Details

analyze704.0ms (5.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	3%	97%	0
0%	3%	97%	1
0%	3%	97%	2
0%	3%	97%	3
0%	3%	97%	4
0%	3%	97%	5
0%	1.5%	98.5%	6
0%	1.5%	98.5%	7
0%	1.5%	98.5%	8
0%	1.5%	98.5%	9
0%	1.5%	98.5%	10
0.6%	0.9%	98.5%	11
0.6%	0.9%	98.5%	12

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample3.1s (23.8%)

Results

3.0s	8256×	body	256	valid
48.0ms	149×	body	256	invalid

preprocess49.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

880×	`fma-neg_binary32`
856×	`exp-diff_binary32`
346×	`cancel-sign-sub-inv_binary32`
317×	`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)) 6931/10000) (fma.f32 (/.f32 sinTheta_O v) sinTheta_i (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 -1 (fma.f32 sinTheta_O (/.f32 sinTheta_i 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)) 6931/10000) (fma.f32 (/.f32 sinTheta_O v) sinTheta_i (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 -1 (fma.f32 sinTheta_O (/.f32 sinTheta_i 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 sinTheta_O (/.f32 v cosTheta_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 cosTheta_O (/.f32 v sinTheta_O)) (.f32 (/.f32 cosTheta_i v) sinTheta_i)) (/.f32 -1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_O (/.f32 v sinTheta_O)) (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 cosTheta_i (/.f32 sinTheta_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 6931/10000 (+.f32 (-.f32 (/.f32 cosTheta_O (/.f32 cosTheta_i v)) (/.f32 sinTheta_i (/.f32 cosTheta_i sinTheta_O))) (/.f32 -1 cosTheta_i)))) (/.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 sinTheta_O (/.f32 v cosTheta_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 cosTheta_O (/.f32 v sinTheta_O)))))) (/.f32 1/2 v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (.f32 sinTheta_i (/.f32 cosTheta_i v))) (fma.f32 (/.f32 cosTheta_O v) sinTheta_O (/.f32 1 v)))) (/.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 (.f32 sinTheta_O (/.f32 cosTheta_i v)) (+.f32 (fma.f32 (/.f32 sinTheta_i v) cosTheta_O (/.f32 1 v)) -6931/10000))))
(*.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 (/.f32 cosTheta_i cosTheta_O) v) (*.f32 (/.f32 sinTheta_i cosTheta_O) sinTheta_O)) (/.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)) 6931/10000) (fma.f32 (/.f32 sinTheta_O v) sinTheta_i (/.f32 1 v)))))
(*.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (fma.f32 -1 (fma.f32 sinTheta_O (/.f32 sinTheta_i 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 6931/10000 (-.f32 (.f32 (/.f32 cosTheta_i sinTheta_i) cosTheta_O) (-.f32 (/.f32 (*.f32 v sinTheta_O) sinTheta_i) (/.f32 -1 sinTheta_i))))) (/.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 (.f32 (/.f32 cosTheta_i sinTheta_O) cosTheta_O) (+.f32 (*.f32 (/.f32 sinTheta_i sinTheta_O) v) (+.f32 (/.f32 1 sinTheta_O) -6931/10000)))) (/.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)

simplify26.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

696×	`fma-def_binary32`
512×	`exp-sum_binary32`
492×	`fma-neg_binary32`
435×	`sub-neg_binary32`
429×	`exp-diff_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	22	35
1	53	33
2	147	31
3	584	29
4	2863	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 (/.f32 sinTheta_O v) sinTheta_i (/.f32 1 v)))) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

0.1b

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

▶

0.1b

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

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize114.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	7.3b	(/.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)

series31.0ms (0.2%)

Counts

4 → 120

Calls

48 calls:

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

rewrite149.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	57
1	506	54
2	7906	54

Stop Event

1×	node limit

Counts

4 → 185

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))
(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
((#(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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simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

945×	`associate-/l*_binary32`
693×	`associate-l_binary32`
589×	`associate-/r*_binary32`
364×	`fma-def_binary32`
260×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	4231
1	423	3930
2	1608	3576

Stop Event

1×	node limit

Counts

305 → 225

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

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

localize74.0ms (0.6%)

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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
✓	0.1b	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
✓	0.1b	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

Compiler

Compiled 90 to 42 computations (53.3% saved)

series45.0ms (0.4%)

Counts

4 → 156

Calls

48 calls:

Time	Variable		Point	Expression
21.0ms	cosTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
3.0ms	cosTheta_i	@	0	(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
1.0ms	cosTheta_O	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	v	@	-inf	(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite118.0ms (0.9%)

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	4119	63

Stop Event

1×	node limit

Counts

4 → 202

Calls

Call 1

Inputs
(exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000)
(-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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 0 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) (cbrt.f32 (exp.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 2) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i 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_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 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simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

817×	`associate-/l*_binary32`
642×	`associate-r_binary32`
560×	`associate-l_binary32`
455×	`associate-/r*_binary32`
285×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	123	3494
1	401	3235
2	1420	2620

Stop Event

1×	node limit

Counts

358 → 255

Calls

Call 1

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

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

eval338.0ms (2.6%)

Compiler: Compiled 15660 to 8611 computations (45% saved)

prune96.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	469	11	480
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	471	11	482

Error

0.0b

Counts

482 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	30.5b	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(.f32 (+.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 1/2 v))
▶	0.1b	(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)) 1/2) v)
	28.3b	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
▶	28.3b	(.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v))
	0.1b	(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_O (/.f32 cosTheta_i v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)))) 3)
▶	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))

Compiler

Compiled 548 to 400 computations (27% saved)

localize70.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 107 to 44 computations (58.9% saved)

series19.0ms (0.1%)

Counts

4 → 168

Calls

48 calls:

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

rewrite110.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

834×	`log-prod_binary32`
730×	`fma-def_binary32`
504×	`fma-neg_binary32`
303×	`expm1-udef_binary32`
303×	`log1p-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	54
1	341	50
2	4755	50

Stop Event

1×	node limit

Counts

4 → 295

Calls

Call 1

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

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

simplify142.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-/l*_binary32`
544×	`associate-r_binary32`
462×	`associate-l_binary32`
387×	`associate-/r*_binary32`
288×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	98	4167
1	312	4083
2	1084	3257
3	6287	3235

Stop Event

1×	node limit

Counts

463 → 340

Calls

Call 1

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

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

localize25.0ms (0.2%)

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)

series3.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
2.0ms	v	@	-inf	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
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))

rewrite49.0ms (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))))))))

simplify12.0ms (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 → 24

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

localize43.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v))
✓	0.1b	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
	7.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 48 to 22 computations (54.2% saved)

series12.0ms (0.1%)

Counts

2 → 52

Calls

18 calls:

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

rewrite51.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

600×	`log-prod_binary32`
355×	`pow-prod-down_binary32`
325×	`pow-unpow_binary32`
289×	`pow2_binary32`
206×	`pow1/3_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	248	24
2	3218	5

Stop Event

1×	node limit

Counts

2 → 33

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x . 1)))))

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

simplify76.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1184
1	154	1156
2	525	1088
3	3621	1056
4	4957	1056
5	7159	1056

Stop Event

1×	node limit

Counts

85 → 47

Calls

Call 1

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

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

localize112.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series50.0ms (0.4%)

Counts

3 → 52

Calls

27 calls:

Time	Variable		Point	Expression
21.0ms	cosTheta_i	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
11.0ms	v	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
3.0ms	v	@	-inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
3.0ms	v	@	inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
2.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))

rewrite247.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	65
1	360	65
2	5221	59

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-/l*_binary32`
543×	`associate-r_binary32`
447×	`associate-l_binary32`
390×	`associate-/r*_binary32`
236×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1627
1	313	1469
2	1156	1324
3	6644	1289

Stop Event

1×	node limit

Counts

280 → 273

Calls

Call 1

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

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

localize138.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
	0.0b	(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
✓	0.1b	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
✓	3.2b	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 98 to 47 computations (52% saved)

series59.0ms (0.5%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
29.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
10.0ms	v	@	-inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
8.0ms	v	@	inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
3.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
1.0ms	sinTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))

rewrite89.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`fma-def_binary32`
468×	`fma-neg_binary32`
367×	`expm1-udef_binary32`
367×	`log1p-udef_binary32`
213×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	36
1	421	34
2	5640	34

Stop Event

1×	node limit

Counts

3 → 89

Calls

Call 1

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

Outputs

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

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

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

955×	`times-frac_binary32`
658×	`associate-/l*_binary32`
540×	`fma-neg_binary32`
497×	`associate-r_binary32`
409×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	2080
1	357	1962
2	1166	1888
3	7355	1888

Stop Event

1×	node limit

Counts

173 → 127

Calls

Call 1

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

eval666.0ms (5.2%)

Compiler: Compiled 29832 to 16509 computations (44.7% saved)

prune441.0ms (3.4%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	1080	15	1095
Fresh	3	3	6
Picked	1	0	1
Done	4	0	4
Total	1088	18	1106

Error

0.0b

Counts

1106 → 18

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(/.f32 1/2 v)
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	0.7b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	31.2b	(sqrt.f32 (/.f32 1/4 (*.f32 v v)))
	0.1b	(/.f32 (.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 6931/10000)) 1/2) v)
	30.7b	(.f32 (-.f32 1 (.f32 sinTheta_O (/.f32 sinTheta_i v))) (/.f32 1/2 v))
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)))) 3)
▶	0.1b	(.f32 (+.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 1/2 v))
	0.1b	(pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) 2)
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 (.f32 (exp.f32 6931/10000) 1/2) v))
	27.6b	(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))
	0.1b	(.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)) 1/2) v)

Compiler

Compiled 786 to 596 computations (24.2% saved)

localize113.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f32 cosTheta_i cosTheta_O)
	0.0b	(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
	0.1b	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
✓	0.3b	(/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)

Compiler

Compiled 89 to 41 computations (53.9% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite63.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

724×	`pow1_binary32`
679×	`add-log-exp_binary32`
679×	`log1p-expm1-u_binary32`
679×	`expm1-log1p-u_binary32`
667×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	145	9
2	1795	9

Stop Event

1×	node limit

Counts

1 → 41

Calls

Call 1

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

simplify12.0ms (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

53 → 42

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

localize9.0ms (0.1%)

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

localize54.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.1b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

Compiler

Compiled 32 to 16 computations (50% saved)

series4.0ms (0%)

Counts

1 → 16

Calls

9 calls:

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

rewrite98.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

465×	`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	10
1	188	10
2	2502	10

Stop Event

1×	node limit

Counts

1 → 67

Calls

Call 1

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

Outputs

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

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

647×	`unswap-sqr_binary32`
488×	`times-frac_binary32`
331×	`associate-/l*_binary32`
228×	`associate--r+_binary32`
226×	`associate-r_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	512
1	156	512
2	522	464
3	3422	416
4	4971	400

Stop Event

1×	node limit

Counts

83 → 81

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))

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

localize127.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
✓	0.0b	(-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
✓	0.1b	(exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
	7.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 173 to 87 computations (49.7% saved)

series10.0ms (0.1%)

Counts

3 → 70

Calls

27 calls:

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

rewrite92.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

660×	`log-prod_binary32`
444×	`fma-def_binary32`
351×	`pow2_binary32`
243×	`pow1/3_binary32`
239×	`expm1-udef_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	47
1	267	47
2	3960	41

Stop Event

1×	node limit

Counts

3 → 197

Calls

Call 1

Inputs

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

(-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))

(+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))

Outputs

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

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

simplify60.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

603×	`times-frac_binary32`
439×	`associate-/l*_binary32`
411×	`cancel-sign-sub-inv_binary32`
352×	`fma-neg_binary32`
350×	`associate-r_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	1279
1	288	1109
2	925	1109
3	5035	1097

Stop Event

1×	node limit

Counts

267 → 233

Calls

Call 1

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

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

localize152.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
	0.0b	(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
	0.1b	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
✓	3.5b	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 101 to 48 computations (52.5% saved)

series37.0ms (0.3%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
36.0ms	v	@	0	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
1.0ms	v	@	inf	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
1.0ms	v	@	-inf	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

392×	`log-prod_binary32`
319×	`exp-prod_binary32`
249×	`pow2_binary32`
226×	`pow-prod-down_binary32`
221×	`cbrt-unprod_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	205	9
2	2549	9

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 1 (fma.f32 (/.f32 1/2 v) (exp.f32 6931/10000) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 1 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 6931/30000)) (cbrt.f32 (*.f32 (pow.f32 (*.f32 v 2) -2) (exp.f32 6931/5000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 (pow.f32 (*.f32 v 2) -2) (exp.f32 6931/5000))) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 6931/30000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 6931/20000)) (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 6931/20000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (E.f32) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (*.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 6931/30000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (pow.f32 (E.f32) (-.f32 (log.f32 v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (exp.f32 (-.f32 (log.f32 v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (E.f32) (+.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (E.f32))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (E.f32) (/.f32 48038761/100000000 (+.f32 6931/10000 (log.f32 (*.f32 v 2))))) (pow.f32 (E.f32) (/.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (+.f32 6931/10000 (log.f32 (*.f32 v 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 1/2))) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (+.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (E.f32))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (log.f32 (*.f32 v 2))))) (exp.f32 (/.f32 (pow.f32 (log.f32 (/.f32 1/2 v)) 2) (+.f32 6931/10000 (log.f32 (*.f32 v 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (+.f32 6931/10000 (log.f32 1/2))) v)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (*.f32 (pow.f32 (*.f32 v 2) -2) (exp.f32 6931/5000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (exp.f32 6931/10000)) (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (*.f32 (pow.f32 (/.f32 1/2 v) 3) (pow.f32 (exp.f32 6931/10000) 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 expm1.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3))))))

simplify37.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

617×	`fma-def_binary32`
404×	`exp-sum_binary32`
389×	`associate-l_binary32`
335×	`associate--r+_binary32`
335×	`associate-/r*_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	168
1	48	156
2	102	108
3	233	108
4	495	108
5	1199	108
6	3979	108

Stop Event

1×	node limit

Counts

43 → 35

Calls

Call 1

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

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

eval1.1s (8.8%)

Compiler: Compiled 44219 to 24433 computations (44.7% saved)

prune427.0ms (3.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	1271	9	1280
Fresh	4	9	13
Picked	1	0	1
Done	4	0	4
Total	1280	18	1298

Error

0.0b

Counts

1298 → 18

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 (exp.f32 (-.f32 (log.f32 v) 6931/10000))))
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 1/2 (pow.f32 (E.f32) (-.f32 (log.f32 v) 6931/10000))))
▶	0.1b	(.f32 (+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O)) v) (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 1/2 v))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	30.0b	1
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))
▶	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) 2)
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (pow.f32 (E.f32) (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(/.f32 (.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 6931/10000)) 1/2) v)
	0.1b	(.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	0.7b	(exp.f32 (/.f32 -1 v))
	0.1b	(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)) 1/2) v)

Compiler

Compiled 824 to 638 computations (22.6% saved)

localize62.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))
	0.0b	(*.f32 cosTheta_i cosTheta_O)
	0.1b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	0.3b	(/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v)

Compiler

Compiled 61 to 39 computations (36.1% saved)

series13.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

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

rewrite60.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

782×	`log-prod_binary32`
380×	`prod-diff_binary32`
270×	`expm1-udef_binary32`
270×	`log1p-udef_binary32`
216×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	314	21
2	4117	21

Stop Event

1×	node limit

Counts

1 → 29

Calls

Call 1

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

Outputs

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

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

835×	`times-frac_binary32`
502×	`unswap-sqr_binary32`
486×	`associate-/l*_binary32`
406×	`associate-r_binary32`
384×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	70	1134
1	215	1130
2	768	1088
3	5225	1036
4	7206	1036

Stop Event

1×	node limit

Counts

65 → 46

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(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	@	0	(exp.f32 (/.f32 -1 v))
0.0ms	v	@	-inf	(exp.f32 (/.f32 -1 v))

rewrite60.0ms (0.5%)

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 (pow.f32 (/.f32 -1 (cbrt.f32 v)) 2)) (/.f32 -1 (cbrt.f32 v)))))) (#(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 (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))))))))

simplify32.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

729×	`distribute-neg-frac_binary32`
579×	`associate-/r/_binary32`
536×	`unswap-sqr_binary32`
425×	`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	960	98
5	4048	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 (/.f32 1/2 (*.f32 v v))) (/.f32 1 v))
(+.f32 1 (-.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 1 v)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (+.f32 1 (/.f32 -1 v)))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (/.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)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(-.f32 (+.f32 1 (-.f32 (/.f32 1/2 (*.f32 v v)) (/.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 (+.f32 1 (/.f32 -1 v)) (+.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 -1/6 (pow.f32 v 3))))
(+.f32 (+.f32 1 (/.f32 -1 v)) (.f32 (/.f32 1 (.f32 v v)) (-.f32 1/2 (/.f32 1/6 v))))
(+.f32 (/.f32 -1 v) (+.f32 1 (.f32 (/.f32 1 (.f32 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 (/.f32 1/2 (*.f32 v v))) (/.f32 1 v))
(+.f32 1 (-.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 1 v)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (+.f32 1 (/.f32 -1 v)))
(+.f32 1 (+.f32 (/.f32 1/2 (*.f32 v v)) (/.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)))
(+.f32 (/.f32 1/2 (*.f32 v v)) (-.f32 1 (+.f32 (/.f32 1 v) (/.f32 1/6 (pow.f32 v 3)))))
(-.f32 (+.f32 1 (-.f32 (/.f32 1/2 (*.f32 v v)) (/.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 (+.f32 1 (/.f32 -1 v)) (+.f32 (/.f32 1/2 (*.f32 v v)) (/.f32 -1/6 (pow.f32 v 3))))
(+.f32 (+.f32 1 (/.f32 -1 v)) (.f32 (/.f32 1 (.f32 v v)) (-.f32 1/2 (/.f32 1/6 v))))
(+.f32 (/.f32 -1 v) (+.f32 1 (.f32 (/.f32 1 (.f32 v v)) (+.f32 1/2 (/.f32 -1/6 v)))))

localize145.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 6931/10000 (/.f32 1 v))
	0.1b	(exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
✓	0.1b	(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
	7.3b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 154 to 91 computations (40.9% saved)

series2.0ms (0%)

Counts

2 → 11

Calls

6 calls:

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

rewrite75.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`pow1_binary32`
668×	`add-log-exp_binary32`
668×	`log1p-expm1-u_binary32`
668×	`expm1-log1p-u_binary32`
656×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	148	16
2	1800	16

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

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

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

871×	`distribute-neg-frac_binary32`
849×	`fma-neg_binary32`
536×	`unswap-sqr_binary32`
529×	`times-frac_binary32`
382×	`associate-/r*_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	24	156
1	63	150
2	145	136
3	371	128
4	1173	124
5	5373	124

Stop Event

1×	node limit

Counts

65 → 63

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

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

localize90.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f32 (/.f32 1/2 v))
	0.0b	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
	0.1b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	3.5b	(pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 73 to 46 computations (37% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
0.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
0.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))

rewrite57.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

476×	`pow1_binary32`
466×	`add-sqr-sqrt_binary32`
454×	`*-un-lft-identity_binary32`
444×	`add-log-exp_binary32`
444×	`log1p-expm1-u_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	105	6
2	1213	6

Stop Event

1×	node limit

Counts

1 → 25

Calls

Call 1

Inputs
(log.f32 (/.f32 1/2 v))

Outputs

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

simplify35.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

155×	`fma-neg_binary32`
118×	`fma-def_binary32`
56×	`cancel-sign-sub-inv_binary32`
44×	`sub-neg_binary32`
39×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	116
1	28	108
2	40	108
3	60	108
4	109	108
5	203	108
6	335	108
7	508	108
8	656	108
9	777	108
10	797	108

Stop Event

1×

saturated

Counts

37 → 28

Calls

Call 1

Inputs
(+.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)))

Outputs
(+.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 -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)))

localize132.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
✓	0.1b	(sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
✓	0.5b	(pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)
✓	3.2b	(exp.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))

Compiler

Compiled 121 to 68 computations (43.8% saved)

series5.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite109.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`unpow-prod-down_binary32`
400×	`log-prod_binary32`
307×	`exp-prod_binary32`
251×	`pow2_binary32`
233×	`prod-exp_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	31
1	237	29
2	2519	29

Stop Event

1×	node limit

Counts

3 → 181

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1/2 v) (pow.f32 (exp.f32 1) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (cbrt.f32 (*.f32 (*.f32 1/4 (pow.f32 v -2)) (exp.f32 6931/5000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 (*.f32 1/4 (pow.f32 v -2)) (exp.f32 6931/5000))) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 1/3) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (sqrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3)) 1/3) (pow.f32 (sqrt.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 3)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (*.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 2) 1/3) (cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 5/2) 1/3) (cbrt.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 2) 3) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 3) (pow.f32 (sqrt.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) 6931/10000) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) (pow.f32 (exp.f32 1) (*.f32 1/3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (exp.f32 1) (*.f32 1/2 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 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(#(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)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (log.f32 (sqrt.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)) (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 5/6) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3))) (pow.f32 (/.f32 1 (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (pow.f32 (/.f32 1 (+.f32 6931/10000 (log.f32 (*.f32 v 2)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4)) (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/4) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 1 1/3) (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/4) 1/2) (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 5/6) 1/2) (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 4) 1/3) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 5/4) 1/3) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (pow.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 2) 3) (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 3) (pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (+.f32 332956652491/1000000000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 3))) (sqrt.f32 (fma.f32 (log.f32 (/.f32 1/2 v)) (-.f32 (log.f32 (/.f32 1/2 v)) 6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (-.f32 48038761/100000000 (pow.f32 (log.f32 (/.f32 1/2 v)) 2))) (sqrt.f32 (+.f32 6931/10000 (log.f32 (*.f32 v 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1/2) (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 2) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))) 2)) (cbrt.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (sqrt.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (sqrt.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)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 3/2 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 1/4 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 1) 1))))))

simplify64.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

666×	`fma-def_binary32`
429×	`associate-/r*_binary32`
411×	`exp-sum_binary32`
384×	`associate-l_binary32`
367×	`fma-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	496
1	55	468
2	112	420
3	241	420
4	514	420
5	1250	420
6	4095	420

Stop Event

1×	node limit

Counts

217 → 193

Calls

Call 1

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

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

eval686.0ms (5.3%)

Compiler: Compiled 21821 to 15064 computations (31% saved)

prune218.0ms (1.7%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	787	12	799
Fresh	6	7	13
Picked	1	0	1
Done	2	2	4
Total	796	21	817

Error

0.0b

Counts

817 → 21

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (-.f32 (log.f32 1/2) (log.f32 v)))) 2)))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (pow.f32 (.f32 (pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 3) (pow.f32 (sqrt.f32 (pow.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/6)) 3)) 2)))
	0.1b	(*.f32 (pow.f32 (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2)) (cbrt.f32 (pow.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))) (cbrt.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))
	0.1b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	30.0b	1
	0.1b	(/.f32 (.f32 (pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v) 6931/10000)) 1/2) v)
	0.1b	(.f32 (pow.f32 (exp.f32 (neg.f32 (fma.f32 cosTheta_i cosTheta_O -1))) (/.f32 1 (neg.f32 v))) (/.f32 (.f32 (exp.f32 6931/10000) 1/2) v))
	0.1b	(pow.f32 (sqrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) 2)
	0.1b	(.f32 (+.f32 (/.f32 (.f32 cosTheta_i (*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) cosTheta_O)) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
	0.1b	(*.f32 (pow.f32 (E.f32) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	0.7b	(exp.f32 (/.f32 -1 v))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (pow.f32 (E.f32) (pow.f32 (sqrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)))
	0.1b	(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)) 1/2) v)
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 1/2 (exp.f32 (-.f32 (log.f32 v) 6931/10000))))
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 1/2 (pow.f32 (E.f32) (-.f32 (log.f32 v) 6931/10000))))
	0.1b	(*.f32 (exp.f32 (/.f32 -1 v)) (pow.f32 (E.f32) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(.f32 (pow.f32 (E.f32) (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (fma.f32 sinTheta_i sinTheta_O 1)) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 504 to 403 computations (20% saved)

regimes266.0ms (2.1%)

Counts

49 → 1

Calls

Call 1

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

Outputs

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

Calls

11 calls:

38.0ms	sinTheta_O
27.0ms	(+.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))))
26.0ms	v
24.0ms	cosTheta_i
23.0ms	sinTheta_i

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.1b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 1045 to 675 computations (35.4% saved)

regimes207.0ms (1.6%)

Counts

47 → 1

Calls

Call 1

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

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

Calls

11 calls:

22.0ms	sinTheta_i
22.0ms	cosTheta_O
21.0ms	cosTheta_i
20.0ms	sinTheta_O
19.0ms	(+.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
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.1b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.1b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.1b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 967 to 618 computations (36.1% saved)

regimes66.0ms (0.5%)

Counts

16 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(.f32 (-.f32 1 (.f32 sinTheta_O (/.f32 sinTheta_i v))) (/.f32 1/2 v))
(exp.f32 (/.f32 -1 v))
(sqrt.f32 (/.f32 1/4 (*.f32 v v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
(.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v))
(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)) 1/2) v)
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(/.f32 (.f32 (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)) 1/2) v)
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

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

Calls

7 calls:

11.0ms	sinTheta_O
9.0ms	cosTheta_i
9.0ms	v
9.0ms	cosTheta_O
8.0ms	sinTheta_i

Results

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

Compiler

Compiled 198 to 140 computations (29.3% saved)

regimes56.0ms (0.4%)

Counts

12 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(.f32 (-.f32 1 (.f32 sinTheta_O (/.f32 sinTheta_i v))) (/.f32 1/2 v))
(exp.f32 (/.f32 -1 v))
(sqrt.f32 (/.f32 1/4 (*.f32 v v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (exp.f32 (.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O))) (/.f32 1/2 v))
(.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v))

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

Calls

7 calls:

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

Results

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

Compiler

Compiled 139 to 102 computations (26.6% saved)

regimes63.0ms (0.5%)

Counts

8 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(.f32 (-.f32 1 (.f32 sinTheta_O (/.f32 sinTheta_i v))) (/.f32 1/2 v))
(exp.f32 (/.f32 -1 v))
(sqrt.f32 (/.f32 1/4 (*.f32 v v)))
(exp.f32 (*.f32 cosTheta_O (/.f32 cosTheta_i v)))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

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

Calls

6 calls:

12.0ms	sinTheta_i
12.0ms	sinTheta_O
12.0ms	v
10.0ms	(*.f32 cosTheta_i cosTheta_O)
7.0ms	cosTheta_O

Results

Error	Segments	Branch
0.7b	1	`cosTheta_i`
0.7b	1	`cosTheta_O`
0.7b	1	`sinTheta_i`
0.7b	1	`sinTheta_O`
0.7b	1	`v`
0.7b	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 88 to 66 computations (25% saved)

regimes22.0ms (0.2%)

Accuracy

Total -0.7b remaining (-2.3%)

Threshold costs -0.7b (-2.3%)

Counts

3 → 1

Calls

Call 1

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

Outputs
1

Calls

5 calls:

5.0ms	cosTheta_O
5.0ms	v
4.0ms	cosTheta_i
4.0ms	sinTheta_O
3.0ms	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 50 to 40 computations (20% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary32`
9×	`+-commutative_binary32`
6×	`sub-neg_binary32`
3×	`neg-sub0_binary32`
3×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	127
1	65	127
2	77	127
3	83	127
4	87	127
5	88	127

Stop Event

1×

saturated

Calls

Call 1

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

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

end72.0ms (0.6%)

Stop Event

1×

fuel

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 377 to 311 computations (17.5% saved)

Iter	Nodes	Cost
0	17	116
1	28	108
2	40	108
3	60	108
4	109	108
5	203	108
6	335	108
7	508	108
8	656	108
9	777	108
10	797	108

Iter	Nodes	Cost
0	17	116
1	28	108
2	40	108
3	60	108
4	109	108
5	203	108
6	335	108
7	508	108
8	656	108
9	777	108
10	797	108

Iter	Nodes	Cost
0	17	116
1	28	108
2	40	108
3	60	108
4	109	108
5	203	108
6	335	108
7	508	108
8	656	108
9	777	108
10	797	108