Details

analyze1.1s (6.3%)

Algorithm

1×

Search

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample4.9s (27.2%)

Results

4.8s	8256×	body	256	valid
43.0ms	126×	body	256	invalid

Bogosity

preprocess79.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
0
2
3
2
4

Call 2

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval2.0ms (0%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.1b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

0.1b

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

▶

0.1b

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

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize176.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.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	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	7.9b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series100.0ms (0.6%)

Counts

4 → 120

Calls

48 calls:

Time	Variable		Point	Expression
13.0ms	cosTheta_i	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
11.0ms	v	@	-inf	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
7.0ms	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)))))
7.0ms	sinTheta_O	@	0	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	sinTheta_O	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

rewrite154.0ms (0.9%)

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	74
1	506	68
2	7921	68

Stop Event

1×	node limit

Counts

4 → 164

Calls

Call 1

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

simplify163.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

938×	`associate-/l*_binary32`
695×	`associate-l_binary32`
594×	`associate-/r*_binary32`
387×	`fma-def_binary32`
264×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	5028
1	465	4889
2	1786	4204

Stop Event

1×	node limit

Counts

284 → 219

Calls

Call 1

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

localize113.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 90 to 42 computations (53.3% saved)

series35.0ms (0.2%)

Counts

4 → 180

Calls

54 calls:

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

rewrite159.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 196

Calls

Call 1

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

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

simplify205.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

860×	`associate-/r*_binary32`
743×	`associate-l_binary32`
589×	`fma-def_binary32`
450×	`associate-*r/_binary32`
406×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

376 → 275

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))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v) (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v) (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 2))) (pow.f32 v 2))) (+.f32 (/.f32 (.f32 cosTheta_i (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) cosTheta_O)) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) (pow.f32 cosTheta_O 3))) (pow.f32 v 3))) (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))))
(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (*.f32 sinTheta_i sinTheta_O))) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.f32 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O)))) v) (+.f32 (exp.f32 6931/10000) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (*.f32 sinTheta_i sinTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2)))))
(+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (+.f32 (/.f32 (.f32 (exp.f32 6931/10000) (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O)))) v) (+.f32 (exp.f32 6931/10000) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (*.f32 sinTheta_i sinTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))))))
(exp.f32 6931/10000)
(+.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 (.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)))
(+.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))) (+.f32 (exp.f32 6931/10000) (.f32 -1/6 (/.f32 (.f32 (pow.f32 (-.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (.f32 -1 (.f32 sinTheta_i sinTheta_O))) 3) (exp.f32 6931/10000)) (pow.f32 v 3))))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))))))
(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2)))))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) v)) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (.f32 1/2 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))))))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 6931/10000 (+.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)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (.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)))
(/.f32 (*.f32 cosTheta_i cosTheta_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)))
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(.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))
(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v))))
(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (+.f32 (.f32 -1/12 (/.f32 (.f32 (pow.f32 sinTheta_i 3) (.f32 (pow.f32 sinTheta_O 3) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 4))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))
(*.f32 1/2 (/.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) v))

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

eval280.0ms (1.6%)

Compiler: Compiled 16055 to 9121 computations (43.2% saved)

prune209.0ms (1.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	481	13	494
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	483	13	496

Error

0.1b

Counts

496 → 13

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
	30.5b	(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
	0.1b	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	0.9b	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
▶	0.1b	(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
▶	28.2b	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
▶	28.4b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	28.2b	(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
	30.5b	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	0.1b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
	0.1b	(exp.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 2) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (-.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
▶	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 534 to 402 computations (24.7% saved)

localize88.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 98 to 46 computations (53.1% saved)

series68.0ms (0.4%)

Counts

4 → 180

Calls

45 calls:

Time	Variable		Point	Expression
22.0ms	v	@	0	(log.f32 (/.f32 1/2 v))
11.0ms	v	@	inf	(log.f32 (/.f32 1/2 v))
9.0ms	v	@	-inf	(log.f32 (/.f32 1/2 v))
3.0ms	sinTheta_i	@	inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
2.0ms	cosTheta_i	@	0	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite144.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

588×	`fma-def_binary32`
438×	`fma-neg_binary32`
366×	`expm1-udef_binary32`
366×	`log1p-udef_binary32`
225×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	72
1	447	64
2	6127	60

Stop Event

1×	node limit

Counts

4 → 174

Calls

Call 1

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

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

simplify140.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

779×	`associate-l_binary32`
615×	`associate-/r*_binary32`
385×	`fma-def_binary32`
285×	`associate-*r/_binary32`
285×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	5494
1	505	5115
2	2009	4647

Stop Event

1×	node limit

Counts

354 → 241

Calls

Call 1

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

localize23.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 22 to 8 computations (63.6% saved)

series5.0ms (0%)

Counts

1 → 16

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta_O	@	0	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
1.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
1.0ms	v	@	inf	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	v	@	-inf	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_i	@	-inf	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

rewrite53.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`pow1_binary32`
720×	`add-log-exp_binary32`
720×	`log1p-expm1-u_binary32`
720×	`expm1-log1p-u_binary32`
703×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	141	9
2	1909	9

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

840×	`associate-*l/_binary32`
816×	`associate-/l/_binary32`
816×	`fma-def_binary32`
775×	`associate-*r/_binary32`
343×	`times-frac_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	352
1	87	352
2	279	324
3	2019	304
4	6922	296
5	7209	296
6	7488	296
7	7849	296

Stop Event

1×	node limit

Counts

36 → 27

Calls

Call 1

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

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

localize28.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 26 to 9 computations (65.4% saved)

series8.0ms (0%)

Counts

2 → 72

Calls

18 calls:

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

rewrite56.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

789×	`pow1_binary32`
727×	`add-log-exp_binary32`
726×	`log1p-expm1-u_binary32`
726×	`expm1-log1p-u_binary32`
710×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	167	16
2	2285	16

Stop Event

1×	node limit

Counts

2 → 53

Calls

Call 1

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

Outputs

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

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

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

850×	`associate-*l/_binary32`
833×	`associate-/l/_binary32`
775×	`associate-*r/_binary32`
523×	`fma-def_binary32`
349×	`times-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	924
1	96	904
2	316	884
3	2167	864
4	7691	864

Stop Event

1×	node limit

Counts

125 → 64

Calls

Call 1

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

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

localize67.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
✓	0.1b	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
	7.6b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 71 to 36 computations (49.3% saved)

series10.0ms (0.1%)

Counts

3 → 37

Calls

27 calls:

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

rewrite155.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 266

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify68.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	773
1	242	754
2	843	732
3	5484	640

Stop Event

1×	node limit

Counts

303 → 293

Calls

Call 1

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

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

localize91.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 93 to 43 computations (53.8% saved)

series18.0ms (0.1%)

Counts

2 → 120

Calls

30 calls:

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

rewrite129.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

561×	`prod-diff_binary32`
354×	`expm1-udef_binary32`
354×	`log1p-udef_binary32`
298×	`fma-def_binary32`
205×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	52
1	412	52
2	5343	52

Stop Event

1×	node limit

Counts

2 → 54

Calls

Call 1

Inputs

(pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

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

Outputs

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

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

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

853×	`associate-/r*_binary32`
738×	`associate-l_binary32`
570×	`fma-def_binary32`
449×	`associate-*r/_binary32`
405×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	5048
1	560	4789
2	2168	4720

Stop Event

1×	node limit

Counts

174 → 115

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

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

eval535.0ms (3%)

Compiler: Compiled 26149 to 15214 computations (41.8% saved)

prune186.0ms (1%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	967	18	985
Fresh	5	3	8
Picked	1	0	1
Done	3	1	4
Total	976	22	998

Error

0.0b

Counts

998 → 22

Alt Table

Click to see full alt table

Status	Error	Program
	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)))
	0.1b	(exp.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 2) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (-.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	2.1b	(.f32 (.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (E.f32) (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (/.f32 1/2 v))
▶	0.4b	(.f32 (cbrt.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) (/.f32 1/2 v))
	28.4b	(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
	0.1b	(*.f32 (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 3)) (/.f32 1/2 v))
	28.3b	(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
	28.4b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
	0.1b	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	29.9b	1
	0.1b	(.f32 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
	30.0b	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
	28.4b	(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
	0.4b	(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
▶	28.2b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
▶	0.1b	(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
	30.0b	(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
✓	28.4b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

Compiler

Compiled 861 to 654 computations (24% saved)

localize92.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 70 to 44 computations (37.1% saved)

series11.0ms (0.1%)

Counts

3 → 84

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	v	@	-inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	cosTheta_i	@	0	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	v	@	inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
1.0ms	cosTheta_O	@	0	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
0.0ms	cosTheta_i	@	inf	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

rewrite120.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

543×	`fma-def_binary32`
453×	`fma-neg_binary32`
308×	`expm1-udef_binary32`
308×	`log1p-udef_binary32`
253×	`log-pow_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	49
1	366	47
2	5070	47

Stop Event

1×	node limit

Counts

3 → 177

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

simplify128.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

995×	`times-frac_binary32`
600×	`associate-/l*_binary32`
474×	`associate-r_binary32`
406×	`associate-l_binary32`
377×	`associate-/r*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	101	2451
1	291	2131
2	1083	1994
3	7787	1989

Stop Event

1×	node limit

Counts

261 → 220

Calls

Call 1

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

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

localize26.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 24 to 10 computations (58.3% saved)

series2.0ms (0%)

Counts

1 → 9

Calls

9 calls:

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

rewrite86.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

40 → 34

Calls

Call 1

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

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

localize27.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f32 sinTheta_i sinTheta_O)
✓	0.0b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
✓	7.9b	(/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v))

Compiler

Compiled 26 to 9 computations (65.4% saved)

series7.0ms (0%)

Counts

3 → 72

Calls

24 calls:

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

rewrite59.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

799×	`pow1_binary32`
738×	`add-log-exp_binary32`
737×	`log1p-expm1-u_binary32`
737×	`expm1-log1p-u_binary32`
721×	`add-exp-log_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	164	20
2	2351	20

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

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

Outputs

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

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

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

simplify104.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

850×	`associate-*l/_binary32`
833×	`associate-/l/_binary32`
775×	`associate-*r/_binary32`
523×	`fma-def_binary32`
349×	`times-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	924
1	96	904
2	316	884
3	2167	864
4	7691	864

Stop Event

1×	node limit

Counts

154 → 93

Calls

Call 1

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

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

localize42.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 36 to 29 computations (19.4% saved)

series4.0ms (0%)

Counts

3 → 23

Calls

9 calls:

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

rewrite111.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 154

Calls

Call 1

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

Outputs

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

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

simplify61.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

177 → 173

Calls

Call 1

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

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

localize74.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
✓	0.1b	(exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
✓	0.3b	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
✓	0.3b	(*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))

Compiler

Compiled 82 to 57 computations (30.5% saved)

series62.0ms (0.3%)

Counts

4 → 124

Calls

36 calls:

Time	Variable		Point	Expression
27.0ms	cosTheta_i	@	-inf	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
4.0ms	cosTheta_O	@	inf	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
3.0ms	cosTheta_i	@	0	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
3.0ms	v	@	inf	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))
3.0ms	cosTheta_O	@	0	(cbrt.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))

rewrite153.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`log-prod_binary32`
339×	`pow2_binary32`
330×	`pow-prod-down_binary32`
236×	`expm1-udef_binary32`
236×	`log1p-udef_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	59
1	273	59
2	3384	50

Stop Event

1×	node limit

Counts

4 → 241

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 20793/10000 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 20793/10000 (.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 20793/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 1/2 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)) (.f32 1/2 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (exp.f32 3) 6931/10000)) (log.f32 (pow.f32 (exp.f32 3) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (exp.f32 3) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (log.f32 (pow.f32 (exp.f32 3) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (exp.f32 (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) 2)) (.f32 1/3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (exp.f32 (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (sqrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (.f32 1/2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 8989829617257/1000000000000 (pow.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 3)) (+.f32 432348849/100000000 (-.f32 (pow.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2) (.f32 20793/10000 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 432348849/100000000 (pow.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2)) (-.f32 20793/10000 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(#(struct:change #<rule egg-rr> (2) ((x fma.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)) 6931/10000)))))

simplify129.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-in_binary32`
500×	`distribute-lft-in_binary32`
383×	`cancel-sign-sub-inv_binary32`
234×	`associate-r_binary32`
218×	`distribute-rgt-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	4217
1	839	3798
2	3057	3495

Stop Event

1×	node limit

Counts

365 → 302

Calls

Call 1

Inputs
(*.f32 3 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 3 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
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(exp.f32 20793/10000)
(+.f32 (.f32 3 (/.f32 (.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) (exp.f32 20793/10000)) v)) (exp.f32 20793/10000))
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(+.f32 (.f32 9/2 (/.f32 (.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 3) (exp.f32 20793/10000)) (pow.f32 v 3))) (+.f32 (.f32 3 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 20793/10000)) v)) (+.f32 (.f32 9/2 (/.f32 (.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) 2) (exp.f32 20793/10000)) (pow.f32 v 2))) (exp.f32 20793/10000))))
(exp.f32 20793/10000)
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(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
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(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
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(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
6931/10000
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
6931/10000
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))

Outputs
(*.f32 3 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 20793/10000 (*.f32 (/.f32 -1 v) 3))
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 3 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (-.f32 6931/10000 (/.f32 1 v))))
(fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 3 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (-.f32 6931/10000 (/.f32 1 v))))
(fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)
(+.f32 (.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (*.f32 3 (-.f32 6931/10000 (/.f32 1 v))))
(*.f32 3 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (-.f32 6931/10000 (/.f32 1 v))))
(fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)
(.f32 3 (/.f32 (.f32 cosTheta_i cosTheta_O) v))
(*.f32 3 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(.f32 3 (.f32 (/.f32 cosTheta_i v) cosTheta_O))
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20793/10000
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(fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)
20793/10000
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(*.f32 3 (+.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (-.f32 6931/10000 (/.f32 1 v))))
(fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)
(pow.f32 (exp.f32 (*.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3)
(cbrt.f32 (pow.f32 (exp.f32 3) (-.f32 6931/10000 (/.f32 1 v))))
(cbrt.f32 (pow.f32 (exp.f32 3) (+.f32 6931/10000 (/.f32 -1 v))))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
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(fma.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (pow.f32 (pow.f32 (exp.f32 3) (+.f32 6931/10000 (/.f32 -1 v))) 7) 1/18) (pow.f32 (pow.f32 (pow.f32 (exp.f32 3) (+.f32 6931/10000 (/.f32 -1 v))) 7) 1/18)) (cbrt.f32 (pow.f32 (exp.f32 3) (+.f32 6931/10000 (/.f32 -1 v)))))
(fma.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 3) 7) 1/18) (pow.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 3) 7) 1/18)) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
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(/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v)
(/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
6931/10000
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
6931/10000
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))

eval1.1s (6.1%)

Compiler: Compiled 20911 to 15181 computations (27.4% saved)

prune204.0ms (1.1%)

Pruning

26 alts after pruning (23 fresh and 3 done)

	Pruned	Kept	Total
New	884	19	903
Fresh	12	4	16
Picked	1	0	1
Done	2	3	5
Total	899	26	925

Error

0.0b

Counts

925 → 26

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(.f32 (.f32 (pow.f32 (E.f32) 6931/10000) (pow.f32 (E.f32) (*.f32 (/.f32 -1 v) 1))) (/.f32 1/2 v))
✓	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	0.1b	(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
▶	0.1b	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
	30.0b	(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
▶	0.1b	(*.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))) (/.f32 1/2 v))
	0.4b	(.f32 (cbrt.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3)))) (/.f32 1/2 v))
	15.2b	(*.f32 (/.f32 (exp.f32 (/.f32 332956652491/1000000000000 (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v)))) (exp.f32 (/.f32 (pow.f32 v -3) (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v))))) (/.f32 1/2 v))
✓	28.2b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
▶	28.4b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
	0.1b	(.f32 (pow.f32 (exp.f32 3) (.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1/3)) (/.f32 1/2 v))
	30.0b	(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
	0.4b	(.f32 (pow.f32 (exp.f32 (.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
	0.2b	(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
	0.1b	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	0.8b	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
▶	25.4b	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	30.0b	(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
✓	28.4b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	29.9b	1
	0.1b	(exp.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 2) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (-.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	19.7b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 937 to 754 computations (19.5% saved)

localize61.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 48 to 38 computations (20.8% saved)

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite91.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`prod-diff_binary32`
536×	`log-prod_binary32`
315×	`fma-def_binary32`
224×	`expm1-udef_binary32`
224×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	274	32
2	3627	32

Stop Event

1×	node limit

Counts

2 → 180

Calls

Call 1

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

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (/.f32 1/2 v)) (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 -1 v))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (*.f32 (/.f32 -1 v) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (log.f32 (pow.f32 (E.f32) (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (/.f32 -1 v) 1 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (neg.f32 (/.f32 1 (cbrt.f32 v))) (cbrt.f32 (pow.f32 v -2)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (+.f32 (/.f32 -1 v) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 -1 (/.f32 1 v) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) (fma.f32 (neg.f32 (cbrt.f32 (pow.f32 v -2))) (/.f32 1 (cbrt.f32 v)) (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 -1 v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 1/2 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (*.f32 1/2 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 2 (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))) (*.f32 1/3 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1 (neg.f32 (*.f32 (/.f32 -1 v) -1))) (fma.f32 (neg.f32 (/.f32 -1 v)) -1 (*.f32 (/.f32 -1 v) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 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simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

819×	`fma-def_binary32`
746×	`associate-/r*_binary32`
728×	`associate-*l/_binary32`
445×	`associate-/l/_binary32`
441×	`associate-*r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	60	646
1	159	557
2	485	451
3	2117	425

Stop Event

1×	node limit

Counts

204 → 203

Calls

Call 1

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

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

localize17.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 16 to 7 computations (56.3% saved)

series3.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite58.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

681×	`pow1_binary32`
628×	`add-log-exp_binary32`
628×	`log1p-expm1-u_binary32`
628×	`expm1-log1p-u_binary32`
613×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	125	7
2	1672	7

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify24.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	252
1	9	252
2	13	252
3	16	252
4	17	252

Stop Event

1×

saturated

Counts

58 → 23

Calls

Call 1

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

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

localize42.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f32 sinTheta_i sinTheta_O)
✓	0.0b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
	7.9b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)

Compiler

Compiled 22 to 8 computations (63.6% saved)

series40.0ms (0.2%)

Counts

1 → 16

Calls

9 calls:

Time	Variable		Point	Expression
35.0ms	v	@	inf	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
1.0ms	sinTheta_i	@	0	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
1.0ms	sinTheta_O	@	0	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
1.0ms	v	@	-inf	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
0.0ms	sinTheta_i	@	inf	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))

rewrite81.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

780×	`pow1_binary32`
720×	`add-log-exp_binary32`
720×	`log1p-expm1-u_binary32`
720×	`expm1-log1p-u_binary32`
703×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	141	9
2	1909	9

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

Inputs
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))

Outputs

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

simplify141.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

836×	`associate-*l/_binary32`
818×	`fma-def_binary32`
816×	`associate-/l/_binary32`
779×	`associate-*r/_binary32`
343×	`times-frac_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	29	368
1	84	360
2	277	324
3	2032	304
4	6951	296
5	7238	296
6	7519	296
7	7880	296

Stop Event

1×	node limit

Counts

36 → 27

Calls

Call 1

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

Outputs
1
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(+.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) 1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 1/2 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 1 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (*.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_i)) (/.f32 (.f32 1/2 (.f32 sinTheta_O sinTheta_O)) v) 1))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.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 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O)))))))
(+.f32 1 (+.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 (.f32 (.f32 1/6 (pow.f32 sinTheta_i 3)) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))))
(+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) (.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 1/2 (.f32 sinTheta_O (.f32 sinTheta_O (.f32 (/.f32 sinTheta_i v) (/.f32 sinTheta_i v)))) (fma.f32 1/6 (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1)))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) (fma.f32 1/6 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1))
1
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(+.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) 1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 1/2 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 1 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (*.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_i)) (/.f32 (.f32 1/2 (.f32 sinTheta_O sinTheta_O)) v) 1))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.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 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O)))))))
(+.f32 1 (+.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 (.f32 (.f32 1/6 (pow.f32 sinTheta_i 3)) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))))
(+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) (.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 1/2 (.f32 sinTheta_O (.f32 sinTheta_O (.f32 (/.f32 sinTheta_i v) (/.f32 sinTheta_i v)))) (fma.f32 1/6 (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1)))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) (fma.f32 1/6 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1))
1
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(+.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) 1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 1/2 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 1 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (*.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_i)) (/.f32 (.f32 1/2 (.f32 sinTheta_O sinTheta_O)) v) 1))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.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 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O)))))))
(+.f32 1 (+.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 (.f32 (.f32 1/6 (pow.f32 sinTheta_i 3)) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))))
(+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) (.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 1/2 (.f32 sinTheta_O (.f32 sinTheta_O (.f32 (/.f32 sinTheta_i v) (/.f32 sinTheta_i v)))) (fma.f32 1/6 (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1)))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) (fma.f32 1/6 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1))
1
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 sinTheta_i (/.f32 v sinTheta_O)))
(+.f32 1 (*.f32 (/.f32 sinTheta_i v) sinTheta_O))
(fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1)
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) 1)
(fma.f32 sinTheta_i (/.f32 sinTheta_O v) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (.f32 1/2 (/.f32 (*.f32 (pow.f32 sinTheta_i 2) (pow.f32 sinTheta_O 2)) (pow.f32 v 2)))))
(+.f32 1 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O))))))
(+.f32 1 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(fma.f32 1/2 (.f32 (.f32 sinTheta_O (/.f32 sinTheta_i v)) (*.f32 sinTheta_O (/.f32 sinTheta_i v))) (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_i)) (/.f32 (.f32 1/2 (.f32 sinTheta_O sinTheta_O)) v) 1))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) 1)
(+.f32 1 (+.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v) (+.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 (+.f32 (/.f32 sinTheta_i (/.f32 v sinTheta_O)) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 sinTheta_O 3))) (.f32 1/2 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (.f32 sinTheta_O sinTheta_O)))))))
(+.f32 1 (+.f32 (fma.f32 1/2 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v)) (.f32 (/.f32 sinTheta_i v) sinTheta_O)) (/.f32 (.f32 (.f32 1/6 (pow.f32 sinTheta_i 3)) (pow.f32 sinTheta_O 3)) (pow.f32 v 3))))
(+.f32 (fma.f32 (/.f32 sinTheta_i v) sinTheta_O 1) (fma.f32 1/6 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 (/.f32 v sinTheta_O) 3)) (.f32 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) v) (/.f32 (.f32 sinTheta_O sinTheta_O) v))))
(fma.f32 sinTheta_O (/.f32 sinTheta_i v) (fma.f32 1/2 (.f32 sinTheta_O (.f32 sinTheta_O (.f32 (/.f32 sinTheta_i v) (/.f32 sinTheta_i v)))) (fma.f32 1/6 (pow.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1)))
(fma.f32 sinTheta_O (+.f32 (/.f32 sinTheta_i v) (/.f32 (.f32 sinTheta_i (.f32 sinTheta_i 1/2)) (/.f32 v (/.f32 sinTheta_O v)))) (fma.f32 1/6 (pow.f32 (*.f32 sinTheta_i (/.f32 sinTheta_O v)) 3) 1))

localize63.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 39 to 30 computations (23.1% saved)

series3.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite105.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 104

Calls

Call 1

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

Outputs

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

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

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

140 → 126

Calls

Call 1

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

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

localize155.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 6931/10000 (/.f32 1 v))
✓	0.1b	(exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))
✓	0.4b	(/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))
✓	13.2b	(/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v)))

Compiler

Compiled 101 to 83 computations (17.8% saved)

series5.0ms (0%)

Counts

4 → 39

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	v	@	0	(/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v)))
1.0ms	v	@	inf	(/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v)))
0.0ms	v	@	-inf	(/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v)))
0.0ms	v	@	inf	(exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))
0.0ms	v	@	0	(/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))

rewrite100.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

505×	`log-prod_binary32`
301×	`pow2_binary32`
270×	`pow-prod-down_binary32`
208×	`expm1-udef_binary32`
208×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	263	45
2	3162	45

Stop Event

1×	node limit

Counts

4 → 197

Calls

Call 1

Inputs
(/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v)))
(/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))
(+.f32 6931/10000 (/.f32 1 v))

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

simplify62.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

772×	`fma-neg_binary32`
599×	`fma-def_binary32`
494×	`cancel-sign-sub-inv_binary32`
445×	`associate-/r/_binary32`
287×	`distribute-lft-out_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	558
1	186	556
2	468	540
3	1281	520
4	4053	520

Stop Event

1×	node limit

Counts

236 → 236

Calls

Call 1

Inputs
(/.f32 1 v)
(-.f32 (/.f32 1 v) 6931/10000)
(-.f32 (+.f32 (/.f32 1 v) (*.f32 48038761/100000000 v)) 6931/10000)
(-.f32 (+.f32 (/.f32 1 v) (+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (.f32 48038761/100000000 v))) 6931/10000)
(/.f32 10000/6931 (pow.f32 v 2))
(-.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (+.f32 (.f32 10000000000000000/2307722558415121 (/.f32 1 (pow.f32 v 5))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(/.f32 10000/6931 (pow.f32 v 2))
(-.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (+.f32 (.f32 10000000000000000/2307722558415121 (/.f32 1 (pow.f32 v 5))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(*.f32 48038761/100000000 v)
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (.f32 48038761/100000000 v))
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (+.f32 (.f32 2307722558415121/10000000000000000 (pow.f32 v 3)) (*.f32 48038761/100000000 v)))
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (+.f32 (.f32 2307722558415121/10000000000000000 (pow.f32 v 3)) (+.f32 (.f32 48038761/100000000 v) (.f32 -15994825052375203651/100000000000000000000 (pow.f32 v 4)))))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (+.f32 (/.f32 1 v) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (+.f32 (/.f32 1 v) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
1
(+.f32 1 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2))))
(-.f32 (+.f32 1 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1346550000000/332956652491 (/.f32 1 (pow.f32 v 4))))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
1
(+.f32 1 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2))))
(-.f32 (+.f32 1 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1346550000000/332956652491 (/.f32 1 (pow.f32 v 4))))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(/.f32 1 v)
6931/10000
6931/10000

Outputs
(/.f32 1 v)
(-.f32 (/.f32 1 v) 6931/10000)
(+.f32 (/.f32 1 v) -6931/10000)
(-.f32 (+.f32 (/.f32 1 v) (*.f32 48038761/100000000 v)) 6931/10000)
(+.f32 (+.f32 (/.f32 1 v) (*.f32 v 48038761/100000000)) -6931/10000)
(+.f32 (/.f32 1 v) (fma.f32 v 48038761/100000000 -6931/10000))
(+.f32 (fma.f32 v 48038761/100000000 (/.f32 1 v)) -6931/10000)
(-.f32 (+.f32 (/.f32 1 v) (+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (.f32 48038761/100000000 v))) 6931/10000)
(+.f32 (/.f32 1 v) (-.f32 (fma.f32 -332956652491/1000000000000 (.f32 v v) (.f32 v 48038761/100000000)) 6931/10000))
(+.f32 (/.f32 1 v) (+.f32 (fma.f32 -332956652491/1000000000000 (.f32 v v) (.f32 v 48038761/100000000)) -6931/10000))
(+.f32 (/.f32 1 v) (fma.f32 v 48038761/100000000 (fma.f32 v (*.f32 v -332956652491/1000000000000) -6931/10000)))
(+.f32 (/.f32 1 v) (fma.f32 v (fma.f32 v -332956652491/1000000000000 48038761/100000000) -6931/10000))
(/.f32 10000/6931 (pow.f32 v 2))
(/.f32 10000/6931 (*.f32 v v))
(-.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3)))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3))) (/.f32 1000000000000/332956652491 (pow.f32 v 4)))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (+.f32 (.f32 10000000000000000/2307722558415121 (/.f32 1 (pow.f32 v 5))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) (/.f32 10000000000000000/2307722558415121 (pow.f32 v 5)))))
(+.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 -100000000/48038761 (pow.f32 v 3)) (/.f32 -10000000000000000/2307722558415121 (pow.f32 v 5)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3))) (/.f32 -10000000000000000/2307722558415121 (pow.f32 v 5))))
(/.f32 10000/6931 (pow.f32 v 2))
(/.f32 10000/6931 (*.f32 v v))
(-.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3)))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3))) (/.f32 1000000000000/332956652491 (pow.f32 v 4)))
(-.f32 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1000000000000/332956652491 (/.f32 1 (pow.f32 v 4)))) (+.f32 (.f32 10000000000000000/2307722558415121 (/.f32 1 (pow.f32 v 5))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) (/.f32 10000000000000000/2307722558415121 (pow.f32 v 5)))))
(+.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 -100000000/48038761 (pow.f32 v 3)) (/.f32 -10000000000000000/2307722558415121 (pow.f32 v 5)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (-.f32 (/.f32 1000000000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3))) (/.f32 -10000000000000000/2307722558415121 (pow.f32 v 5))))
(*.f32 48038761/100000000 v)
(*.f32 v 48038761/100000000)
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (.f32 48038761/100000000 v))
(fma.f32 -332956652491/1000000000000 (.f32 v v) (.f32 v 48038761/100000000))
(.f32 v (+.f32 48038761/100000000 (.f32 v -332956652491/1000000000000)))
(*.f32 v (fma.f32 v -332956652491/1000000000000 48038761/100000000))
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (+.f32 (.f32 2307722558415121/10000000000000000 (pow.f32 v 3)) (*.f32 48038761/100000000 v)))
(fma.f32 -332956652491/1000000000000 (.f32 v v) (fma.f32 2307722558415121/10000000000000000 (pow.f32 v 3) (.f32 v 48038761/100000000)))
(fma.f32 -332956652491/1000000000000 (.f32 v v) (fma.f32 v 48038761/100000000 (.f32 (pow.f32 v 3) 2307722558415121/10000000000000000)))
(fma.f32 v 48038761/100000000 (.f32 (.f32 v v) (+.f32 -332956652491/1000000000000 (*.f32 v 2307722558415121/10000000000000000))))
(.f32 v (+.f32 (.f32 v (fma.f32 v 2307722558415121/10000000000000000 -332956652491/1000000000000)) 48038761/100000000))
(+.f32 (.f32 -332956652491/1000000000000 (pow.f32 v 2)) (+.f32 (.f32 2307722558415121/10000000000000000 (pow.f32 v 3)) (+.f32 (.f32 48038761/100000000 v) (.f32 -15994825052375203651/100000000000000000000 (pow.f32 v 4)))))
(fma.f32 -332956652491/1000000000000 (.f32 v v) (fma.f32 2307722558415121/10000000000000000 (pow.f32 v 3) (fma.f32 48038761/100000000 v (.f32 (pow.f32 v 4) -15994825052375203651/100000000000000000000))))
(fma.f32 -332956652491/1000000000000 (.f32 v v) (fma.f32 (pow.f32 v 3) 2307722558415121/10000000000000000 (fma.f32 (pow.f32 v 4) -15994825052375203651/100000000000000000000 (.f32 v 48038761/100000000))))
(fma.f32 v (.f32 v -332956652491/1000000000000) (fma.f32 v 48038761/100000000 (fma.f32 (pow.f32 v 4) -15994825052375203651/100000000000000000000 (.f32 (pow.f32 v 3) 2307722558415121/10000000000000000))))
(fma.f32 v (fma.f32 v -332956652491/1000000000000 48038761/100000000) (.f32 (pow.f32 v 3) (+.f32 (.f32 v -15994825052375203651/100000000000000000000) 2307722558415121/10000000000000000)))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(+.f32 6931/10000 (/.f32 -1 v))
(-.f32 (+.f32 6931/10000 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 10000/6931 (*.f32 v v))) (/.f32 1 v))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 6931/10000 (/.f32 -1 v)))
(+.f32 6931/10000 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -1 v)))
(-.f32 (+.f32 6931/10000 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (+.f32 (/.f32 1 v) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(-.f32 (+.f32 6931/10000 (/.f32 10000/6931 (*.f32 v v))) (+.f32 (/.f32 1 v) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 100000000/48038761 (pow.f32 v 3)))))
(+.f32 6931/10000 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 -100000000/48038761 (pow.f32 v 3)) (/.f32 -1 v))))
(+.f32 6931/10000 (-.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) (/.f32 -1 v))))
(+.f32 6931/10000 (-.f32 (/.f32 -1 v) (.f32 (/.f32 1 (.f32 v v)) (-.f32 (/.f32 100000000/48038761 v) 10000/6931))))
6931/10000
(-.f32 6931/10000 (/.f32 1 v))
(+.f32 6931/10000 (/.f32 -1 v))
(-.f32 (+.f32 6931/10000 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (/.f32 1 v))
(-.f32 (+.f32 6931/10000 (/.f32 10000/6931 (*.f32 v v))) (/.f32 1 v))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 6931/10000 (/.f32 -1 v)))
(+.f32 6931/10000 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -1 v)))
(-.f32 (+.f32 6931/10000 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (+.f32 (/.f32 1 v) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3)))))
(-.f32 (+.f32 6931/10000 (/.f32 10000/6931 (*.f32 v v))) (+.f32 (/.f32 1 v) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 100000000/48038761 (pow.f32 v 3)))))
(+.f32 6931/10000 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 (/.f32 -100000000/48038761 (pow.f32 v 3)) (/.f32 -1 v))))
(+.f32 6931/10000 (-.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) (/.f32 -1 v))))
(+.f32 6931/10000 (-.f32 (/.f32 -1 v) (.f32 (/.f32 1 (.f32 v v)) (-.f32 (/.f32 100000000/48038761 v) 10000/6931))))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (.f32 (.f32 v v) (+.f32 (/.f32 1 v) 6931/10000))))
(exp.f32 (/.f32 (/.f32 1 (*.f32 v v)) (+.f32 (/.f32 1 v) 6931/10000)))
(exp.f32 (/.f32 (/.f32 1 v) (+.f32 1 (*.f32 v 6931/10000))))
(exp.f32 (/.f32 1 (fma.f32 v (*.f32 v 6931/10000) v)))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (.f32 (.f32 v v) (+.f32 (/.f32 1 v) 6931/10000))))
(exp.f32 (/.f32 (/.f32 1 (*.f32 v v)) (+.f32 (/.f32 1 v) 6931/10000)))
(exp.f32 (/.f32 (/.f32 1 v) (+.f32 1 (*.f32 v 6931/10000))))
(exp.f32 (/.f32 1 (fma.f32 v (*.f32 v 6931/10000) v)))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (.f32 (.f32 v v) (+.f32 (/.f32 1 v) 6931/10000))))
(exp.f32 (/.f32 (/.f32 1 (*.f32 v v)) (+.f32 (/.f32 1 v) 6931/10000)))
(exp.f32 (/.f32 (/.f32 1 v) (+.f32 1 (*.f32 v 6931/10000))))
(exp.f32 (/.f32 1 (fma.f32 v (*.f32 v 6931/10000) v)))
(exp.f32 (/.f32 1 (*.f32 (pow.f32 v 2) (+.f32 6931/10000 (/.f32 1 v)))))
(exp.f32 (/.f32 1 (.f32 (.f32 v v) (+.f32 (/.f32 1 v) 6931/10000))))
(exp.f32 (/.f32 (/.f32 1 (*.f32 v v)) (+.f32 (/.f32 1 v) 6931/10000)))
(exp.f32 (/.f32 (/.f32 1 v) (+.f32 1 (*.f32 v 6931/10000))))
(exp.f32 (/.f32 1 (fma.f32 v (*.f32 v 6931/10000) v)))
1
(+.f32 1 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2))))
(+.f32 1 (/.f32 10000/6931 (*.f32 v v)))
(-.f32 (+.f32 1 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (/.f32 10000/6931 (*.f32 v v))) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 1 (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (+.f32 1 (/.f32 10000/6931 (*.f32 v v))) (/.f32 -100000000/48038761 (pow.f32 v 3)))
(-.f32 (+.f32 1 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1346550000000/332956652491 (/.f32 1 (pow.f32 v 4))))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 1346550000000/332956652491 (pow.f32 v 4)))) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1346550000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (+.f32 1 (/.f32 1346550000000/332956652491 (pow.f32 v 4))) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1346550000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) -1)))
(+.f32 (/.f32 10000/6931 (.f32 v v)) (+.f32 1 (.f32 (/.f32 1 (pow.f32 v 3)) (-.f32 (/.f32 1346550000000/332956652491 v) 100000000/48038761))))
1
(+.f32 1 (*.f32 10000/6931 (/.f32 1 (pow.f32 v 2))))
(+.f32 1 (/.f32 10000/6931 (*.f32 v v)))
(-.f32 (+.f32 1 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2)))) (.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (/.f32 10000/6931 (*.f32 v v))) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (+.f32 1 (/.f32 -100000000/48038761 (pow.f32 v 3))))
(+.f32 (+.f32 1 (/.f32 10000/6931 (*.f32 v v))) (/.f32 -100000000/48038761 (pow.f32 v 3)))
(-.f32 (+.f32 1 (+.f32 (.f32 10000/6931 (/.f32 1 (pow.f32 v 2))) (.f32 1346550000000/332956652491 (/.f32 1 (pow.f32 v 4))))) (*.f32 100000000/48038761 (/.f32 1 (pow.f32 v 3))))
(-.f32 (+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (/.f32 1346550000000/332956652491 (pow.f32 v 4)))) (/.f32 100000000/48038761 (pow.f32 v 3)))
(+.f32 1 (+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1346550000000/332956652491 (pow.f32 v 4)) (/.f32 100000000/48038761 (pow.f32 v 3)))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (+.f32 1 (/.f32 1346550000000/332956652491 (pow.f32 v 4))) (/.f32 100000000/48038761 (pow.f32 v 3))))
(+.f32 (/.f32 10000/6931 (*.f32 v v)) (-.f32 (/.f32 1346550000000/332956652491 (pow.f32 v 4)) (+.f32 (/.f32 100000000/48038761 (pow.f32 v 3)) -1)))
(+.f32 (/.f32 10000/6931 (.f32 v v)) (+.f32 1 (.f32 (/.f32 1 (pow.f32 v 3)) (-.f32 (/.f32 1346550000000/332956652491 v) 100000000/48038761))))
(/.f32 1 v)
6931/10000
6931/10000

eval1.5s (8.6%)

Compiler: Compiled 17595 to 13887 computations (21.1% saved)

prune248.0ms (1.4%)

Pruning

34 alts after pruning (27 fresh and 7 done)

	Pruned	Kept	Total
New	782	13	795
Fresh	4	14	18
Picked	1	0	1
Done	0	7	7
Total	787	34	821

Error

0.0b

Counts

821 → 34

Alt Table

Click to see full alt table

Status	Error	Program
	19.5b	(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (.f32 (/.f32 (/.f32 1 v) 1) (/.f32 (/.f32 1 v) (+.f32 6931/10000 (/.f32 1 v)))))) (/.f32 1/2 v))
	0.1b	(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
✓	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	25.4b	(/.f32 cosTheta_i (/.f32 v cosTheta_O))
✓	0.1b	(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
	30.0b	(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
	15.2b	(*.f32 (/.f32 (exp.f32 (/.f32 332956652491/1000000000000 (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v)))) (exp.f32 (/.f32 (pow.f32 v -3) (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v))))) (/.f32 1/2 v))
✓	28.2b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
	0.2b	(.f32 (/.f32 (exp.f32 (.f32 v (+.f32 (*.f32 v (fma.f32 v 2307722558415121/10000000000000000 -332956652491/1000000000000)) 48038761/100000000))) (exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))) (/.f32 1/2 v))
✓	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(*.f32 (pow.f32 (E.f32) 6931/10000) (pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))
✓	28.4b	(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
	0.1b	(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
	0.1b	(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
	0.1b	(.f32 (pow.f32 (exp.f32 3) (.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1/3)) (/.f32 1/2 v))
	0.1b	(*.f32 (pow.f32 (exp.f32 1/2) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (pow.f32 (exp.f32 1/2) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
	30.0b	(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
	0.4b	(.f32 (pow.f32 (exp.f32 (.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 1/2 v))
	0.2b	(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
	0.1b	(.f32 (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (/.f32 1/2 v))
	0.1b	(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
	0.8b	(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
	30.0b	(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
✓	25.4b	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	30.0b	(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
✓	28.4b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	29.9b	1
	8.0b	(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
	19.7b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	0.4b	(.f32 (cbrt.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3)))) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (E.f32) (/.f32 -1 v)))
	15.2b	(*.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (pow.f32 (pow.f32 (E.f32) (/.f32 (pow.f32 v -2) (-.f32 48038761/100000000 (pow.f32 v -2)))) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))

Compiler

Compiled 630 to 517 computations (17.9% saved)

regimes699.0ms (3.9%)

Counts

65 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (cbrt.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3)))) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 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 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (.f32 (/.f32 (/.f32 1 v) 1) (/.f32 (/.f32 1 v) (+.f32 6931/10000 (/.f32 1 v)))))) (/.f32 1/2 v))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (E.f32) (/.f32 -1 v)))
(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))
(.f32 (cbrt.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))) (/.f32 1/2 v))
(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(.f32 (pow.f32 (exp.f32 3) (.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1/3)) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
(*.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))) (/.f32 1/2 v))
(.f32 (.f32 (pow.f32 (E.f32) 6931/10000) (pow.f32 (E.f32) (*.f32 (/.f32 -1 v) 1))) (/.f32 1/2 v))
(.f32 (.f32 (pow.f32 (exp.f32 2/3) (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (/.f32 1/2 v))
(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(*.f32 (pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
(.f32 (/.f32 (exp.f32 (.f32 v (+.f32 (*.f32 v (fma.f32 v 2307722558415121/10000000000000000 -332956652491/1000000000000)) 48038761/100000000))) (exp.f32 (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))) (/.f32 1/2 v))
(*.f32 (pow.f32 (E.f32) 6931/10000) (pow.f32 (E.f32) (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))
(exp.f32 (pow.f32 (cbrt.f32 (+.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) 3))
(.f32 (.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (E.f32) (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (/.f32 1/2 v))
(*.f32 (/.f32 (exp.f32 (/.f32 332956652491/1000000000000 (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v)))) (exp.f32 (/.f32 (pow.f32 v -3) (+.f32 (+.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 6931/10000 v))))) (/.f32 1/2 v))
(*.f32 (pow.f32 (E.f32) (pow.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 3)) (/.f32 1/2 v))
(*.f32 (pow.f32 (exp.f32 1/2) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) (pow.f32 (exp.f32 1/2) (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(*.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (pow.f32 (pow.f32 (E.f32) (/.f32 (pow.f32 v -2) (-.f32 48038761/100000000 (pow.f32 v -2)))) (-.f32 6931/10000 (/.f32 1 v)))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (pow.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) 2) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (-.f32 (/.f32 (-.f32 (fma.f32 cosTheta_i cosTheta_O (*.f32 sinTheta_i (neg.f32 sinTheta_O))) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(*.f32 (pow.f32 (cbrt.f32 (exp.f32 2)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))) (pow.f32 (cbrt.f32 (E.f32)) (+.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O (fma.f32 sinTheta_i sinTheta_O -1)) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))

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

Calls

11 calls:

95.0ms	(+.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))))
86.0ms	sinTheta_i
83.0ms	(+.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))))
76.0ms	sinTheta_O
66.0ms	cosTheta_O

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(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 1082 to 724 computations (33.1% saved)

regimes565.0ms (3.1%)

Counts

43 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (cbrt.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3)))) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 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 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (.f32 (/.f32 (/.f32 1 v) 1) (/.f32 (/.f32 1 v) (+.f32 6931/10000 (/.f32 1 v)))))) (/.f32 1/2 v))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (pow.f32 (E.f32) (/.f32 -1 v)))

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

Calls

11 calls:

77.0ms	v
76.0ms	cosTheta_O
67.0ms	(+.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))))
60.0ms	sinTheta_i
55.0ms	cosTheta_i

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(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 587 to 382 computations (34.9% saved)

regimes275.0ms (1.5%)

Counts

42 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(*.f32 (pow.f32 (E.f32) (+.f32 6931/10000 (/.f32 -1 v))) (/.f32 1/2 v))
(/.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (exp.f32 (/.f32 1 v)))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (cbrt.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3)))) (/.f32 1/2 v))
(.f32 (pow.f32 (exp.f32 (.f32 3 (-.f32 6931/10000 (/.f32 1 v)))) 1/3) (/.f32 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 (pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
(.f32 (/.f32 (exp.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v)))) (exp.f32 (.f32 (/.f32 (/.f32 1 v) 1) (/.f32 (/.f32 1 v) (+.f32 6931/10000 (/.f32 1 v)))))) (/.f32 1/2 v))

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

Calls

11 calls:

52.0ms	v
47.0ms	(+.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))))
24.0ms	cosTheta_O
23.0ms	sinTheta_i
23.0ms	sinTheta_O

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(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 575 to 373 computations (35.1% saved)

regimes166.0ms (0.9%)

Counts

32 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)
(*.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

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

Calls

7 calls:

58.0ms	sinTheta_i
20.0ms	cosTheta_i
18.0ms	sinTheta_O
18.0ms	cosTheta_O
16.0ms	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 292 to 171 computations (41.4% saved)

regimes138.0ms (0.8%)

Counts

28 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (/.f32 1/2 v) (exp.f32 (-.f32 (/.f32 1 v) 6931/10000)))
(/.f32 (*.f32 (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))) 1/2) v)

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

Calls

7 calls:

36.0ms	v
18.0ms	sinTheta_i
17.0ms	cosTheta_O
17.0ms	cosTheta_i
15.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

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

Compiler

Compiled 243 to 140 computations (42.4% saved)

regimes297.0ms (1.6%)

Counts

26 → 1

Calls

Call 1

Inputs
1
1
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 1 (/.f32 v (*.f32 cosTheta_i cosTheta_O)))
(+.f32 1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(-.f32 (+.f32 1 (*.f32 cosTheta_i (/.f32 cosTheta_O v))) 1)
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 (/.f32 1 v) (.f32 cosTheta_i cosTheta_O)))
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(+.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) 1)
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 1)
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) (neg.f32 v)))
(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
(*.f32 (exp.f32 (/.f32 -1 v)) (/.f32 1/2 v))
(exp.f32 (*.f32 (/.f32 cosTheta_i 1) (/.f32 cosTheta_O v)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))
(+.f32 1 (expm1.f32 (*.f32 (/.f32 sinTheta_i v) sinTheta_O)))
(exp.f32 (.f32 -1 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))

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

Calls

7 calls:

175.0ms	sinTheta_i
43.0ms	v
16.0ms	sinTheta_O
15.0ms	cosTheta_O
15.0ms	cosTheta_i

Results

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

Compiler

Compiled 223 to 124 computations (44.4% saved)

regimes113.0ms (0.6%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

8 calls:

37.0ms	cosTheta_i
12.0ms	cosTheta_O
11.0ms	sinTheta_i
11.0ms	v
11.0ms	sinTheta_O

Results

Error	Segments	Branch
8.0b	1	`cosTheta_i`
8.0b	1	`cosTheta_O`
8.0b	1	`sinTheta_i`
8.0b	1	`sinTheta_O`
8.0b	1	`v`
8.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
8.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
8.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 191 to 108 computations (43.5% saved)

regimes42.0ms (0.2%)

Counts

9 → 1

Calls

Call 1

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

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

Calls

7 calls:

6.0ms	sinTheta_O
6.0ms	cosTheta_O
6.0ms	v
6.0ms	sinTheta_i
6.0ms	cosTheta_i

Results

Error	Segments	Branch
19.5b	1	`cosTheta_i`
19.5b	1	`cosTheta_O`
19.5b	1	`sinTheta_i`
19.5b	1	`sinTheta_O`
19.5b	1	`v`
19.5b	1	`(*.f32 cosTheta_i cosTheta_O)`
19.5b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 94 to 59 computations (37.2% saved)

regimes30.0ms (0.2%)

Counts

6 → 1

Calls

Call 1

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

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

Calls

6 calls:

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

Results

Error	Segments	Branch
19.7b	1	`cosTheta_i`
19.7b	1	`cosTheta_O`
19.7b	1	`sinTheta_i`
19.7b	1	`sinTheta_O`
19.7b	1	`v`
19.7b	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 65 to 44 computations (32.3% saved)

regimes20.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Error	Segments	Branch
25.4b	1	`cosTheta_i`
25.4b	1	`cosTheta_O`
25.4b	1	`sinTheta_i`
25.4b	1	`sinTheta_O`
25.4b	1	`v`

Compiler

Compiled 42 to 34 computations (19% saved)

regimes31.0ms (0.2%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1
1

Outputs
1

Calls

5 calls:

8.0ms	cosTheta_i
7.0ms	cosTheta_O
7.0ms	sinTheta_i
5.0ms	sinTheta_O
3.0ms	v

Results

Error	Segments	Branch
29.9b	1	`cosTheta_i`
29.9b	1	`cosTheta_O`
29.9b	1	`sinTheta_i`
29.9b	1	`sinTheta_O`
29.9b	1	`v`

Compiler

Compiled 37 to 32 computations (13.5% saved)

simplify21.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary32`
7×	`+-commutative_binary32`
5×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`neg-sub0_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	135
1	62	135
2	69	135
3	71	135
4	72	135

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 145 to 121 computations (16.6% saved)

soundness0.0ms (0%)

end131.0ms (0.7%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 163 to 128 computations (21.5% saved)