f32 (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) v) 1/9) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/4374 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 1/54 (+.f32 (.f32 2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (+.f32 (.f32 -3 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))) (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3))))) (.f32 1/162 (/.f32 (.f32 sinTheta_i (+.f32 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)) (.f32 -1 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))))) v)))))) (+.f32 (.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) (pow.f32 v 10)) 1/9))) (+.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)) 1/9) (.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 1/2) v) 1/9) (.f32 (+.f32 (.f32 1/18 (+.f32 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)) (.f32 -1 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2))))) (*.f32 1/162 (/.f32 (pow.f32 sinTheta_i 2) (pow.f32 v 2)))) (pow.f32 sinTheta_O 2))))))
(fma.f32 (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18)) (.f32 (pow.f32 sinTheta_O 3) (fma.f32 1/4374 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (fma.f32 1/54 (fma.f32 2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (.f32 -2 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)))) (/.f32 (.f32 1/162 (.f32 sinTheta_i (.f32 0 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v))))) v)))) (+.f32 (fma.f32 1/9 (.f32 sinTheta_i (.f32 sinTheta_O (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 (pow.f32 v 10) 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 (pow.f32 v 10) 1/2)) 1/18)))) (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18))) (.f32 (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (/.f32 v 1/2)) 1/18)) (.f32 (.f32 sinTheta_O sinTheta_O) (fma.f32 1/18 (.f32 0 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v))) (.f32 1/162 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v))))))))
(fma.f32 (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (/.f32 v 1/2)) 1/18)) (.f32 (pow.f32 sinTheta_O 3) (fma.f32 1/4374 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (fma.f32 1/54 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) 0) (.f32 (/.f32 sinTheta_i v) 0)))) (fma.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_O) (.f32 (pow.f32 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (pow.f32 v 10)) 1/2) 1/18) (pow.f32 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (pow.f32 v 10)) 1/2) 1/18))) (.f32 (+.f32 (.f32 sinTheta_O (.f32 sinTheta_O (fma.f32 1/162 (.f32 (/.f32 sinTheta_i v) (/.f32 sinTheta_i v)) 0))) 1) (.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 (/.f32 -1 v) (+.f32 6931/10000 (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (/.f32 v 1/2)) 1/18)))))
(+.f32 (.f32 (.f32 (pow.f32 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) (pow.f32 v 10)) 1/2) 1/18) (pow.f32 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) (pow.f32 v 10)) 1/2) 1/18)) (.f32 1/9 (.f32 sinTheta_i sinTheta_O))) (.f32 (.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 1/18) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 1/18)) (+.f32 (+.f32 (.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 (.f32 1/162 (.f32 sinTheta_i sinTheta_i)) (.f32 v v))) 1) (.f32 (pow.f32 sinTheta_O 3) (fma.f32 1/4374 (pow.f32 (/.f32 sinTheta_i v) 3) 0)))))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))
(pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/9)
(.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v)) 1/18))
(*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (/.f32 v 1/2)) 1/18))
(.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/18))

localize42.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
	7.4b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 51 to 25 computations (51% saved)

series7.0ms (0%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	v	@	-inf	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	0	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
1.0ms	sinTheta_O	@	-inf	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
1.0ms	v	@	0	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	-inf	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))

rewrite62.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

700×	`prod-diff_binary32`
631×	`log-prod_binary32`
223×	`pow1/3_binary32`
215×	`log1p-udef_binary32`
214×	`expm1-udef_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	17
1	276	16
2	3726	14

Stop Event

1×	node limit

Counts

1 → 68

Calls

Call 1

Inputs
(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 v) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 v) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))) (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3)) (*.f32 (*.f32 v 2) (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1) (*.f32 (*.f32 v 2) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3)) 1) (*.f32 (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)) (*.f32 v 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1) 1) (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1) (*.f32 v 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3)) 1/2) (*.f32 (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)) v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1) 1/2) (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1) v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3)) -1/2) (*.f32 (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1) -1/2) (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 1/2 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3))) (*.f32 v (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3))) (*.f32 (neg.f32 v) (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 1/2 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1)) (*.f32 v (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1)) (*.f32 (neg.f32 v) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3)) (/.f32 1/2 v)) (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1) (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (/.f32 1/2 v) (+.f32 1 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 3))) (+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (/.f32 1/2 v) (+.f32 (pow.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) 2) -1)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (pow.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 3) (pow.f32 (/.f32 1/2 v) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 3) (pow.f32 (/.f32 1/2 v) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (/.f32 1/2 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (/.f32 1/2 v) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (/.f32 1/2 v) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1/2 (/.f32 1 v) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1/2 (/.f32 1 v) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1/2 v) 1 (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1/2 v) 1 (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/4 (*.f32 v v))) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (/.f32 1/4 (*.f32 v v))) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (/.f32 1/4 (*.f32 v v))) (cbrt.f32 (/.f32 1/2 v)) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (/.f32 1/4 (*.f32 v v))) (cbrt.f32 (/.f32 1/2 v)) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.f32 (/.f32 1/2 v)) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (/.f32 1/2 v)) (sqrt.f32 (/.f32 1/2 v)) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 -1/2 (/.f32 1 (neg.f32 v)) (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 -1/2 (/.f32 1 (neg.f32 v)) (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1 v) 1/2 (*.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1 v) 1/2 (*.f32 (/.f32 1/2 v) (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))))))

simplify125.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

897×	`associate-/r/_binary32`
802×	`*-commutative_binary32`
577×	`times-frac_binary32`
440×	`sqr-pow_binary32`
336×	`associate-/l*_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	540
1	33	540
2	66	540
3	178	540
4	656	540
5	3180	540
6	3594	540
7	4009	540
8	4124	540
9	4275	540
10	4453	540
11	5738	540
12	6563	540
13	6984	540
14	7439	540

Stop Event

1×	node limit

Counts

104 → 74

Calls

Call 1

Inputs
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))

Outputs
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) sinTheta_O)))
(.f32 -1/2 (.f32 (/.f32 sinTheta_i (*.f32 v v)) sinTheta_O))
(.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (*.f32 v v))))
(.f32 (.f32 sinTheta_i sinTheta_O) (/.f32 -1/2 (*.f32 v v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) sinTheta_O)))
(.f32 -1/2 (.f32 (/.f32 sinTheta_i (*.f32 v v)) sinTheta_O))
(.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (*.f32 v v))))
(.f32 (.f32 sinTheta_i sinTheta_O) (/.f32 -1/2 (*.f32 v v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) sinTheta_O)))
(.f32 -1/2 (.f32 (/.f32 sinTheta_i (*.f32 v v)) sinTheta_O))
(.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (*.f32 v v))))
(.f32 (.f32 sinTheta_i sinTheta_O) (/.f32 -1/2 (*.f32 v v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) sinTheta_O)))
(.f32 -1/2 (.f32 (/.f32 sinTheta_i (*.f32 v v)) sinTheta_O))
(.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (*.f32 v v))))
(.f32 (.f32 sinTheta_i sinTheta_O) (/.f32 -1/2 (*.f32 v v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2)))
(.f32 -1/2 (/.f32 sinTheta_i (/.f32 (.f32 v v) sinTheta_O)))
(.f32 -1/2 (.f32 (/.f32 sinTheta_i (*.f32 v v)) sinTheta_O))
(.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (*.f32 v v))))
(.f32 (.f32 sinTheta_i sinTheta_O) (/.f32 -1/2 (*.f32 v v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 1/2 (/.f32 1 v)) (.f32 -1/2 (/.f32 (*.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(/.f32 1/2 v)
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i sinTheta_O) (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))
(fma.f32 -1/2 (/.f32 sinTheta_i (/.f32 (*.f32 v v) sinTheta_O)) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 (/.f32 sinTheta_i (.f32 v v)) sinTheta_O) (/.f32 1/2 v))
(fma.f32 -1/2 (.f32 sinTheta_O (/.f32 sinTheta_i (.f32 v v))) (/.f32 1/2 v))
(fma.f32 (/.f32 sinTheta_i (.f32 v v)) (.f32 -1/2 sinTheta_O) (/.f32 1/2 v))
(fma.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v) (/.f32 1/2 v))

localize54.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
	0.0b	(+.f32 6931/10000 (/.f32 -1 v))
✓	0.1b	(pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))

Compiler

Compiled 43 to 36 computations (16.3% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	v	@	0	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
1.0ms	v	@	inf	(pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))
0.0ms	v	@	inf	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
0.0ms	v	@	0	(pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v)))
0.0ms	v	@	-inf	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))

rewrite64.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`log-prod_binary32`
307×	`pow2_binary32`
301×	`pow-prod-down_binary32`
263×	`pow-unpow_binary32`
213×	`pow-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	24
1	256	24
2	3082	24

Stop Event

1×	node limit

Counts

2 → 55

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))) (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (/.f32 -1 v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1 (pow.f32 1 (/.f32 -1 v))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (E.f32) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (E.f32) (exp.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (E.f32))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (E.f32) (/.f32 48038761/100000000 (-.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (E.f32) (/.f32 (pow.f32 v -2) (-.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 -1 v))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))) 3))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/2 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))) 2))))))

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

737×	`cancel-sign-sub-inv_binary32`
690×	`fma-neg_binary32`
498×	`associate-l_binary32`
395×	`fma-def_binary32`
351×	`associate-/r/_binary32`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	44	462
1	118	456
2	282	406
3	783	380
4	2952	380
5	6623	376

Stop Event

1×	node limit

Counts

79 → 73

Calls

Call 1

Inputs
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 6931/10000)
(+.f32 (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (*.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (exp.f32 6931/10000))))
(exp.f32 6931/10000)
(+.f32 (*.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (+.f32 (*.f32 -1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (exp.f32 6931/10000))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (*.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))))))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (*.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2)))))
(+.f32 (.f32 1/4 (/.f32 (exp.f32 6931/10000) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) (+.f32 (.f32 -1/2 (/.f32 (exp.f32 6931/10000) (pow.f32 v 2))) (.f32 -1/12 (/.f32 (exp.f32 6931/10000) (pow.f32 v 4))))))

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

localize103.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
✓	0.1b	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.5b	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
	7.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 148 to 87 computations (41.2% saved)

series27.0ms (0.1%)

Counts

3 → 49

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta_O	@	inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
3.0ms	cosTheta_i	@	0	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
3.0ms	v	@	-inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
2.0ms	cosTheta_O	@	0	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
2.0ms	cosTheta_O	@	-inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)

rewrite88.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`log-prod_binary32`
468×	`fma-def_binary32`
299×	`fma-neg_binary32`
286×	`expm1-udef_binary32`
286×	`log1p-udef_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	51
1	357	45
2	4739	39

Stop Event

1×	node limit

Counts

3 → 111

Calls

Call 1

Inputs

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

(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))) (cbrt.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))))) (log.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))) (log.f32 (sqrt.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (/.f32 1 (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))) (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))) 2) (cbrt.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) 1/6) (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 1/3) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) 2) 1/3) (cbrt.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) 1/3) (pow.f32 (sqrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cbrt.f32 (neg.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) (cbrt.f32 (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 1/3 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (log.f32 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (-.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (log.f32 v))) 1))))))

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 48038761/100000000 (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))) (/.f32 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2) (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 2) (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 3)) (/.f32 1 (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2)) (/.f32 1 (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000) (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (-.f32 48038761/100000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 3)) (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 3)) (+.f32 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2) (-.f32 48038761/100000000 (*.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2)) (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 3))) (neg.f32 (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 48038761/100000000 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2))) (neg.f32 (-.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2) 48038761/100000000) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 cosTheta_i (*.f32 cosTheta_O (/.f32 1 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 cosTheta_O (*.f32 cosTheta_i (/.f32 1 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 cosTheta_i cosTheta_O) (/.f32 1 v) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (/.f32 1 v) (*.f32 cosTheta_i cosTheta_O) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) 2) (*.f32 (cbrt.f32 (*.f32 cosTheta_i cosTheta_O)) (/.f32 1 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (cbrt.f32 (pow.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 2)) 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (log.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 2) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (exp.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))) (neg.f32 (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 1) (exp.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (sqrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))) (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))))))

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

595×	`fma-def_binary32`
587×	`associate-/r*_binary32`
315×	`associate-*l/_binary32`
298×	`associate-*r/_binary32`
286×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	163	2368
1	520	2290
2	2098	2182
3	7484	2174

Stop Event

1×	node limit

Counts

160 → 148

Calls

Call 1

Inputs
(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3)
(+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))))
(+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3))) (+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (*.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9)))))
(+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 3) (-.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))) cosTheta_O))) (.f32 1/27 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/3) (pow.f32 cosTheta_O 3)))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3))) (+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3))) (+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (*.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))))))
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3)
(+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_i 2)))) (pow.f32 cosTheta_O 2)))) (+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (*.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9)))))
(+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_i 2)))) (pow.f32 cosTheta_O 2)))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3) (.f32 (-.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9) (.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 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_i 2))))))) (.f32 1/27 (.f32 (pow.f32 cosTheta_i 3) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/3))))) (pow.f32 cosTheta_O 3)))) (+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (*.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))))))
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
(pow.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) 1/3)
6931/10000
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
6931/10000
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
6931/10000
6931/10000
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (exp.f32 6931/10000))))
(exp.f32 6931/10000)
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (exp.f32 6931/10000))))

Outputs
(pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3)
(cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v))
(cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))
(+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))))
(+.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18)))))
(fma.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (*.f32 cosTheta_i cosTheta_O))) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))
(+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2)) 1/3))) (+.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (pow.f32 (/.f32 (*.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9)))))
(fma.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (+.f32 (/.f32 (.f32 1/2 (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 cosTheta_O cosTheta_O))) (pow.f32 v 3)) (.f32 -1/3 (.f32 (.f32 cosTheta_O cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 17) (pow.f32 v 35)) 1/18))))) (cbrt.f32 (/.f32 (.f32 v v) (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 2))))) (+.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v)) (.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18))))))
(fma.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_O cosTheta_O) (pow.f32 v 3)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (.f32 (.f32 -1/3 (.f32 cosTheta_O cosTheta_O)) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18)))) (cbrt.f32 (/.f32 (.f32 v v) (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2))))) (fma.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (*.f32 cosTheta_i cosTheta_O))) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))
(fma.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 cosTheta_i cosTheta_O))) (fma.f32 1/3 (.f32 cosTheta_i (.f32 cosTheta_i (.f32 (fma.f32 (.f32 (.f32 cosTheta_O (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18)) (.f32 cosTheta_O (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18))) -1/3 (/.f32 (.f32 (.f32 1/2 (.f32 cosTheta_O cosTheta_O)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 v 3))) (cbrt.f32 (*.f32 (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2)) v))))) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))
(fma.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 7) (pow.f32 v 16)) 1/18) (.f32 cosTheta_i cosTheta_O))) (fma.f32 1/3 (.f32 cosTheta_i (.f32 cosTheta_i (.f32 (fma.f32 (.f32 (.f32 cosTheta_O (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18)) (.f32 cosTheta_O (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 17) (pow.f32 v 35)) 1/18))) -1/3 (/.f32 (.f32 (.f32 1/2 (.f32 cosTheta_O cosTheta_O)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 v 3))) (cbrt.f32 (*.f32 (/.f32 v (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 -1 v)))) v))))) (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))
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(+.f32 (/.f32 cosTheta_i (/.f32 v (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O))) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 cosTheta_O cosTheta_O))) (.f32 v v)) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O)) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 cosTheta_O cosTheta_O))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(fma.f32 1/2 (.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (.f32 cosTheta_O cosTheta_O)) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(+.f32 (/.f32 cosTheta_i (/.f32 v (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (pow.f32 cosTheta_O 3)))) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(+.f32 (.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 cosTheta_O cosTheta_O))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (pow.f32 cosTheta_O 3))) (fma.f32 1/2 (.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (.f32 cosTheta_O cosTheta_O)) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 cosTheta_i (/.f32 v (*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O))))
(+.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O)))
(fma.f32 (/.f32 cosTheta_i v) (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (/.f32 cosTheta_i (/.f32 v (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O))) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 cosTheta_O cosTheta_O))) (.f32 v v)) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O)) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 cosTheta_O cosTheta_O))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(fma.f32 1/2 (.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (.f32 cosTheta_O cosTheta_O)) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(+.f32 (/.f32 cosTheta_i (/.f32 v (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (pow.f32 cosTheta_O 3)))) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(+.f32 (.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (*.f32 cosTheta_O cosTheta_O))) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (pow.f32 cosTheta_O 3))) (fma.f32 1/2 (.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (.f32 cosTheta_O cosTheta_O)) (/.f32 (.f32 cosTheta_i cosTheta_i) (.f32 v v))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) cosTheta_O) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.f32 (exp.f32 6931/10000) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (/.f32 v (exp.f32 6931/10000))))
(+.f32 (exp.f32 6931/10000) (*.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000)))
(fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (exp.f32 6931/10000))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000)))
(fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (*.f32 v v) (exp.f32 6931/10000))) (+.f32 (exp.f32 6931/10000) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (/.f32 v (exp.f32 6931/10000)))))
(+.f32 (exp.f32 6931/10000) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v)) (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000))))
(fma.f32 1/2 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (exp.f32 6931/10000)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (exp.f32 6931/10000))))
(fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (*.f32 v v) (exp.f32 6931/10000))) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (/.f32 v (exp.f32 6931/10000))) (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (exp.f32 6931/10000))))
(+.f32 (fma.f32 1/6 (/.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 v 3) (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3))) (exp.f32 6931/10000)) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v)) (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000))))
(fma.f32 1/2 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (fma.f32 1/6 (/.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 v 3) (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3))) (fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (exp.f32 6931/10000))))
(exp.f32 6931/10000)
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (exp.f32 6931/10000))
(fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta_i cosTheta_O))) (/.f32 v (exp.f32 6931/10000))) (exp.f32 6931/10000))
(-.f32 (exp.f32 6931/10000) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (exp.f32 6931/10000)))
(fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) (/.f32 v (exp.f32 6931/10000))) (fma.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) 2) (/.f32 (*.f32 v v) (exp.f32 6931/10000))) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) v)) (exp.f32 6931/10000)) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (exp.f32 6931/10000)) (.f32 (/.f32 (-.f32 1 (*.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (exp.f32 6931/10000)) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (exp.f32 6931/10000))))
(fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) (/.f32 v (exp.f32 6931/10000))) (fma.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) 2) (/.f32 (.f32 v v) (exp.f32 6931/10000))) (fma.f32 -1/6 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (exp.f32 6931/10000))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) v)) (fma.f32 -1/6 (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3) (pow.f32 v 3)) (exp.f32 6931/10000)) (exp.f32 6931/10000))) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (fma.f32 -1/6 (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3) (pow.f32 v 3)) (exp.f32 6931/10000)) (exp.f32 6931/10000))) (.f32 (/.f32 (-.f32 1 (*.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (exp.f32 6931/10000) (.f32 v v))) (fma.f32 -1/6 (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3) (pow.f32 v 3)) (exp.f32 6931/10000)) (exp.f32 6931/10000))) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))

localize93.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
✓	0.0b	(+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)
✓	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))
✓	0.5b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))

Compiler

Compiled 117 to 68 computations (41.9% saved)

series102.0ms (0.5%)

Counts

4 → 216

Calls

60 calls:

Time	Variable		Point	Expression
25.0ms	sinTheta_O	@	0	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
7.0ms	v	@	-inf	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
6.0ms	sinTheta_i	@	0	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
6.0ms	cosTheta_O	@	0	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
5.0ms	v	@	inf	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)

rewrite108.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

887×	`log-prod_binary32`
347×	`expm1-udef_binary32`
347×	`log1p-udef_binary32`
290×	`log-pow_binary32`
204×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	86
1	433	80
2	5076	80

Stop Event

1×	node limit

Counts

4 → 160

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))) (cbrt.f32 (exp.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))) (log.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))) (log.f32 (sqrt.f32 (exp.f32 (cbrt.f32 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v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) (cbrt.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (log.f32 (cbrt.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (log.f32 (sqrt.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 6931/10000) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 1 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (exp.f32 2/3) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (pow.f32 (exp.f32 1/3) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1/2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (pow.f32 (exp.f32 1/2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) -6931/10000)) (/.f32 48038761/100000000 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) -6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 3 (.f32 1/3 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (log.f32 (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 2) (cbrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 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6931/10000)) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1/2 (sqrt.f32 v)) (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1/2 v) (cbrt.f32 (pow.f32 (exp.f32 2) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) (cbrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1/2 v) (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) (sqrt.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (cbrt.f32 (/.f32 1/4 (.f32 v v)))) (cbrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (sqrt.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 2)) 1) (cbrt.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 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v) 6931/10000)) v)) 1/6)) (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (/.f32 v (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) (.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (.f32 1/2 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 1/2 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (.f32 1/2 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i 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v))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) 3) (pow.f32 (/.f32 1/2 v) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 1/2 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v))) 1))))))

simplify315.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

713×	`associate-l_binary32`
575×	`*-commutative_binary32`
531×	`fma-def_binary32`
314×	`unswap-sqr_binary32`
301×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	562	21375
1	1961	19068
2	7049	18090

Stop Event

1×	node limit

Counts

376 → 260

Calls

Call 1

Inputs
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))) (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)))
(+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) 1/3)))))
(+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) (+.f32 (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (cbrt.f32 1/2) (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2)))))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) 1/3))) (.f32 1/3 (.f32 (.f32 (-.f32 (.f32 1/6 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) (pow.f32 cosTheta_O 3)) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9) (.f32 cosTheta_O (-.f32 (.f32 1/2 (/.f32 (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) (pow.f32 cosTheta_O 2)) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9) (pow.f32 cosTheta_O 2))))))) (.f32 1/27 (.f32 (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/3) (pow.f32 cosTheta_O 3))))) (.f32 (pow.f32 cosTheta_i 3) (cbrt.f32 1/2))) (pow.f32 (/.f32 (.f32 (pow.f32 v 2) 1) (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 2)) 1/3))))))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) 1) v) 1/3) (cbrt.f32 1/2))
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
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(.f32 1/2 (.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) (pow.f32 1 1/3)))
(+.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) (pow.f32 1 1/3))) (.f32 (+.f32 (.f32 1/6 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9))) (.f32 1/3 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9)))) sinTheta_O))
(+.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) (pow.f32 1 1/3))) (+.f32 (.f32 (+.f32 (.f32 1/6 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9))) (.f32 1/3 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9)))) sinTheta_O) (.f32 (+.f32 (.f32 1/9 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9))) (+.f32 (.f32 1/6 (.f32 (pow.f32 1 1/3) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))) (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (.f32 (+.f32 (.f32 1/9 (.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (cbrt.f32 1/2) 2)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 14)) (pow.f32 v 32)) 1/9))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 v 1) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) 1/3) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))))) (cbrt.f32 1/2))))) (pow.f32 sinTheta_O 2))))
(+.f32 (.f32 1/2 (.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v) (pow.f32 1 1/3))) (+.f32 (.f32 (+.f32 (.f32 1/6 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9))) (.f32 1/3 (.f32 sinTheta_i (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 13)) (pow.f32 v 22)) 1/9)))) sinTheta_O) (+.f32 (.f32 (+.f32 (.f32 1/9 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9))) (+.f32 (.f32 1/6 (.f32 (pow.f32 1 1/3) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))) (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (.f32 (+.f32 (.f32 1/9 (.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (cbrt.f32 1/2) 2)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 14)) (pow.f32 v 32)) 1/9))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 v 1) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) 1/3) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))))) (cbrt.f32 1/2))))) (pow.f32 sinTheta_O 2)) (.f32 (pow.f32 sinTheta_O 3) (+.f32 (.f32 1/9 (.f32 (.f32 sinTheta_i (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9))))) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9))) (+.f32 (.f32 1/3 (.f32 (.f32 sinTheta_i (.f32 (+.f32 (.f32 1/9 (.f32 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (cbrt.f32 1/2) 2)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 14)) (pow.f32 v 32)) 1/9))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (.f32 v 1) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) 1/3) (.f32 (pow.f32 (cbrt.f32 1/2) 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))))) (cbrt.f32 1/2))) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))) (+.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (.f32 (cbrt.f32 1/2) (+.f32 (.f32 2/9 (.f32 (.f32 sinTheta_i (.f32 (pow.f32 (cbrt.f32 1/2) 2) (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9)))))) (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 10)) 1/9))) (.f32 2/3 (.f32 (.f32 (-.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (.f32 sinTheta_i (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9))))) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9))) (.f32 1/27 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/3))))) (pow.f32 (cbrt.f32 1/2) 2)) (pow.f32 (/.f32 (.f32 v 1) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) 1/3)))))) (.f32 1/6 (.f32 (-.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 4))) (+.f32 (.f32 2/3 (.f32 (.f32 sinTheta_i (-.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) (pow.f32 v 3))) (.f32 1/3 (.f32 (pow.f32 sinTheta_i 2) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 17)) (pow.f32 v 35)) 1/9))))) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 4)) (pow.f32 v 13)) 1/9))) (.f32 1/27 (.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/3))))) (pow.f32 1 1/3))))))))))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))

Outputs
(.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2))
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 1 v))) v)) (cbrt.f32 1/2))
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 -1 v)))) v)) (cbrt.f32 1/2))
(*.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v)))) v)) (cbrt.f32 1/2))
(+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (pow.f32 (/.f32 (.f32 1 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))) 7)) (pow.f32 v 16)) 1/9))) (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 (.f32 cosTheta_i (.f32 (cbrt.f32 1/2) cosTheta_O)) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 1 v))) 7) (pow.f32 v 16)) 1/18))) (*.f32 (cbrt.f32 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 sinTheta_i (/.f32 v sinTheta_O))) (/.f32 1 v))) v)) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 1/2) cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 -1 v)))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 -1 v)))) 7) (pow.f32 v 16)) 1/18)))) (*.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (/.f32 -1 v)))) v)) (cbrt.f32 1/2)))
(fma.f32 1/3 (.f32 cosTheta_i (.f32 (.f32 (cbrt.f32 1/2) cosTheta_O) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v)))) 7) (pow.f32 v 16)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v)))) 7) (pow.f32 v 16)) 1/18)))) (*.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 -1 v)))) v)) (cbrt.f32 1/2)))
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(.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v))))) (.f32 (.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18))) -1/3)) (.f32 sinTheta_i (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 4) (pow.f32 v 13)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 4) (pow.f32 v 13)) 1/18)))) (.f32 1/27 (.f32 (pow.f32 sinTheta_i 3) (cbrt.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 7) (pow.f32 v 16))))))))))) (.f32 sinTheta_O (.f32 sinTheta_O (fma.f32 1/9 (.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18))) (fma.f32 1/6 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v))))) (.f32 (.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18))) -1/3)) (.f32 (cbrt.f32 1/2) (.f32 (cbrt.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) v)) (fma.f32 1/9 (.f32 (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 14) (pow.f32 v 32)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 14) (pow.f32 v 32)) 1/18)) (.f32 sinTheta_i (.f32 sinTheta_i (pow.f32 (cbrt.f32 1/2) 2)))) (.f32 (.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v))))) (.f32 (.f32 (.f32 sinTheta_i sinTheta_i) (.f32 (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18) (pow.f32 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 17) (pow.f32 v 35)) 1/18))) -1/3)) (pow.f32 (cbrt.f32 1/2) 2)) (.f32 2/3 (cbrt.f32 (/.f32 v (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v))))))))))))))))))
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)
(.f32 1/2 (.f32 (/.f32 (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)) v) (pow.f32 1 1/3)))
(*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v))) v))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 sinTheta_i sinTheta_O (fma.f32 cosTheta_i cosTheta_O -1)) v))) 1/2) v)

eval2.6s (12.3%)

Compiler: Compiled 67331 to 47082 computations (30.1% saved)

prune186.0ms (0.9%)

Pruning

20 alts after pruning (16 fresh and 4 done)

	Pruned	Kept	Total
New	961	11	972
Fresh	12	5	17
Picked	1	0	1
Done	2	4	6
Total	976	20	996

Error

0.0b

Counts

996 → 20

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))
✓	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	28.0b	(exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
	0.1b	(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
	28.0b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	29.0b	(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
	0.8b	(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
	0.2b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (/.f32 (-.f32 (pow.f32 v -2) 48038761/100000000) (-.f32 (/.f32 -1 v) 6931/10000))))
	30.6b	(+.f32 (/.f32 1/2 v) (.f32 (/.f32 1/2 v) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 3)
	3.0b	(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (/.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (exp.f32 (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
	0.4b	(.f32 (/.f32 1/2 v) (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3))))
✓	30.5b	(/.f32 1/2 v)
✓	0.1b	(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
	0.2b	(*.f32 (/.f32 1/2 v) (sqrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 -1 v)))))
✓	30.6b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
	0.2b	(pow.f32 (E.f32) (fma.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 1 (+.f32 6931/10000 (/.f32 1 v))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
	0.1b	(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))

Compiler

Compiled 402 to 332 computations (17.4% saved)

regimes263.0ms (1.3%)

Counts

56 → 1

Calls

Call 1

Inputs
(/.f32 1/2 v)
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (/.f32 1/2 v) (.f32 (/.f32 1/2 v) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
(exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (/.f32 1/2 v) (cbrt.f32 (exp.f32 (.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3))))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(*.f32 (/.f32 1/2 v) (sqrt.f32 (pow.f32 (exp.f32 2) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)
(*.f32 (/.f32 1/2 v) (pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2))
(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)))) 3)
(*.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) (/.f32 (-.f32 (pow.f32 v -2) 48038761/100000000) (-.f32 (/.f32 -1 v) 6931/10000))))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))
(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 3)
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (exp.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000)))) 3)
(pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 6931/10000))) 3) 1/3)
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 1) (.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (exp.f32 1) (.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 1) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (pow.f32 (exp.f32 1) (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))))
(pow.f32 (sqrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2)
(.f32 (pow.f32 (E.f32) (/.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(.f32 (pow.f32 (exp.f32 (+.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O -1))) (/.f32 1 v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 3)
(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (/.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (exp.f32 (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
(pow.f32 (E.f32) (fma.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 1 (+.f32 6931/10000 (/.f32 1 v))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 2) (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))))
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (cbrt.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 3)
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (exp.f32 (.f32 (.f32 2/3 (+.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000) (log.f32 (/.f32 1/2 v)))) 1/6))) 3)
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000)))))) 3)

Outputs

(pow.f32 (*.f32 (pow.f32 (pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)

Calls

11 calls:

27.0ms	sinTheta_O
26.0ms	sinTheta_i
26.0ms	cosTheta_O
25.0ms	cosTheta_i
23.0ms	(*.f32 cosTheta_i cosTheta_O)

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 1203 to 846 computations (29.7% saved)

regimes205.0ms (1%)

Counts

50 → 1

Calls

Call 1

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

Outputs
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))

Calls

9 calls:

34.0ms	sinTheta_O
24.0ms	sinTheta_i
23.0ms	cosTheta_i
23.0ms	cosTheta_O
19.0ms	v

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 932 to 659 computations (29.3% saved)

regimes172.0ms (0.8%)

Counts

38 → 1

Calls

Call 1

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

Outputs
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))

Calls

9 calls:

46.0ms	cosTheta_i
20.0ms	sinTheta_O
17.0ms	sinTheta_i
16.0ms	cosTheta_O
13.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 644 to 446 computations (30.7% saved)

regimes204.0ms (1%)

Counts

32 → 1

Calls

Call 1

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

Outputs
(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)

Calls

9 calls:

67.0ms	cosTheta_i
38.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
18.0ms	sinTheta_i
17.0ms	cosTheta_O
15.0ms	sinTheta_O

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 520 to 370 computations (28.8% saved)

regimes281.0ms (1.4%)

Counts

28 → 1

Calls

Call 1

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

Outputs
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)

Calls

9 calls:

100.0ms	sinTheta_O
44.0ms	(*.f32 cosTheta_i cosTheta_O)
15.0ms	cosTheta_O
14.0ms	sinTheta_i
13.0ms	cosTheta_i

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 451 to 323 computations (28.4% saved)

regimes167.0ms (0.8%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

9 calls:

51.0ms	(*.f32 cosTheta_i cosTheta_O)
44.0ms	cosTheta_O
11.0ms	sinTheta_i
11.0ms	sinTheta_O
10.0ms	cosTheta_i

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	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)))))`
0.1b	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))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 338 to 241 computations (28.7% saved)

regimes227.0ms (1.1%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

7 calls:

164.0ms	cosTheta_O
25.0ms	(*.f32 sinTheta_i sinTheta_O)
8.0ms	sinTheta_O
7.0ms	sinTheta_i
7.0ms	cosTheta_i

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 166 to 116 computations (30.1% saved)

regimes44.0ms (0.2%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

7 calls:

7.0ms	cosTheta_i
7.0ms	sinTheta_O
6.0ms	sinTheta_i
6.0ms	cosTheta_O
5.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

Error	Segments	Branch
0.8b	1	`cosTheta_i`
0.8b	1	`cosTheta_O`
0.8b	1	`sinTheta_i`
0.8b	1	`sinTheta_O`
0.8b	1	`v`
0.8b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.8b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 129 to 92 computations (28.7% saved)

regimes57.0ms (0.3%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

8 calls:

9.0ms	v
8.0ms	(*.f32 cosTheta_i cosTheta_O)
8.0ms	(*.f32 cosTheta_i cosTheta_O)
7.0ms	cosTheta_i
6.0ms	sinTheta_O

Results

Error	Segments	Branch
28.0b	1	`cosTheta_i`
28.0b	1	`cosTheta_O`
28.0b	1	`sinTheta_i`
28.0b	1	`sinTheta_O`
26.5b	2	`v`
27.0b	2	`(*.f32 cosTheta_i cosTheta_O)`
27.0b	2	`(*.f32 cosTheta_i cosTheta_O)`
28.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 121 to 88 computations (27.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	binary-search

Steps

Time	Left	Right
0.0ms	7.185354021778628e-16	7.228640052361283e-16

Compiler

Compiled 38 to 29 computations (23.7% saved)

regimes104.0ms (0.5%)

Accuracy

Total -1.9b remaining (-6.5%)

Threshold costs -1.9b (-6.5%)

Counts

4 → 1

Calls

Call 1

Inputs
(/.f32 1/2 v)
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(+.f32 (/.f32 1/2 v) (.f32 (/.f32 1/2 v) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))

Outputs
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))

Calls

7 calls:

45.0ms	v
38.0ms	cosTheta_i
4.0ms	sinTheta_i
4.0ms	sinTheta_O
4.0ms	cosTheta_O

Results

Error	Segments	Branch
29.0b	1	`cosTheta_i`
29.0b	1	`cosTheta_O`
29.0b	1	`sinTheta_i`
29.0b	1	`sinTheta_O`
29.0b	1	`v`
29.0b	1	`(*.f32 sinTheta_i sinTheta_O)`
29.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 89 to 66 computations (25.8% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary32`
7×	`+-commutative_binary32`
5×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	8589934766
1	103	8589934766
2	112	8589934766
3	116	8589934766
4	118	8589934766

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(if (<=.f32 v 13600415/18889465931478580854784) (exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(/.f32 1/2 v)

Outputs
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) 6931/10000))) 1/9)) 3)
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/9)) 3)
(pow.f32 (.f32 (pow.f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (+.f32 6931/10000 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 -1 v))))) 2) 1/3) (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v)))) 1/9)) 3)
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (E.f32) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (/.f32 1/2 v) (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))
(.f32 (/.f32 1/2 v) (.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))) 3)
(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 3)
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(if (<=.f32 v 13600415/18889465931478580854784) (exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i))) (*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v)))
(*.f32 sinTheta_O (/.f32 (/.f32 -1/2 (/.f32 v sinTheta_i)) v))
(/.f32 1/2 v)

Compiler

Compiled 228 to 188 computations (17.5% saved)

soundness0.0ms (0%)

end151.0ms (0.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 366 to 281 computations (23.2% saved)