Details

analyze841.0ms (5.4%)

Algorithm

1×

Search

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample4.1s (26.8%)

Results

4.0s	8256×	body	256	valid
53.0ms	143×	body	256	invalid

preprocess63.0ms (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)

simplify51.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(*.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)

localize107.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	6.9b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	7.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series36.0ms (0.2%)

Counts

4 → 120

Calls

48 calls:

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

rewrite242.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 185

Calls

Call 1

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

Outputs
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simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

946×	`associate-/l*_binary32`
693×	`associate-l_binary32`
589×	`associate-/r*_binary32`
364×	`fma-def_binary32`
265×	`associate-*r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

305 → 225

Calls

Call 1

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

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

localize81.0ms (0.5%)

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

Compiler

Compiled 90 to 42 computations (53.3% saved)

series96.0ms (0.6%)

Counts

4 → 180

Calls

54 calls:

Time	Variable		Point	Expression
56.0ms	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))
4.0ms	v	@	-inf	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
2.0ms	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	v	@	inf	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

rewrite128.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 196

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 1) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) -48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (/.f32 1 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (neg.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (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) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (-.f32 (fma.f32 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 sqrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x 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))))))))))
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simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

376 → 276

Calls

Call 1

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

eval359.0ms (2.3%)

Compiler: Compiled 16612 to 9267 computations (44.2% saved)

prune217.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	491	10	501
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	493	10	503

Error

0.0b

Counts

503 → 10

Alt Table

Click to see full alt table

Status	Error	Program
▶	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))
	0.2b	(.f32 (.f32 (exp.f32 6931/10000) (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
▶	28.6b	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.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)))
	28.6b	(.f32 (exp.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 1/2 v))
	30.5b	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
▶	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)))) 3)
	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 390 to 304 computations (22.1% saved)

localize60.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
✓	0.1b	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	7.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 71 to 36 computations (49.3% saved)

series13.0ms (0.1%)

Counts

3 → 37

Calls

27 calls:

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

rewrite95.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 266

Calls

Call 1

Inputs

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

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

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

Outputs

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(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)))))))

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

303 → 293

Calls

Call 1

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

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

localize24.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 20 to 17 computations (15% saved)

series2.0ms (0%)

Counts

1 → 0

Calls

3 calls:

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

rewrite53.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize40.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 43 to 15 computations (65.1% saved)

series59.0ms (0.4%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
46.0ms	sinTheta_O	@	-inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	v	@	inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	0	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	v	@	0	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
1.0ms	sinTheta_i	@	inf	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))

rewrite80.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 211

Calls

Call 1

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

Outputs

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

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

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

simplify112.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

319 → 231

Calls

Call 1

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

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

localize74.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
✓	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	7.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series25.0ms (0.2%)

Counts

3 → 52

Calls

27 calls:

Time	Variable		Point	Expression
4.0ms	cosTheta_O	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
3.0ms	cosTheta_i	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
3.0ms	v	@	0	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
3.0ms	v	@	-inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
2.0ms	v	@	inf	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))

rewrite120.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs

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

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

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

Outputs

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

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

280 → 273

Calls

Call 1

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

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

localize108.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
✓	0.1b	(exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v))
✓	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	3.0b	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 98 to 47 computations (52% saved)

series213.0ms (1.4%)

Counts

4 → 180

Calls

45 calls:

Time	Variable		Point	Expression
69.0ms	v	@	0	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))
48.0ms	cosTheta_i	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
35.0ms	cosTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
11.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
9.0ms	v	@	-inf	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

rewrite123.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

831×	`fma-def_binary32`
535×	`fma-neg_binary32`
385×	`expm1-udef_binary32`
385×	`log1p-udef_binary32`
223×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	66
1	443	62
2	5960	62

Stop Event

1×	node limit

Counts

4 → 241

Calls

Call 1

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

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

simplify179.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

556×	`*-commutative_binary32`
490×	`fma-def_binary32`
384×	`fma-neg_binary32`
382×	`associate-/r/_binary32`
365×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	5266
1	657	4892
2	2592	4638
3	7537	4638

Stop Event

1×	node limit

Counts

421 → 314

Calls

Call 1

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

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

eval826.0ms (5.4%)

Compiler: Compiled 30846 to 18157 computations (41.1% saved)

prune908.0ms (5.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	1216	11	1227
Fresh	3	2	5
Picked	1	0	1
Done	4	0	4
Total	1224	13	1237

Error

0.0b

Counts

1237 → 13

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.1b	(*.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))
	0.1b	(*.f32 (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))) (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (/.f32 1/2 v))
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)))) 3)
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	30.6b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
▶	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v)) (/.f32 (.f32 (exp.f32 6931/10000) 1/2) v))
	27.3b	(exp.f32 (/.f32 cosTheta_O (/.f32 v cosTheta_i)))
▶	30.5b	(/.f32 1/2 v)
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
▶	0.6b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))

Compiler

Compiled 532 to 420 computations (21.1% saved)

localize158.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))
✓	0.0b	(log.f32 (/.f32 1/2 v))
✓	0.0b	(+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))
✓	0.1b	(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))

Compiler

Compiled 78 to 47 computations (39.7% saved)

series22.0ms (0.1%)

Counts

4 → 100

Calls

30 calls:

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

rewrite156.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

659×	`prod-diff_binary32`
632×	`log-prod_binary32`
253×	`fma-def_binary32`
246×	`pow1/3_binary32`
243×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	55
1	275	55
2	3562	55

Stop Event

1×	node limit

Counts

4 → 178

Calls

Call 1

Inputs
(exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
(+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))
(log.f32 (/.f32 1/2 v))
(fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.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 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (pow.f32 v -1) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))) (/.f32 1/2 v))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 2) (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (/.f32 1/2 v)) 2) (.f32 (cbrt.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 1/2 v)) (.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))) (.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 1/2 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 -1/2 (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))) (sqrt.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 1/2 v) (exp.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) 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simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

864×	`times-frac_binary32`
588×	`associate-/l*_binary32`
436×	`associate-r_binary32`
401×	`associate-l_binary32`
324×	`associate-/r*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	99	2025
1	287	1568
2	1054	1495
3	7367	1481

Stop Event

1×	node limit

Counts

278 → 216

Calls

Call 1

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

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

localize10.0ms (0.1%)

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

localize29.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 32 to 16 computations (50% saved)

series10.0ms (0.1%)

Counts

2 → 40

Calls

18 calls:

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

rewrite81.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 179

Calls

Call 1

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

Outputs

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

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

219 → 197

Calls

Call 1

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

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

localize102.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 89 to 41 computations (53.9% saved)

series20.0ms (0.1%)

Counts

2 → 72

Calls

18 calls:

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

rewrite81.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

696×	`fma-def_binary32`
446×	`fma-neg_binary32`
364×	`expm1-udef_binary32`
364×	`log1p-udef_binary32`
210×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	38
1	415	36
2	5666	36

Stop Event

1×	node limit

Counts

2 → 69

Calls

Call 1

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

Outputs

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

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

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

907×	`associate-/l*_binary32`
779×	`associate-r_binary32`
671×	`associate-/r*_binary32`
666×	`associate-l_binary32`
298×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	139	2544
1	471	2436
2	1505	2314
3	7997	2314

Stop Event

1×	node limit

Counts

141 → 99

Calls

Call 1

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

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

localize130.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O))
✓	0.0b	(+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000)
✓	0.1b	(exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))
✓	0.2b	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))

Compiler

Compiled 135 to 61 computations (54.8% saved)

series95.0ms (0.6%)

Counts

3 → 168

Calls

45 calls:

Time	Variable		Point	Expression
33.0ms	sinTheta_O	@	0	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))
7.0ms	cosTheta_O	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))
5.0ms	cosTheta_i	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))
4.0ms	sinTheta_i	@	0	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))
4.0ms	sinTheta_O	@	inf	(cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v) 6931/10000))))

rewrite94.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

728×	`fma-def_binary32`
519×	`fma-neg_binary32`
372×	`expm1-udef_binary32`
372×	`log1p-udef_binary32`
216×	`add-sqr-sqrt_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	69
1	428	63
2	5800	63

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs

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

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

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

Outputs

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

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

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

simplify332.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

456×	`distribute-rgt-in_binary32`
446×	`distribute-lft-in_binary32`
408×	`associate-r_binary32`
307×	`associate-/l/_binary32`
290×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	8810
1	946	8639
2	3978	7174

Stop Event

1×	node limit

Counts

273 → 172

Calls

Call 1

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

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

eval723.0ms (4.7%)

Compiler: Compiled 34392 to 20130 computations (41.5% saved)

prune201.0ms (1.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	1087	8	1095
Fresh	2	6	8
Picked	1	0	1
Done	4	0	4
Total	1094	14	1108

Error

0.0b

Counts

1108 → 14

Alt Table

Click to see full alt table

Status	Error	Program
	30.0b	1
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (*.f32 sinTheta_i sinTheta_O)) 1) v)) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
▶	0.1b	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v))))
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))
▶	0.1b	(*.f32 (exp.f32 6931/10000) (pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v)))))
▶	0.6b	(exp.f32 (/.f32 -1 v))
▶	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(*.f32 (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))) (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (/.f32 1/2 v))
▶	0.1b	(pow.f32 (.f32 (pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3) (cbrt.f32 1/2)) 3)
	0.1b	(*.f32 (exp.f32 6931/10000) (exp.f32 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	0.1b	(pow.f32 (E.f32) (+.f32 (/.f32 (-.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (.f32 sinTheta_i sinTheta_O)) 1) v) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	0.1b	(pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) 6931/10000)))) 3)
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))

Compiler

Compiled 566 to 464 computations (18% saved)

localize114.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
	0.1b	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.3b	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
	7.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 148 to 87 computations (41.2% saved)

series24.0ms (0.2%)

Counts

1 → 24

Calls

9 calls:

Time	Variable		Point	Expression
6.0ms	v	@	-inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
4.0ms	cosTheta_O	@	-inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
3.0ms	cosTheta_i	@	0	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
2.0ms	cosTheta_i	@	inf	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)
2.0ms	cosTheta_O	@	0	(pow.f32 (/.f32 (.f32 1 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))) v) 1/3)

rewrite69.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	23
1	357	20
2	4739	18

Stop Event

1×	node limit

Counts

1 → 24

Calls

Call 1

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

Outputs

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

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

895×	`times-frac_binary32`
412×	`fma-def_binary32`
385×	`unswap-sqr_binary32`
374×	`fma-neg_binary32`
371×	`*-commutative_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	111	1684
1	350	1621
2	1361	1579
3	6727	1575

Stop Event

1×	node limit

Counts

48 → 38

Calls

Call 1

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

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

localize15.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 14 to 11 computations (21.4% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite41.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

31 → 30

Calls

Call 1

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

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

localize47.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 40 to 32 computations (20% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite68.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

498×	`log-prod_binary32`
389×	`exp-prod_binary32`
304×	`pow-prod-down_binary32`
290×	`prod-exp_binary32`
270×	`pow2_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	223	29
2	2610	27

Stop Event

1×	node limit

Counts

2 → 66

Calls

Call 1

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

Outputs

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

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

simplify63.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-l_binary32`
434×	`associate-r_binary32`
339×	`fma-def_binary32`
327×	`associate-/r/_binary32`
303×	`distribute-neg-frac_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	464
1	133	464
2	314	428
3	822	410
4	2995	410
5	6621	410

Stop Event

1×	node limit

Counts

90 → 84

Calls

Call 1

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

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

localize80.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f32 (/.f32 1/2 v))
	0.1b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
✓	0.1b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	3.0b	(exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))

Compiler

Compiled 70 to 45 computations (35.7% saved)

series6.0ms (0%)

Counts

1 → 36

Calls

9 calls:

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

rewrite70.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`log-prod_binary32`
641×	`prod-diff_binary32`
328×	`fma-def_binary32`
291×	`expm1-udef_binary32`
291×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	342	21
2	4414	21

Stop Event

1×	node limit

Counts

1 → 18

Calls

Call 1

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

Outputs

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

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

852×	`associate-/l*_binary32`
775×	`associate-l_binary32`
618×	`associate-/r*_binary32`
276×	`*-commutative_binary32`
237×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1460
1	327	1354
2	1369	1204
3	6865	1179

Stop Event

1×	node limit

Counts

54 → 47

Calls

Call 1

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

localize123.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 85 to 54 computations (36.5% saved)

series4.0ms (0%)

Counts

1 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	v	@	inf	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
1.0ms	v	@	0	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
0.0ms	v	@	-inf	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
0.0ms	cosTheta_i	@	0	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))
0.0ms	cosTheta_O	@	0	(pow.f32 (exp.f32 1) (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (/.f32 -1 v))))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`log-prod_binary32`
659×	`prod-diff_binary32`
265×	`expm1-udef_binary32`
265×	`log1p-udef_binary32`
257×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	314	19
2	3973	19

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

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

Outputs

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

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

862×	`times-frac_binary32`
584×	`associate-/l*_binary32`
434×	`associate-r_binary32`
397×	`associate-l_binary32`
322×	`associate-/r*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	1351
1	256	1096
2	985	968
3	7128	949

Stop Event

1×	node limit

Counts

57 → 43

Calls

Call 1

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

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

eval592.0ms (3.8%)

Compiler: Compiled 19681 to 14400 computations (26.8% saved)

prune491.0ms (3.2%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	748	10	758
Fresh	5	4	9
Picked	1	0	1
Done	2	2	4
Total	756	16	772

Error

0.0b

Counts

772 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	0.1b	(pow.f32 (*.f32 (pow.f32 (/.f32 (exp.f32 (-.f32 6931/10000 (/.f32 1 v))) v) 1/3) (cbrt.f32 1/2)) 3)
	0.1b	(/.f32 (.f32 (.f32 1/2 (exp.f32 (/.f32 -1 v))) (exp.f32 6931/10000)) v)
	0.1b	(*.f32 (pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 2))) (cbrt.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) (/.f32 1/2 v))
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)))
	0.2b	(.f32 (exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v)) (/.f32 (*.f32 (exp.f32 6931/10000) 1/2) v))
	0.2b	(*.f32 (pow.f32 (pow.f32 (E.f32) (pow.f32 v -1/2)) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (sqrt.f32 v))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
	30.0b	1
	0.1b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.1b	(*.f32 (exp.f32 6931/10000) (pow.f32 (exp.f32 1) (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	0.1b	(*.f32 (exp.f32 6931/10000) (exp.f32 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
	0.1b	(pow.f32 (exp.f32 1) (+.f32 (/.f32 -1 v) (-.f32 6931/10000 (log.f32 (*.f32 v 2)))))
✓	0.6b	(exp.f32 (/.f32 -1 v))
	0.2b	(*.f32 (exp.f32 (/.f32 -1 v)) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
✓	0.1b	(.f32 (exp.f32 6931/10000) (.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v))))
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 (/.f32 -1 v) 6931/10000)))) 3)
	0.2b	(*.f32 (pow.f32 (exp.f32 (cbrt.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (cbrt.f32 (pow.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 2))) (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))

Compiler

Compiled 295 to 251 computations (14.9% saved)

regimes333.0ms (2.2%)

Counts

41 → 1

Calls

Call 1

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

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

Calls

11 calls:

50.0ms	sinTheta_O
40.0ms	cosTheta_i
32.0ms	(*.f32 sinTheta_i sinTheta_O)
27.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
23.0ms	(*.f32 cosTheta_i cosTheta_O)

Results

Error	Segments	Branch
0.1b	1	`cosTheta_i`
0.1b	1	`cosTheta_O`
0.1b	1	`sinTheta_i`
0.1b	1	`sinTheta_O`
0.1b	1	`v`
0.1b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.1b	1	`(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 771 to 541 computations (29.8% saved)

regimes136.0ms (0.9%)

Counts

33 → 1

Calls

Call 1

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

Calls

9 calls:

22.0ms	sinTheta_O
15.0ms	cosTheta_O
15.0ms	sinTheta_i
15.0ms	cosTheta_i
15.0ms	v

Results

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

Compiler

Compiled 534 to 371 computations (30.5% saved)

regimes121.0ms (0.8%)

Counts

20 → 1

Calls

Call 1

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

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

Calls

7 calls:

22.0ms	sinTheta_O
21.0ms	sinTheta_i
21.0ms	cosTheta_O
17.0ms	cosTheta_i
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 256 to 182 computations (28.9% saved)

regimes101.0ms (0.7%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

7 calls:

53.0ms	sinTheta_i
9.0ms	cosTheta_i
7.0ms	sinTheta_O
7.0ms	cosTheta_O
7.0ms	v

Results

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

Compiler

Compiled 157 to 114 computations (27.4% saved)

regimes40.0ms (0.3%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Error	Segments	Branch
0.6b	1	`cosTheta_i`
0.6b	1	`cosTheta_O`
0.6b	1	`sinTheta_i`
0.6b	1	`sinTheta_O`
0.6b	1	`v`
0.6b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.6b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 98 to 75 computations (23.5% saved)

regimes74.0ms (0.5%)

Accuracy

Total -0.7b remaining (-2.2%)

Threshold costs -0.7b (-2.2%)

Counts

3 → 1

Calls

Call 1

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

Outputs
1

Calls

6 calls:

38.0ms	cosTheta_O
4.0ms	v
4.0ms	cosTheta_i
3.0ms	sinTheta_i
3.0ms	sinTheta_O

Results

Error	Segments	Branch
30.0b	1	`cosTheta_i`
30.0b	1	`cosTheta_O`
30.0b	1	`sinTheta_i`
30.0b	1	`sinTheta_O`
30.0b	1	`v`
30.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 60 to 48 computations (20% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`*-commutative_binary32`
10×	`+-commutative_binary32`
8×	`sub-neg_binary32`
5×	`neg-sub0_binary32`
5×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	4294967372
1	60	4294967372
2	71	4294967372
3	83	4294967372
4	91	4294967372
5	96	4294967372
6	98	4294967372

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 96 to 81 computations (15.6% saved)

soundness0.0ms (0%)

end134.0ms (0.9%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 151 to 128 computations (15.2% saved)