Details

analyze1.1s (7.7%)

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)

sample3.5s (25.5%)

Results

3.4s	8256×	body	256	valid
66.0ms	138×	body	256	invalid

Bogosity

preprocess69.0ms (0.5%)

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)

simplify39.0ms (0.3%)

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

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	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	(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

▶

0.0b

(*.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

(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)

localize117.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	7.5b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series109.0ms (0.8%)

Counts

4 → 120

Calls

48 calls:

Time	Variable		Point	Expression
27.0ms	sinTheta_i	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
11.0ms	cosTheta_i	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
10.0ms	v	@	-inf	(+.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	v	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
3.0ms	v	@	inf	(+.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))))

rewrite131.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

439×	`log1p-udef_binary32`
253×	`add-sqr-sqrt_binary32`
245×	`*-un-lft-identity_binary32`
245×	`pow1_binary32`
236×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	57
1	489	54
2	7721	54

Stop Event

1×	node limit

Counts

4 → 203

Calls

Call 1

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

simplify130.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

594×	`fma-def_binary32`
461×	`associate--l+_binary32`
442×	`distribute-neg-in_binary32`
356×	`sub-neg_binary32`
352×	`unsub-neg_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	2612
1	199	2273
2	563	2043
3	1960	2037
4	5288	2037
5	7205	2037

Stop Event

1×	node limit

Counts

323 → 228

Calls

Call 1

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

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

localize136.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 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)))
✓	0.0b	(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)

series32.0ms (0.2%)

Counts

4 → 156

Calls

48 calls:

Time	Variable		Point	Expression
7.0ms	sinTheta_i	@	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))))
1.0ms	cosTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	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))))
1.0ms	sinTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	sinTheta_O	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite115.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

747×	`log-prod_binary32`
552×	`prod-diff_binary32`
281×	`expm1-udef_binary32`
281×	`log1p-udef_binary32`
277×	`fma-def_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	63
1	314	63
2	4123	63

Stop Event

1×	node limit

Counts

4 → 202

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)))
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))) (log.f32 (sqrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (log.f32 (cbrt.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 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 v cosTheta_O)) 3) 332956652491/1000000000000) (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (-.f32 48038761/100000000 (.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 cosTheta_i (/.f32 v cosTheta_O)) -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 0 (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 (log.f32 (.f32 (cbrt.f32 (exp.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 (exp.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)))))))) (log.f32 (cbrt.f32 (exp.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 (log.f32 (sqrt.f32 (exp.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))))))) (log.f32 (sqrt.f32 (exp.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 (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 (/.f32 sinTheta_O v) (/.f32 1 v))) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (neg.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x 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)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x 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))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (.f32 3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.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))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.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))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.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 (-.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 pow.f32 (exp.f32 (sqrt.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 (-.f32 (fma.f32 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simplify82.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

817×	`associate-/l*_binary32`
641×	`associate-r_binary32`
559×	`associate-l_binary32`
456×	`associate-/r*_binary32`
285×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	3494
1	401	3235
2	1421	2620

Stop Event

1×	node limit

Counts

358 → 255

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

eval316.0ms (2.3%)

Compiler: Compiled 15187 to 8222 computations (45.9% saved)

prune108.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	477	6	483
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	479	6	485

Error

0.0b

Counts

485 → 6

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
▶	0.0b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	0.3b	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
▶	30.6b	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	0.0b	(*.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))
▶	28.4b	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))

Compiler

Compiled 226 to 170 computations (24.8% saved)

localize126.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
✓	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))
	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series9.0ms (0.1%)

Counts

3 → 54

Calls

27 calls:

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

rewrite143.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

702×	`fma-def_binary32`
361×	`fma-neg_binary32`
303×	`expm1-udef_binary32`
303×	`log1p-udef_binary32`
274×	`log-div_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	57
1	343	57
2	5039	51

Stop Event

1×	node limit

Counts

3 → 276

Calls

Call 1

Inputs

(-.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))

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

Outputs

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

simplify223.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

807×	`sub-neg_binary32`
507×	`unsub-neg_binary32`
462×	`fma-def_binary32`
403×	`+-commutative_binary32`
386×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	848
1	119	709
2	305	646
3	878	646
4	2464	646
5	4633	646
6	6144	646
7	6654	646
8	7278	646
9	7417	646
10	7469	646
11	7939	646

Stop Event

1×	node limit

Counts

330 → 302

Calls

Call 1

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

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

localize40.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.4b	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))

Compiler

Compiled 19 to 16 computations (15.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

667×	`pow1_binary32`
624×	`add-log-exp_binary32`
624×	`log1p-expm1-u_binary32`
624×	`expm1-log1p-u_binary32`
613×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	9
2	1697	9

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 6931/10000) (*.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (*.f32 (exp.f32 6931/10000) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 (exp.f32 6931/10000) 1/2)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (exp.f32 6931/10000)) (neg.f32 v))))) (#(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 (exp.f32 6931/10000) (*.f32 v 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (*.f32 (/.f32 1/4 (*.f32 v v)) (exp.f32 6931/5000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (exp.f32 6931/10000) 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 (exp.f32 6931/10000) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (exp.f32 6931/10000) (*.f32 v 2))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
1×	`associate-*r/_binary32`
1×	`associate-*l/_binary32`
1×	`associate-/r/_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	108
1	10	108
2	14	108
3	18	108
4	19	108

Stop Event

1×

saturated

Counts

34 → 23

Calls

Call 1

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

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

localize40.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
✓	0.1b	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
✓	0.2b	(*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))

Compiler

Compiled 41 to 15 computations (63.4% saved)

series54.0ms (0.4%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
41.0ms	sinTheta_i	@	0	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
1.0ms	sinTheta_i	@	0	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
1.0ms	v	@	inf	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	-inf	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
1.0ms	v	@	0	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))

rewrite75.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

559×	`log-prod_binary32`
345×	`pow-prod-down_binary32`
275×	`pow2_binary32`
271×	`pow-unpow_binary32`
196×	`pow1/3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	37
1	235	31
2	3113	31

Stop Event

1×	node limit

Counts

3 → 202

Calls

Call 1

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

Outputs

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

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

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

simplify140.0ms (1%)

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

310 → 222

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 (/.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))))))
(/.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))
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))))))
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)))

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))
(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)
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1
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1
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(-.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))))
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))))
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))))
(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))

localize46.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 sinTheta_i sinTheta_O)
✓	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.0b	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v)
✓	0.0b	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))

Compiler

Compiled 54 to 22 computations (59.3% saved)

series61.0ms (0.4%)

Counts

4 → 72

Calls

42 calls:

Time	Variable		Point	Expression
41.0ms	sinTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
2.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
1.0ms	cosTheta_O	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
1.0ms	cosTheta_O	@	inf	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v)
1.0ms	v	@	-inf	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))

rewrite107.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`log-prod_binary32`
621×	`fma-def_binary32`
315×	`fma-neg_binary32`
260×	`pow1/3_binary32`
254×	`log1p-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	277	38
2	3946	38

Stop Event

1×	node limit

Counts

4 → 128

Calls

Call 1

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

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

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Rules

961×	`times-frac_binary32`
663×	`associate-/l*_binary32`
558×	`fma-neg_binary32`
495×	`associate-r_binary32`
405×	`associate-l_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	2000
1	327	1812
2	1093	1652
3	7138	1640

Stop Event

1×	node limit

Counts

200 → 165

Calls

Call 1

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

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

localize64.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
✓	0.0b	(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))
	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 71 to 36 computations (49.3% saved)

series13.0ms (0.1%)

Counts

3 → 37

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
1.0ms	v	@	-inf	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
1.0ms	cosTheta_i	@	0	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
1.0ms	v	@	inf	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
1.0ms	cosTheta_O	@	0	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))

rewrite114.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

644×	`log-prod_binary32`
452×	`fma-def_binary32`
344×	`pow2_binary32`
279×	`fma-neg_binary32`
238×	`pow1/3_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	44
1	264	38
2	3851	32

Stop Event

1×	node limit

Counts

3 → 266

Calls

Call 1

Inputs

(+.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)))

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

Outputs

((#(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 (/.f32 cosTheta_i v) cosTheta_O))) (/.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2) (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(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 1 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (cbrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.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 (/.f32 cosTheta_i v) cosTheta_O) 3)) (/.f32 1 (fma.f32 (*.f32 (/.f32 cosTheta_i 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 (/.f32 cosTheta_i v) cosTheta_O) 2)) (/.f32 1 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000) (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3)) (fma.f32 (*.f32 (/.f32 cosTheta_i 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 (/.f32 cosTheta_i v) cosTheta_O) 3)) (+.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2) (-.f32 48038761/100000000 (/.f32 6931/10000 (/.f32 v (*.f32 cosTheta_i cosTheta_O))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2)) (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3))) (neg.f32 (fma.f32 (*.f32 (/.f32 cosTheta_i 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 (/.f32 cosTheta_i v) cosTheta_O) 2))) (neg.f32 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i 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 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2) 1/2)))) (#(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> 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simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

697×	`times-frac_binary32`
689×	`distribute-rgt-in_binary32`
487×	`associate-/l*_binary32`
367×	`associate-r_binary32`
322×	`associate-l_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	773
1	242	754
2	843	732
3	5472	640

Stop Event

1×	node limit

Counts

303 → 293

Calls

Call 1

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

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

eval899.0ms (6.5%)

Compiler: Compiled 23782 to 14176 computations (40.4% saved)

prune797.0ms (5.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1086	7	1093
Fresh	1	0	1
Picked	1	0	1
Done	4	0	4
Total	1092	7	1099

Error

0.0b

Counts

1099 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	30.0b	1
	0.0b	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (/.f32 1/2 v))
▶	28.2b	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
▶	0.3b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
▶	0.0b	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
▶	27.9b	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))

Compiler

Compiled 178 to 144 computations (19.1% saved)

localize54.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 46 to 37 computations (19.6% saved)

series60.0ms (0.4%)

Counts

4 → 44

Calls

12 calls:

Time	Variable		Point	Expression
34.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
13.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))
9.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
1.0ms	v	@	0	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
1.0ms	v	@	-inf	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

rewrite122.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`prod-diff_binary32`
487×	`log-prod_binary32`
311×	`fma-def_binary32`
299×	`pow2_binary32`
207×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	47
1	244	47
2	3260	47

Stop Event

1×	node limit

Counts

4 → 295

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (.f32 (/.f32 -1 v) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (/.f32 -1 v) 1 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (neg.f32 (/.f32 1 (cbrt.f32 v))) (cbrt.f32 (pow.f32 v -2)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (+.f32 (/.f32 -1 v) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 -1 (/.f32 1 v) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 -1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (.f32 2 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 1/2 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (.f32 1/2 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 2 (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))) (.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1 (neg.f32 (.f32 (/.f32 -1 v) -1))) (fma.f32 (neg.f32 (/.f32 -1 v)) -1 (.f32 (/.f32 -1 v) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (neg.f32 (.f32 (/.f32 -1 v) -1))) (fma.f32 (neg.f32 (/.f32 -1 v)) -1 (.f32 (/.f32 -1 v) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 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(#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.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) (neg.f32 (.f32 (/.f32 1 (cbrt.f32 v)) (/.f32 1 (pow.f32 (cbrt.f32 v) 2))))) (fma.f32 (neg.f32 (/.f32 1 (cbrt.f32 v))) (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (.f32 (/.f32 1 (cbrt.f32 v)) (/.f32 1 (pow.f32 (cbrt.f32 v) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (neg.f32 (.f32 (/.f32 1 (cbrt.f32 v)) (/.f32 1 (pow.f32 (cbrt.f32 v) 2))))) (fma.f32 (neg.f32 (/.f32 1 (cbrt.f32 v))) (/.f32 1 (pow.f32 (cbrt.f32 v) 2)) (.f32 (/.f32 1 (cbrt.f32 v)) (/.f32 1 (pow.f32 (cbrt.f32 v) 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (neg.f32 (.f32 (/.f32 1 (cbrt.f32 v)) 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(#(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))) 2) 1/2)))) (#(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 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 (/.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))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 6931/10000 (log.f32 (.f32 v 2))) (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) -1)))) (#(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 (pow.f32 (cbrt.f32 (log.f32 1/2)) 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)))))))

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

831×	`fma-def_binary32`
706×	`associate-/r*_binary32`
680×	`associate-*l/_binary32`
438×	`associate-/l/_binary32`
432×	`associate-*r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	59	846
1	151	787
2	466	669
3	2002	631

Stop Event

1×	node limit

Counts

339 → 321

Calls

Call 1

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

localize29.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
✓	0.2b	(*.f32 cosTheta_O (/.f32 cosTheta_i v))

Compiler

Compiled 22 to 8 computations (63.6% saved)

series13.0ms (0.1%)

Counts

2 → 72

Calls

18 calls:

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

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

755×	`pow1_binary32`
695×	`add-log-exp_binary32`
695×	`log1p-expm1-u_binary32`
695×	`expm1-log1p-u_binary32`
678×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	142	16
2	1864	16

Stop Event

1×	node limit

Counts

2 → 49

Calls

Call 1

Inputs
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))

Outputs

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

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

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

832×	`associate-*l/_binary32`
816×	`associate-/l/_binary32`
787×	`associate-*r/_binary32`
732×	`fma-def_binary32`
343×	`times-frac_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	30	784
1	88	784
2	280	756
3	2029	736
4	6967	728
5	7290	728
6	7641	728

Stop Event

1×	node limit

Counts

121 → 59

Calls

Call 1

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

Outputs
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
1
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1)
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(fma.f32 (/.f32 1/2 v) (/.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 v (.f32 cosTheta_i cosTheta_O))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (*.f32 cosTheta_O 1/2)) 1))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 v (/.f32 v cosTheta_O)))) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (pow.f32 cosTheta_O 3)) (pow.f32 v 3))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_i 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (fma.f32 1/2 (.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (.f32 cosTheta_O 1/2)) 1)))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 v (/.f32 v cosTheta_O)))) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
1
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1)
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(fma.f32 (/.f32 1/2 v) (/.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 v (.f32 cosTheta_i cosTheta_O))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (*.f32 cosTheta_O 1/2)) 1))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 v (/.f32 v cosTheta_O)))) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (pow.f32 cosTheta_O 3)) (pow.f32 v 3))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_i 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (fma.f32 1/2 (.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (.f32 cosTheta_O 1/2)) 1)))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 v (/.f32 v cosTheta_O)))) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(pow.f32 (exp.f32 (/.f32 cosTheta_i v)) cosTheta_O)
1
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1)
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(fma.f32 (/.f32 1/2 v) (/.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 v (.f32 cosTheta_i cosTheta_O))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (*.f32 cosTheta_O 1/2)) 1))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 v (/.f32 v cosTheta_O)))) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (pow.f32 cosTheta_O 3)) (pow.f32 v 3))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_i 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (fma.f32 1/2 (.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (.f32 cosTheta_O 1/2)) 1)))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 v (/.f32 v cosTheta_O)))) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1))
1
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) 1)
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1)
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 1)
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))))
(fma.f32 (/.f32 1/2 v) (/.f32 (.f32 cosTheta_i cosTheta_O) (/.f32 v (.f32 cosTheta_i cosTheta_O))) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (*.f32 cosTheta_O 1/2)) 1))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 v (/.f32 v cosTheta_O)))) 1)
(+.f32 1 (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (pow.f32 cosTheta_O 3)) (pow.f32 v 3))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))))
(+.f32 1 (fma.f32 1/2 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (*.f32 cosTheta_O cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_O 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (*.f32 cosTheta_O cosTheta_O) v)) (fma.f32 1/6 (/.f32 (pow.f32 cosTheta_O 3) (/.f32 (pow.f32 v 3) (pow.f32 cosTheta_i 3))) (/.f32 cosTheta_i (/.f32 v cosTheta_O)))))
(+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (fma.f32 1/2 (.f32 (.f32 cosTheta_O (/.f32 cosTheta_i v)) (.f32 cosTheta_O (/.f32 cosTheta_i v))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) (fma.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O (.f32 cosTheta_O 1/2)) 1)))
(fma.f32 cosTheta_O (+.f32 (/.f32 cosTheta_i v) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 v (/.f32 v cosTheta_O)))) (fma.f32 1/6 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 1))

localize28.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 26 to 9 computations (65.4% saved)

localize51.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.0b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

Compiler

Compiled 32 to 16 computations (50% saved)

series15.0ms (0.1%)

Counts

2 → 40

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta_O	@	inf	(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
1.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
1.0ms	v	@	-inf	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
1.0ms	v	@	inf	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
1.0ms	cosTheta_O	@	0	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

rewrite121.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

464×	`log-prod_binary32`
362×	`prod-diff_binary32`
360×	`exp-prod_binary32`
273×	`pow-prod-down_binary32`
239×	`pow2_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	18
1	188	18
2	2504	18

Stop Event

1×	node limit

Counts

2 → 179

Calls

Call 1

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

Outputs

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

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

647×	`unswap-sqr_binary32`
488×	`times-frac_binary32`
331×	`associate-/l*_binary32`
270×	`cancel-sign-sub-inv_binary32`
230×	`associate-r_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	782
1	157	782
2	523	644
3	3428	596
4	5014	580

Stop Event

1×	node limit

Counts

219 → 197

Calls

Call 1

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

Outputs
(exp.f32 (/.f32 -1 v))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (exp.f32 (/.f32 -1 v)))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))))
(fma.f32 (/.f32 cosTheta_i v) (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (exp.f32 (/.f32 -1 v)))
(*.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v)))
(*.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (exp.f32 (/.f32 -1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (/.f32 -1 v))))
(+.f32 (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O)) v)) (exp.f32 (/.f32 -1 v))))
(fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_i))) v)) (exp.f32 (/.f32 -1 v))))
(fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_i))) v)) (*.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v))))
(.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (exp.f32 (/.f32 -1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (fma.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (/.f32 -1 v)))))
(+.f32 (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))) (fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O)) v)) (exp.f32 (/.f32 -1 v)))))
(fma.f32 1/6 (.f32 (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3)) (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_i))) v)) (exp.f32 (/.f32 -1 v)))))
(+.f32 (.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v))) (.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3)))))
(fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 (/.f32 v cosTheta_O) 3)) (exp.f32 (/.f32 -1 v))) (.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O))))))
(exp.f32 (/.f32 -1 v))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (exp.f32 (/.f32 -1 v)))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v))
(+.f32 (exp.f32 (/.f32 -1 v)) (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))))
(fma.f32 (/.f32 cosTheta_i v) (*.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (exp.f32 (/.f32 -1 v)))
(*.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v)))
(*.f32 (exp.f32 (/.f32 -1 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (exp.f32 (/.f32 -1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (/.f32 -1 v))))
(+.f32 (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O)) v)) (exp.f32 (/.f32 -1 v))))
(fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_i))) v)) (exp.f32 (/.f32 -1 v))))
(fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (.f32 cosTheta_i cosTheta_i))) v)) (*.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v))))
(.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (exp.f32 (/.f32 -1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O)) v) (fma.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (pow.f32 v 3)) (fma.f32 1/2 (/.f32 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O))) (*.f32 v v)) (exp.f32 (/.f32 -1 v)))))
(+.f32 (/.f32 cosTheta_i (/.f32 (/.f32 v cosTheta_O) (exp.f32 (/.f32 -1 v)))) (fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3))) (fma.f32 1/2 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) v) (/.f32 (.f32 (exp.f32 (/.f32 -1 v)) (.f32 cosTheta_O cosTheta_O)) v)) (exp.f32 (/.f32 -1 v)))))
(fma.f32 1/6 (.f32 (.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 cosTheta_O 3)) (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3))) (fma.f32 (/.f32 cosTheta_i v) (.f32 (exp.f32 (/.f32 -1 v)) cosTheta_O) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 (/.f32 -1 v)) v) (/.f32 (.f32 cosTheta_O (.f32 cosTheta_O (*.f32 cosTheta_i cosTheta_i))) v)) (exp.f32 (/.f32 -1 v)))))
(+.f32 (.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (exp.f32 (/.f32 -1 v))) (.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O))) (/.f32 (.f32 1/6 (pow.f32 cosTheta_i 3)) (pow.f32 (/.f32 v cosTheta_O) 3)))))
(fma.f32 1/6 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 (/.f32 v cosTheta_O) 3)) (exp.f32 (/.f32 -1 v))) (.f32 (exp.f32 (/.f32 -1 v)) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 1) (/.f32 (.f32 cosTheta_i (.f32 cosTheta_i 1/2)) (*.f32 (/.f32 v cosTheta_O) (/.f32 v cosTheta_O))))))
1
(-.f32 (+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 1 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v)))
(+.f32 1 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v)) (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(+.f32 1 (+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 -1 v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(+.f32 1 (.f32 (+.f32 (/.f32 (.f32 1/2 (fma.f32 cosTheta_i cosTheta_O -1)) v) 1) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(-.f32 (+.f32 (.f32 1/6 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 3) (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) (/.f32 1 v))
(-.f32 (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (pow.f32 v 3)) (+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v)) (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (/.f32 1 v))
(+.f32 (+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (pow.f32 v 3)) 1)) (/.f32 -1 v))
(+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 3) 1))
(+.f32 (.f32 (+.f32 (/.f32 (.f32 1/2 (fma.f32 cosTheta_i cosTheta_O -1)) v) 1) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 3) 1))
1
(-.f32 (+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 1 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v)))
(+.f32 1 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(-.f32 (+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v)) (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
(+.f32 1 (+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 -1 v)))
(+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(+.f32 1 (.f32 (+.f32 (/.f32 (.f32 1/2 (fma.f32 cosTheta_i cosTheta_O -1)) v) 1) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(-.f32 (+.f32 (.f32 1/6 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 3) (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/2 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))) (/.f32 1 v))
(-.f32 (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (pow.f32 v 3)) (+.f32 1 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v)) (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (/.f32 1 v))
(+.f32 (+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (pow.f32 v 3)) 1)) (/.f32 -1 v))
(+.f32 (fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (*.f32 v v)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 3) 1))
(+.f32 (.f32 (+.f32 (/.f32 (.f32 1/2 (fma.f32 cosTheta_i cosTheta_O -1)) v) 1) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (fma.f32 1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 3) 1))
(/.f32 -1 v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(/.f32 -1 v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_O (/.f32 cosTheta_i v))
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (/.f32 1 v))
(+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 -1 v))
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)

localize94.0ms (0.7%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 36 to 29 computations (19.4% saved)

series4.0ms (0%)

Counts

3 → 23

Calls

9 calls:

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

rewrite98.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

443×	`log-prod_binary32`
350×	`exp-prod_binary32`
285×	`prod-exp_binary32`
258×	`pow2_binary32`
255×	`pow-prod-down_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	216	31
2	2656	31

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

Outputs

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

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	432
1	119	426
2	282	376
3	780	350
4	2941	350
5	6578	346

Stop Event

1×	node limit

Counts

177 → 173

Calls

Call 1

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

eval478.0ms (3.5%)

Compiler: Compiled 16671 to 11648 computations (30.1% saved)

prune212.0ms (1.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	939	9	948
Fresh	2	0	2
Picked	0	1	1
Done	3	1	4
Total	944	11	955

Error

0.0b

Counts

955 → 11

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(*.f32 (pow.f32 (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))) (pow.f32 (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (/.f32 1/2 v))
▶	0.0b	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
	0.0b	(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)))))
✓	0.0b	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	30.0b	(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
▶	0.0b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))))) 3)
▶	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
▶	0.3b	(exp.f32 (/.f32 -1 v))
	30.0b	1
	0.3b	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 337 to 291 computations (13.6% saved)

localize93.0ms (0.7%)

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 6931/10000 (/.f32 1 v))))) 3)
✓	0.0b	(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))
	0.0b	(-.f32 6931/10000 (/.f32 1 v))
✓	1.0b	(cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))))

Compiler

Compiled 66 to 51 computations (22.7% saved)

series16.0ms (0.1%)

Counts

3 → 12

Calls

9 calls:

Time	Variable		Point	Expression
4.0ms	v	@	inf	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))))) 3)
3.0ms	v	@	inf	(cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))))
3.0ms	v	@	-inf	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))))) 3)
1.0ms	v	@	-inf	(cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))))
1.0ms	v	@	0	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))))) 3)

rewrite84.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`log-prod_binary32`
358×	`pow-prod-down_binary32`
330×	`pow2_binary32`
299×	`pow-unpow_binary32`
246×	`pow-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	313	41
2	3494	41

Stop Event

1×	node limit

Counts

3 → 116

Calls

Call 1

Inputs

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

(pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v)))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (cbrt.f32 (*.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 (exp.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))) (log.f32 (sqrt.f32 (exp.f32 (cbrt.f32 (*.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 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))) (cbrt.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))) (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (cbrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 1/2 v)) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 1/3) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (cbrt.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 2) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 3) 1/9)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (cbrt.f32 (*.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 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 1/3 (-.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))) 1/3))))) (#(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)))) 1))))))

((#(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)))) (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 (exp.f32 6931/10000) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (pow.f32 (E.f32) (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (pow.f32 (E.f32) (*.f32 (/.f32 -1 v) 1)))))) (#(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 1 (+.f32 6931/10000 (/.f32 -1 v))) (exp.f32 (+.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))) (pow.f32 (exp.f32 1/3) (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (E.f32) (/.f32 -1 v)) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (E.f32) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))) (pow.f32 (exp.f32 1/3) (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (exp.f32 (/.f32 1 v)) (exp.f32 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 (neg.f32 (exp.f32 6931/10000)) (neg.f32 (exp.f32 (/.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 332956652491/1000000000000 (+.f32 48038761/100000000 (+.f32 (pow.f32 v -2) (/.f32 6931/10000 v))))) (pow.f32 (E.f32) (/.f32 (pow.f32 v -3) (+.f32 48038761/100000000 (+.f32 (pow.f32 v -2) (/.f32 6931/10000 v))))))))) (#(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 (+.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 (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 +.f32 0 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (*.f32 (/.f32 1 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))) (*.f32 (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))) (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2)) (*.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 1/2 v)) (*.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) (sqrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6) (*.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6) (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 1/2 v)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (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)))) (*.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 (pow.f32 (cbrt.f32 v) 2)) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 (sqrt.f32 v)) (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (sqrt.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1/2 v) (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 (*.f32 (/.f32 1/2 v) (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 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) (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 (+.f32 6931/10000 (/.f32 -1 v))) (sqrt.f32 (/.f32 1/2 v))) (sqrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))) 1) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))) (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))) 2) (cbrt.f32 (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))) (cbrt.f32 (/.f32 1/2 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (exp.f32 (*.f32 2/3 (-.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (*.f32 v 2))))) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6)) (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6))))) (#(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 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))))))) (#(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 (exp.f32 6931/10000) (*.f32 (*.f32 v 2) (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 1/2 (exp.f32 6931/10000)) (*.f32 v (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 -1/2 (exp.f32 6931/10000)) (*.f32 (neg.f32 v) (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) 1/2) (*.f32 (exp.f32 (/.f32 1 v)) v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) 1) (*.f32 (exp.f32 (/.f32 1 v)) (*.f32 v 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (exp.f32 6931/10000) -1/2) (*.f32 (exp.f32 (/.f32 1 v)) (neg.f32 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 1/2 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (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 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 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 sqrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 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))))))

simplify51.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

896×	`fma-neg_binary32`
885×	`distribute-neg-frac_binary32`
536×	`unswap-sqr_binary32`
531×	`times-frac_binary32`
417×	`associate-/r*_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	27	186
1	71	180
2	158	166
3	398	158
4	1287	154
5	5760	154

Stop Event

1×	node limit

Counts

128 → 124

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))))

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)))
(+.f32 (exp.f32 6931/10000) (.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 -1 (+.f32 (/.f32 1/2 v) (/.f32 -1/6 (.f32 v v))))))
(fma.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 -1 (+.f32 (/.f32 1/2 v) (/.f32 -1/6 (*.f32 v v)))) (exp.f32 6931/10000))
(fma.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 (/.f32 -1/6 (*.f32 v v)) (+.f32 -1 (/.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)))
(+.f32 (exp.f32 6931/10000) (.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 -1 (+.f32 (/.f32 1/2 v) (/.f32 -1/6 (.f32 v v))))))
(fma.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 -1 (+.f32 (/.f32 1/2 v) (/.f32 -1/6 (*.f32 v v)))) (exp.f32 6931/10000))
(fma.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 (/.f32 -1/6 (*.f32 v v)) (+.f32 -1 (/.f32 1/2 v))) (exp.f32 6931/10000))

localize75.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 24 to 10 computations (58.3% saved)

series3.0ms (0%)

Counts

1 → 9

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	cosTheta_i	@	0	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_i	@	inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_i	@	-inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_O	@	-inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_O	@	inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

rewrite60.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

950×	`pow1_binary32`
883×	`add-log-exp_binary32`
883×	`log1p-expm1-u_binary32`
883×	`expm1-log1p-u_binary32`
865×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	168	10
2	2329	10

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`
2×	`associate-/l*_binary32`
2×	`associate-/r/_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	39
1	12	39
2	16	39
3	19	39
4	20	39

Stop Event

1×

saturated

Counts

40 → 34

Calls

Call 1

Inputs
1
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
1
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
1
1

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

localize46.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 14 to 11 computations (21.4% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	v	@	inf	(exp.f32 (/.f32 -1 v))
0.0ms	v	@	-inf	(exp.f32 (/.f32 -1 v))
0.0ms	v	@	0	(exp.f32 (/.f32 -1 v))

rewrite39.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

430×	`pow1_binary32`
414×	`add-sqr-sqrt_binary32`
408×	`*-un-lft-identity_binary32`
394×	`add-log-exp_binary32`
394×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	96	6
2	1096	6

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

725×	`distribute-neg-frac_binary32`
593×	`associate-/r/_binary32`
536×	`unswap-sqr_binary32`
439×	`associate-/r*_binary32`
289×	`times-frac_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	98
1	52	98
2	123	98
3	309	98
4	980	98
5	4124	98

Stop Event

1×	node limit

Counts

31 → 30

Calls

Call 1

Inputs
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 (*.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (/.f32 1 v))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
1
(-.f32 1 (/.f32 1 v))
(-.f32 (+.f32 (*.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (/.f32 1 v))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))

Outputs
1
(-.f32 1 (/.f32 1 v))
(+.f32 1 (/.f32 -1 v))
(-.f32 (+.f32 (*.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (/.f32 1 v))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (/.f32 1 v)))
(+.f32 (-.f32 1 (/.f32 1 v)) (/.f32 (/.f32 1/2 v) v))
(+.f32 (-.f32 1 (/.f32 1 v)) (/.f32 1/2 (*.f32 v v)))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 -1 v)))
(-.f32 (-.f32 1 (/.f32 1 v)) (/.f32 -1/2 (*.f32 v v)))
(+.f32 1 (-.f32 (/.f32 -1 v) (/.f32 -1/2 (*.f32 v v))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(+.f32 1 (-.f32 (/.f32 (/.f32 1/2 v) v) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (+.f32 (/.f32 -1 v) (/.f32 -1/6 (pow.f32 v 3)))))
(+.f32 1 (-.f32 (/.f32 -1/6 (pow.f32 v 3)) (-.f32 (/.f32 1 v) (/.f32 1/2 (*.f32 v v)))))
(+.f32 (+.f32 1 (/.f32 -1 v)) (*.f32 (/.f32 (/.f32 1 v) v) (+.f32 1/2 (/.f32 -1/6 v))))
1
(-.f32 1 (/.f32 1 v))
(+.f32 1 (/.f32 -1 v))
(-.f32 (+.f32 (*.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (/.f32 1 v))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (/.f32 1 v)))
(+.f32 (-.f32 1 (/.f32 1 v)) (/.f32 (/.f32 1/2 v) v))
(+.f32 (-.f32 1 (/.f32 1 v)) (/.f32 1/2 (*.f32 v v)))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 -1 v)))
(-.f32 (-.f32 1 (/.f32 1 v)) (/.f32 -1/2 (*.f32 v v)))
(+.f32 1 (-.f32 (/.f32 -1 v) (/.f32 -1/2 (*.f32 v v))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (pow.f32 v 2))) 1) (+.f32 (.f32 1/6 (/.f32 1 (pow.f32 v 3))) (/.f32 1 v)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(+.f32 1 (-.f32 (/.f32 (/.f32 1/2 v) v) (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (+.f32 (/.f32 -1 v) (/.f32 -1/6 (pow.f32 v 3)))))
(+.f32 1 (-.f32 (/.f32 -1/6 (pow.f32 v 3)) (-.f32 (/.f32 1 v) (/.f32 1/2 (*.f32 v v)))))
(+.f32 (+.f32 1 (/.f32 -1 v)) (*.f32 (/.f32 (/.f32 1 v) v) (+.f32 1/2 (/.f32 -1/6 v))))

localize48.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 39 to 30 computations (23.1% saved)

series6.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
3.0ms	v	@	-inf	(+.f32 6931/10000 (/.f32 -1 v))
1.0ms	v	@	0	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
0.0ms	v	@	inf	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
0.0ms	v	@	inf	(pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v)))
0.0ms	v	@	-inf	(pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v)))

rewrite84.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

503×	`log-prod_binary32`
301×	`pow2_binary32`
299×	`pow-prod-down_binary32`
263×	`pow-unpow_binary32`
214×	`pow-pow_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	248	31
2	3097	31

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

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

Outputs

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

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	45	531
1	119	525
2	282	475
3	779	449
4	2945	449
5	6584	445

Stop Event

1×	node limit

Counts

140 → 126

Calls

Call 1

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

localize133.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)
✓	0.3b	(cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))
✓	0.4b	(pow.f32 (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2)
✓	15.4b	(cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))

Compiler

Compiled 144 to 125 computations (13.2% saved)

series35.0ms (0.3%)

Counts

4 → 40

Calls

12 calls:

Time	Variable		Point	Expression
23.0ms	v	@	inf	(pow.f32 (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2)
3.0ms	v	@	inf	(cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))
2.0ms	v	@	-inf	(cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))
2.0ms	v	@	inf	(cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2))
1.0ms	v	@	0	(pow.f32 (cbrt.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2)

rewrite86.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

431×	`log-prod_binary32`
370×	`prod-exp_binary32`
334×	`exp-prod_binary32`
266×	`pow2_binary32`
251×	`pow-prod-down_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	250	45
2	2794	44

Stop Event

1×	node limit

Counts

4 → 209

Calls

Call 1

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

Outputs
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simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

818×	`fma-def_binary32`
687×	`times-frac_binary32`
539×	`associate-l_binary32`
508×	`associate-r_binary32`
397×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	158	1501
1	496	1276
2	1626	1131

Stop Event

1×	node limit

Counts

249 → 252

Calls

Call 1

Inputs
(cbrt.f32 48038761/100000000)
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (cbrt.f32 48038761/100000000))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2))))))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (+.f32 (.f32 1/3 (/.f32 (-.f32 (.f32 332956652491/3375000000000 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (.f32 -6931/7500 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5)) 1/3) (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3)))))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 3)))) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2)))))))
(cbrt.f32 48038761/100000000)
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (cbrt.f32 48038761/100000000))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2))))))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (+.f32 (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2)))) (.f32 1/3 (/.f32 (+.f32 (.f32 6931/7500 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5)) 1/3) (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))))) (.f32 332956652491/3375000000000 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 3)))))))
(pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2)
(+.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) (.f32 -6931/45000 (.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) v)))
(+.f32 (.f32 (+.f32 (.f32 -48038761/1012500000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2)) (.f32 48038761/8100000000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2))) (pow.f32 v 2)) (+.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) (.f32 -6931/45000 (.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (*.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) v))))
(+.f32 (.f32 (pow.f32 v 3) (+.f32 (.f32 -5660263092347/273375000000000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2)) (.f32 332956652491/91125000000000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2)))) (+.f32 (.f32 (+.f32 (.f32 -48038761/1012500000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2)) (.f32 48038761/8100000000 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2))) (pow.f32 v 2)) (+.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) (.f32 -6931/45000 (.f32 (pow.f32 (exp.f32 (.f32 1/9 (+.f32 (.f32 -1 (log.f32 v)) (log.f32 -1)))) 2) v)))))
(pow.f32 48038761/100000000 1/9)
(+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (pow.f32 48038761/100000000 1/9))
(+.f32 (.f32 -800000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 100000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (pow.f32 48038761/100000000 1/9))))
(+.f32 (.f32 8000000000000/242725399665939 (.f32 (/.f32 1 (pow.f32 v 3)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -800000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 100000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (pow.f32 48038761/100000000 1/9) (.f32 -136000000000000/728176198997817 (.f32 (/.f32 1 (pow.f32 v 3)) (pow.f32 48038761/100000000 1/9))))))))
(pow.f32 48038761/100000000 1/9)
(+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (pow.f32 48038761/100000000 1/9))
(+.f32 (.f32 -800000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 100000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (pow.f32 48038761/100000000 1/9))))
(+.f32 (.f32 -800000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -20000/62379 (.f32 (/.f32 1 v) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 100000000/3891139641 (.f32 (/.f32 1 (pow.f32 v 2)) (pow.f32 48038761/100000000 1/9))) (+.f32 (.f32 -1 (/.f32 (+.f32 (.f32 -8000000000000/242725399665939 (pow.f32 48038761/100000000 1/9)) (*.f32 136000000000000/728176198997817 (pow.f32 48038761/100000000 1/9))) (pow.f32 v 3))) (pow.f32 48038761/100000000 1/9)))))
(cbrt.f32 6931/10000)
(+.f32 (cbrt.f32 6931/10000) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))
(+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v)))))
(+.f32 (.f32 1/3 (/.f32 (-.f32 (.f32 1/27 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) (.f32 2/9 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (pow.f32 1 1/3)))) (.f32 (pow.f32 (cbrt.f32 6931/10000) 2) (pow.f32 v 3)))) (+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (.f32 -1/3 (*.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))))
(cbrt.f32 6931/10000)
(+.f32 (cbrt.f32 6931/10000) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))
(+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v)))))
(+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (+.f32 (.f32 1/3 (/.f32 (+.f32 (.f32 -2/9 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (pow.f32 1 1/3))) (.f32 1/27 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))) (.f32 (pow.f32 (cbrt.f32 6931/10000) 2) (pow.f32 v 3)))) (.f32 -1/3 (*.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))))
(/.f32 1 (pow.f32 v 2))
(-.f32 (/.f32 1 (pow.f32 v 2)) (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
48038761/100000000
(-.f32 48038761/100000000 (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
48038761/100000000
(-.f32 48038761/100000000 (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))

Outputs
(cbrt.f32 48038761/100000000)
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (cbrt.f32 48038761/100000000))
(fma.f32 -6931/15000 (*.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 1 v)) (cbrt.f32 48038761/100000000))
(fma.f32 -6931/15000 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) v) (cbrt.f32 48038761/100000000))
(fma.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 -6931/15000 v) (cbrt.f32 48038761/100000000))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2))))))
(+.f32 (fma.f32 -6931/15000 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 1 v)) (cbrt.f32 48038761/100000000)) (.f32 1/3 (/.f32 (+.f32 1 (.f32 -48038761/75000000 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (*.f32 v v)))))
(fma.f32 -6931/15000 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) v) (fma.f32 1/3 (/.f32 (+.f32 1 (.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000)) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (*.f32 v v))) (cbrt.f32 48038761/100000000)))
(fma.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 -6931/15000 v) (fma.f32 (/.f32 1/3 (pow.f32 (cbrt.f32 48038761/100000000) 2)) (/.f32 (fma.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000 1) (*.f32 v v)) (cbrt.f32 48038761/100000000)))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (+.f32 (.f32 1/3 (/.f32 (-.f32 (.f32 332956652491/3375000000000 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (.f32 -6931/7500 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5)) 1/3) (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3)))))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 3)))) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2)))))))
(+.f32 (fma.f32 -6931/15000 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 1 v)) (cbrt.f32 48038761/100000000)) (.f32 1/3 (+.f32 (/.f32 (+.f32 1 (.f32 -48038761/75000000 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (.f32 v v))) (/.f32 (fma.f32 6931/7500 (.f32 (+.f32 1 (.f32 -48038761/75000000 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))))) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5)))) (/.f32 332956652491/3375000000000 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 3))))))
(fma.f32 -6931/15000 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) v) (fma.f32 1/3 (+.f32 (/.f32 (+.f32 1 (.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000)) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (.f32 v v))) (/.f32 (fma.f32 (.f32 (+.f32 1 (.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5)))) 6931/7500 (/.f32 332956652491/3375000000000 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 3)))) (cbrt.f32 48038761/100000000)))
(+.f32 (fma.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 -6931/15000 v) (cbrt.f32 48038761/100000000)) (.f32 (/.f32 1/3 (pow.f32 (cbrt.f32 48038761/100000000) 2)) (+.f32 (/.f32 (fma.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000 1) (.f32 v v)) (/.f32 (fma.f32 (fma.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000 1) (*.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 5))) 6931/7500) (/.f32 332956652491/3375000000000 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (pow.f32 v 3)))))
(cbrt.f32 48038761/100000000)
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (cbrt.f32 48038761/100000000))
(fma.f32 -6931/15000 (*.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 1 v)) (cbrt.f32 48038761/100000000))
(fma.f32 -6931/15000 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) v) (cbrt.f32 48038761/100000000))
(fma.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 -6931/15000 v) (cbrt.f32 48038761/100000000))
(+.f32 (.f32 -6931/15000 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2)) 1/3) (/.f32 1 v))) (+.f32 (cbrt.f32 48038761/100000000) (.f32 1/3 (/.f32 (-.f32 1 (.f32 48038761/75000000 (pow.f32 (/.f32 1 (cbrt.f32 48038761/100000000)) 1/3))) (*.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (pow.f32 v 2))))))
(+.f32 (fma.f32 -6931/15000 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 1 v)) (cbrt.f32 48038761/100000000)) (.f32 1/3 (/.f32 (+.f32 1 (.f32 -48038761/75000000 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))))) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (*.f32 v v)))))
(fma.f32 -6931/15000 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) v) (fma.f32 1/3 (/.f32 (+.f32 1 (.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000)) (.f32 (pow.f32 (cbrt.f32 48038761/100000000) 2) (*.f32 v v))) (cbrt.f32 48038761/100000000)))
(fma.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 48038761/100000000) 2))) (/.f32 -6931/15000 v) (fma.f32 (/.f32 1/3 (pow.f32 (cbrt.f32 48038761/100000000) 2)) (/.f32 (fma.f32 (cbrt.f32 (/.f32 1 (cbrt.f32 48038761/100000000))) -48038761/75000000 1) (*.f32 v v)) (cbrt.f32 48038761/100000000)))
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(fma.f32 -1/3 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) v) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (*.f32 v v)) (cbrt.f32 6931/10000)))
(+.f32 (.f32 1/3 (/.f32 (-.f32 (.f32 1/27 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) (.f32 2/9 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (pow.f32 1 1/3)))) (.f32 (pow.f32 (cbrt.f32 6931/10000) 2) (pow.f32 v 3)))) (+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (.f32 -1/3 (*.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))))
(fma.f32 1/3 (/.f32 (fma.f32 -2/9 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (/.f32 1/27 (pow.f32 (cbrt.f32 6931/10000) 2))) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (.f32 (/.f32 1 (.f32 v v)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)))) (.f32 -1/3 (*.f32 (/.f32 1 v) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))))))))
(+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (.f32 v v)) (fma.f32 1/3 (/.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) -5/27) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (/.f32 (.f32 -1/3 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))) v))))
(fma.f32 1/3 (/.f32 (/.f32 -5/27 (pow.f32 (cbrt.f32 6931/10000) 2)) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (fma.f32 -1/3 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) v) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (.f32 v v)) (cbrt.f32 6931/10000))))
(cbrt.f32 6931/10000)
(+.f32 (cbrt.f32 6931/10000) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))
(+.f32 (cbrt.f32 6931/10000) (.f32 -1/3 (.f32 (/.f32 1 v) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))))))
(fma.f32 -1/3 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) v) (cbrt.f32 6931/10000))
(+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v)))))
(+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (.f32 (/.f32 1 (.f32 v v)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)))) (.f32 -1/3 (.f32 (/.f32 1 v) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))))))
(+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (.f32 v v)) (/.f32 (.f32 -1/3 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))) v)))
(fma.f32 -1/3 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) v) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (*.f32 v v)) (cbrt.f32 6931/10000)))
(+.f32 (cbrt.f32 6931/10000) (+.f32 (.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)) 1/3) (/.f32 1 (pow.f32 v 2)))) (+.f32 (.f32 1/3 (/.f32 (+.f32 (.f32 -2/9 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (pow.f32 1 1/3))) (.f32 1/27 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))) (.f32 (pow.f32 (cbrt.f32 6931/10000) 2) (pow.f32 v 3)))) (.f32 -1/3 (*.f32 (pow.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) 1/3) (/.f32 1 v))))))
(fma.f32 1/3 (/.f32 (fma.f32 -2/9 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) (/.f32 1/27 (pow.f32 (cbrt.f32 6931/10000) 2))) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (.f32 (/.f32 1 (.f32 v v)) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7)))) (.f32 -1/3 (*.f32 (/.f32 1 v) (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))))))))
(+.f32 (cbrt.f32 6931/10000) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (.f32 v v)) (fma.f32 1/3 (/.f32 (.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)) -5/27) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (/.f32 (.f32 -1/3 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2)))) v))))
(fma.f32 1/3 (/.f32 (/.f32 -5/27 (pow.f32 (cbrt.f32 6931/10000) 2)) (.f32 (pow.f32 v 3) (pow.f32 (cbrt.f32 6931/10000) 2))) (fma.f32 -1/3 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 2))) v) (fma.f32 -1/9 (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (cbrt.f32 6931/10000) 7))) (.f32 v v)) (cbrt.f32 6931/10000))))
(/.f32 1 (pow.f32 v 2))
(/.f32 1 (*.f32 v v))
(-.f32 (/.f32 1 (pow.f32 v 2)) (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v))
(+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))
48038761/100000000
(-.f32 48038761/100000000 (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 48038761/100000000 (/.f32 6931/5000 v))
(+.f32 48038761/100000000 (/.f32 -6931/5000 v))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))
48038761/100000000
(-.f32 48038761/100000000 (*.f32 6931/5000 (/.f32 1 v)))
(-.f32 48038761/100000000 (/.f32 6931/5000 v))
(+.f32 48038761/100000000 (/.f32 -6931/5000 v))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))
(-.f32 (+.f32 48038761/100000000 (/.f32 1 (pow.f32 v 2))) (*.f32 6931/5000 (/.f32 1 v)))
(+.f32 48038761/100000000 (-.f32 (/.f32 1 (*.f32 v v)) (/.f32 6931/5000 v)))
(+.f32 48038761/100000000 (+.f32 (/.f32 1 (*.f32 v v)) (/.f32 -6931/5000 v)))

eval614.0ms (4.5%)

Compiler: Compiled 19761 to 16612 computations (15.9% saved)

prune137.0ms (1%)

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	747	6	753
Fresh	2	2	4
Picked	1	0	1
Done	0	6	6
Total	750	14	764

Error

0.0b

Counts

764 → 14

Alt Table

Click to see full alt table

Status	Error	Program
✓	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	18.9b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	0.0b	(pow.f32 (pow.f32 (pow.f32 (*.f32 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) v)) 1/6) 2) 3)
✓	0.0b	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
	30.0b	1
✓	0.0b	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	30.0b	(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
✓	0.0b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (pow.f32 (E.f32) (-.f32 6931/10000 (/.f32 1 v))))) 3)
	24.8b	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	30.0b	(+.f32 1 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
	0.0b	(.f32 (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (/.f32 1/2 v))
✓	0.3b	(exp.f32 (/.f32 -1 v))
	0.3b	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 200 to 169 computations (15.5% saved)

regimes147.0ms (1.1%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

11 calls:

17.0ms	sinTheta_i
16.0ms	sinTheta_O
16.0ms	cosTheta_i
15.0ms	cosTheta_O
14.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	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)))))`
0.0b	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)))))`
0.0b	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))))`
0.0b	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))))`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 521 to 360 computations (30.9% saved)

regimes137.0ms (1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

11 calls:

24.0ms	cosTheta_O
14.0ms	sinTheta_O
14.0ms	(+.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))))
13.0ms	(*.f32 sinTheta_i sinTheta_O)
12.0ms	cosTheta_i

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	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)))))`
0.0b	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)))))`
0.0b	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))))`
0.0b	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))))`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 393 to 259 computations (34.1% saved)

regimes72.0ms (0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

7 calls:

12.0ms	cosTheta_O
11.0ms	sinTheta_O
10.0ms	cosTheta_i
10.0ms	sinTheta_i
8.0ms	(*.f32 cosTheta_i cosTheta_O)

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 188 to 121 computations (35.6% saved)

regimes69.0ms (0.5%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 177 to 112 computations (36.7% saved)

regimes105.0ms (0.8%)

Counts

14 → 1

Calls

Call 1

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

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

Calls

7 calls:

37.0ms	(*.f32 cosTheta_i cosTheta_O)
26.0ms	cosTheta_i
9.0ms	sinTheta_i
8.0ms	cosTheta_O
8.0ms	sinTheta_O

Results

Error	Segments	Branch
0.3b	1	`cosTheta_i`
0.3b	1	`cosTheta_O`
0.3b	1	`sinTheta_i`
0.3b	1	`sinTheta_O`
0.3b	1	`v`
0.3b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.3b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 128 to 87 computations (32% saved)

regimes53.0ms (0.4%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Error	Segments	Branch
0.3b	1	`cosTheta_i`
0.3b	1	`cosTheta_O`
0.3b	1	`sinTheta_i`
0.3b	1	`sinTheta_O`
0.3b	1	`v`
0.3b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.3b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 112 to 77 computations (31.3% saved)

regimes78.0ms (0.6%)

Counts

8 → 1

Calls

Call 1

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

Outputs
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Calls

7 calls:

42.0ms	cosTheta_O
7.0ms	v
6.0ms	sinTheta_i
6.0ms	sinTheta_O
5.0ms	cosTheta_i

Results

Error	Segments	Branch
18.9b	1	`cosTheta_i`
18.9b	1	`cosTheta_O`
18.9b	1	`sinTheta_i`
18.9b	1	`sinTheta_O`
18.9b	1	`v`
18.9b	1	`(*.f32 cosTheta_i cosTheta_O)`
18.9b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 89 to 62 computations (30.3% saved)

regimes21.0ms (0.2%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0.0b (-0%)

Counts

3 → 1

Calls

Call 1

Inputs
1
1
1

Outputs
1

Calls

5 calls:

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

Results

Error	Segments	Branch
30.0b	1	`cosTheta_i`
30.0b	1	`cosTheta_O`
30.0b	1	`sinTheta_i`
30.0b	1	`sinTheta_O`
30.0b	1	`v`

Compiler

Compiled 38 to 33 computations (13.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
4×	`+-commutative_binary32`
3×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	97
1	44	97
2	49	97
3	51	97
4	52	97

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 104 to 90 computations (13.5% saved)

soundness251.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

807×	`sub-neg_binary32`
507×	`unsub-neg_binary32`
462×	`fma-def_binary32`
403×	`+-commutative_binary32`
386×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	848
1	119	709
2	305	646
3	878	646
4	2464	646
5	4633	646
6	6144	646
7	6654	646
8	7278	646
9	7417	646
10	7469	646
11	7939	646

Stop Event

1×	node limit

Compiler

Compiled 54 to 49 computations (9.3% saved)

end79.0ms (0.6%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 145 to 122 computations (15.9% saved)