Details

analyze960.0ms (4.9%)

Algorithm

1×

Search

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

Compiler

Compiled 69 to 51 computations (26.1% saved)

sample3.9s (19.9%)

Results

3.8s	8256×	body	256	valid
36.0ms	111×	body	256	invalid

preprocess64.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
0
2
3
2
4

Call 2

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval1.0ms (0%)

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

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

0.0b

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

▶

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))

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize132.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
✓	0.1b	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v))
✓	7.5b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	8.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series70.0ms (0.4%)

Counts

4 → 120

Calls

48 calls:

Time	Variable		Point	Expression
20.0ms	v	@	inf	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
9.0ms	cosTheta_i	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
7.0ms	sinTheta_i	@	0	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
6.0ms	v	@	-inf	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))
2.0ms	v	@	0	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

rewrite163.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 203

Calls

Call 1

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

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

simplify151.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

323 → 228

Calls

Call 1

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

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

localize159.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 90 to 42 computations (53.3% saved)

series57.0ms (0.3%)

Counts

4 → 180

Calls

54 calls:

Time	Variable		Point	Expression
24.0ms	sinTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	cosTheta_i	@	0	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	v	@	inf	(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
1.0ms	v	@	inf	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
1.0ms	cosTheta_i	@	0	(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

rewrite205.0ms (1.1%)

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)
(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(*.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 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 1 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 (neg.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (+.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 -1 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 (neg.f32 (pow.f32 (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 2)) (cbrt.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (-.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 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (+.f32 6931/10000 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 2 (.f32 1/3 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (.f32 1/3 (-.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 (.f32 1/2 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (.f32 1/2 (-.f32 (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 (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 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (pow.f32 (cbrt.f32 (-.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 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 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simplify169.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

860×	`associate-/r*_binary32`
743×	`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))
(-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.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 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
(-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))
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Outputs
6931/10000
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(/.f32 cosTheta_i (/.f32 v cosTheta_O))
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
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6931/10000
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
6931/10000
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(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
6931/10000
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(+.f32 (.f32 1/4 (/.f32 (.f32 (pow.f32 sinTheta_i 2) (.f32 (pow.f32 sinTheta_O 2) (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (+.f32 (.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 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))) (.f32 v v)) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) (pow.f32 sinTheta_O 3)))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) v)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (*.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3)) (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 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))) (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 (.f32 (pow.f32 sinTheta_i 3) -1/12) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3))) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_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 (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 (+.f32 6931/10000 (/.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 1/2 (/.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) v))
(+.f32 (.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))))) (pow.f32 v 2))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) v)))
(fma.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))) (.f32 v v)) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.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 (.f32 sinTheta_i -1/2) (/.f32 (*.f32 v v) 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 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))) (.f32 v v)) (*.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.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 (.f32 sinTheta_i -1/2) (/.f32 (*.f32 v v) 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 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) (.f32 sinTheta_O sinTheta_O)))) (fma.f32 -1/2 (/.f32 (.f32 sinTheta_i (.f32 sinTheta_O (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))))) (.f32 v v)) (fma.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 4) (.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) (pow.f32 sinTheta_O 3)))) (.f32 1/2 (/.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 cosTheta_i (/.f32 v cosTheta_O))) (/.f32 1 v))) v)))))
(fma.f32 1/4 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (pow.f32 v 3)) (.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 sinTheta_O sinTheta_O))) (fma.f32 -1/2 (.f32 (.f32 sinTheta_i (/.f32 sinTheta_O v)) (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v)) (fma.f32 1/2 (/.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) v) (*.f32 -1/12 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3)) (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 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))) (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 (.f32 (pow.f32 sinTheta_i 3) -1/12) (/.f32 (pow.f32 v 4) (pow.f32 sinTheta_O 3))) (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_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 (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))))

eval624.0ms (3.2%)

Compiler: Compiled 16139 to 8858 computations (45.1% saved)

prune122.0ms (0.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	496	8	504
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	498	8	506

Error

0.0b

Counts

506 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	28.7b	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
▶	0.0b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	0.2b	(*.f32 (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) (/.f32 1/2 v))
	0.0b	(*.f32 (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) (/.f32 1/2 v))
	0.3b	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
	30.5b	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
▶	30.5b	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))

Compiler

Compiled 310 to 236 computations (23.9% saved)

localize144.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
✓	0.0b	(+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)))
✓	0.0b	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
	8.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series20.0ms (0.1%)

Counts

3 → 52

Calls

27 calls:

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

rewrite161.0ms (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	68
1	360	68
2	5231	62

Stop Event

1×	node limit

Counts

3 → 233

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify76.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	1688
1	308	1532
2	1164	1390
3	6881	1352

Stop Event

1×	node limit

Counts

285 → 278

Calls

Call 1

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

localize24.0ms (0.1%)

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)
0.0ms	v	@	inf	(/.f32 (exp.f32 6931/10000) v)
0.0ms	v	@	-inf	(/.f32 (exp.f32 6931/10000) v)

rewrite64.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 30

Calls

Call 1

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

Outputs

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

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

30 → 30

Calls

Call 1

Inputs

Outputs

localize77.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 41 to 15 computations (63.4% saved)

series26.0ms (0.1%)

Counts

3 → 108

Calls

27 calls:

Time	Variable		Point	Expression
3.0ms	sinTheta_O	@	inf	(exp.f32 (*.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i)))
2.0ms	sinTheta_O	@	0	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
2.0ms	sinTheta_i	@	inf	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
1.0ms	sinTheta_O	@	inf	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
1.0ms	v	@	inf	(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))

rewrite110.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 202

Calls

Call 1

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

Outputs

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

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

simplify139.0ms (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

310 → 222

Calls

Call 1

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

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

localize62.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v)))
✓	0.0b	(-.f32 (+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))
✓	0.1b	(+.f32 6931/10000 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	8.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 71 to 36 computations (49.3% saved)

series9.0ms (0%)

Counts

3 → 37

Calls

27 calls:

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

rewrite104.0ms (0.5%)

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))

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 48038761/100000000 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))) (/.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2) (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (cbrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2)) (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3)) (/.f32 1 (fma.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2)) (/.f32 1 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000) (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)) (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3)) (fma.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3)) (+.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2) (-.f32 48038761/100000000 (/.f32 6931/10000 (/.f32 v (*.f32 cosTheta_i cosTheta_O))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2)) (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 332956652491/1000000000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 3))) (neg.f32 (fma.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000) 48038761/100000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 48038761/100000000 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2))) (neg.f32 (-.f32 6931/10000 (*.f32 (/.f32 cosTheta_i v) cosTheta_O))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 (*.f32 (/.f32 cosTheta_i v) cosTheta_O) 2) 48038761/100000000) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O -6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O 6931/10000)) 2)))) (#(struct:change #<rule egg-rr> 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simplify59.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	79	773
1	242	754
2	843	732
3	5477	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
(-.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)))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/6 (/.f32 (.f32 (pow.f32 cosTheta_i 3) (.f32 (pow.f32 cosTheta_O 3) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 3))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))
(+.f32 (/.f32 (.f32 cosTheta_i (.f32 cosTheta_O (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) v) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (*.f32 (pow.f32 cosTheta_O 2) (exp.f32 (-.f32 6931/10000 (/.f32 1 v))))) (pow.f32 v 2))) (exp.f32 (-.f32 6931/10000 (/.f32 1 v)))))
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(exp.f32 6931/10000)
(+.f32 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (exp.f32 6931/10000)) v) (exp.f32 6931/10000))
(+.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))
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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
(-.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
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(-.f32 6931/10000 (/.f32 (-.f32 1 (*.f32 cosTheta_i cosTheta_O)) v))
(-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
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(-.f32 6931/10000 (/.f32 (-.f32 1 (*.f32 cosTheta_i cosTheta_O)) v))
(-.f32 6931/10000 (/.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) 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_O (neg.f32 cosTheta_i) 1) v))
(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
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(exp.f32 (-.f32 6931/10000 (/.f32 1 v)))
(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))
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(exp.f32 6931/10000)
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(+.f32 (fma.f32 1/6 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (exp.f32 6931/10000)) (fma.f32 1/2 (.f32 (/.f32 (exp.f32 6931/10000) v) (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v)) (.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000))))
(fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (fma.f32 1/2 (.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v))) (fma.f32 1/6 (/.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 v 3) (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 3))) (exp.f32 6931/10000))))
(+.f32 (fma.f32 1/6 (/.f32 (exp.f32 6931/10000) (pow.f32 (/.f32 v (fma.f32 cosTheta_i cosTheta_O -1)) 3)) (exp.f32 6931/10000)) (.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 (fma.f32 cosTheta_i cosTheta_O -1) (.f32 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v) 1/2))))
(exp.f32 6931/10000)
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (exp.f32 6931/10000))
(+.f32 (exp.f32 6931/10000) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (/.f32 v (exp.f32 6931/10000))))
(+.f32 (exp.f32 6931/10000) (*.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000)))
(fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (exp.f32 6931/10000))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (exp.f32 6931/10000)))
(fma.f32 1/2 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (/.f32 (*.f32 v v) (exp.f32 6931/10000))) (+.f32 (exp.f32 6931/10000) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) (/.f32 v (exp.f32 6931/10000)))))
(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 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000))))
(fma.f32 1/2 (.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) (.f32 v v))) (fma.f32 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) (exp.f32 6931/10000) (exp.f32 6931/10000)))
(+.f32 (exp.f32 6931/10000) (.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 (fma.f32 cosTheta_i cosTheta_O -1) (.f32 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v) 1/2))))
(+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) (exp.f32 6931/10000)) v)) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 2) (exp.f32 6931/10000)) (pow.f32 v 2))) (+.f32 (.f32 -1/6 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (.f32 cosTheta_i cosTheta_O))) 3) (exp.f32 6931/10000)) (pow.f32 v 3))) (exp.f32 6931/10000))))
(fma.f32 -1 (/.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) (/.f32 v (exp.f32 6931/10000))) (fma.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) 2) (/.f32 (.f32 v v) (exp.f32 6931/10000))) (fma.f32 -1/6 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta_i cosTheta_O))) 3) (/.f32 (pow.f32 v 3) (exp.f32 6931/10000))) (exp.f32 6931/10000))))
(-.f32 (fma.f32 1/2 (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 v v)) (exp.f32 6931/10000)) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 v 3) (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3))) (exp.f32 6931/10000))) (.f32 (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v) (exp.f32 6931/10000)))
(-.f32 (fma.f32 1/2 (.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) 2) (.f32 v v))) (fma.f32 -1/6 (/.f32 (exp.f32 6931/10000) (/.f32 (pow.f32 v 3) (pow.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) 3))) (exp.f32 6931/10000))) (*.f32 (/.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) v) (exp.f32 6931/10000)))
(+.f32 (.f32 (exp.f32 6931/10000) (+.f32 (.f32 -1/6 (pow.f32 (/.f32 (fma.f32 cosTheta_O (neg.f32 cosTheta_i) 1) v) 3)) 1)) (.f32 (/.f32 (exp.f32 6931/10000) v) (+.f32 (fma.f32 cosTheta_i cosTheta_O -1) (.f32 (/.f32 (pow.f32 (fma.f32 cosTheta_i cosTheta_O -1) 2) v) 1/2))))

localize161.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 134 to 68 computations (49.3% saved)

series91.0ms (0.5%)

Counts

1 → 60

Calls

15 calls:

Time	Variable		Point	Expression
29.0ms	v	@	-inf	(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)
16.0ms	cosTheta_O	@	-inf	(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)
7.0ms	v	@	inf	(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)
5.0ms	cosTheta_O	@	0	(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)
5.0ms	cosTheta_i	@	0	(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)

rewrite80.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
325×	`expm1-udef_binary32`
325×	`log1p-udef_binary32`
302×	`fma-def_binary32`
274×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	23
1	411	23
2	4849	23

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(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)

Outputs

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

simplify161.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

527×	`associate-r_binary32`
399×	`unswap-sqr_binary32`
364×	`fma-def_binary32`
333×	`*-commutative_binary32`
308×	`associate-l_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	6049
1	1436	5245
2	6705	5113

Stop Event

1×	node limit

Counts

82 → 63

Calls

Call 1

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

Outputs
(exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))
(exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))))
(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(+.f32 (.f32 1/3 (.f32 (.f32 cosTheta_i (+.f32 (.f32 2 (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 3) cosTheta_O) v)) (/.f32 (.f32 (pow.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 3) cosTheta_O) v))) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))) 2)) 1/3))) (exp.f32 (-.f32 6931/10000 (+.f32 (/.f32 1 v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
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(exp.f32 (-.f32 (-.f32 6931/10000 (/.f32 1 v)) (/.f32 sinTheta_i (/.f32 v sinTheta_O))))
(exp.f32 (-.f32 6931/10000 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
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(fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 2))) (.f32 sinTheta_O (.f32 (/.f32 sinTheta_i (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -3))) (fma.f32 1/3 (/.f32 (-.f32 (fma.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 2))) -4/3) (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (fma.f32 -2 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) (.f32 (/.f32 (pow.f32 sinTheta_i 3) (/.f32 (pow.f32 v 3) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -7/6))) (fma.f32 1/27 (/.f32 (pow.f32 (.f32 (/.f32 sinTheta_i (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -3) 3) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 2)) (.f32 2/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 5))) (.f32 (.f32 (/.f32 sinTheta_i (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -3) (-.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) 9/2) (.f32 (.f32 1/3 (pow.f32 (.f32 (/.f32 sinTheta_i (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -3) 2)) (cbrt.f32 (exp.f32 (neg.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))))))))) (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 2) (pow.f32 sinTheta_O 3))) (+.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) (.f32 1/3 (/.f32 (.f32 sinTheta_O sinTheta_O) (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 2) (-.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (/.f32 (.f32 v v) (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) 9/2) (.f32 (.f32 1/3 (pow.f32 (.f32 (/.f32 sinTheta_i (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v)))) 3))) -3) 2)) (cbrt.f32 (exp.f32 (neg.f32 (+.f32 6931/10000 (-.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)) (/.f32 1 v))))))))))))))
(fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2))) (.f32 sinTheta_O (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3))))) (fma.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (/.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2) (-.f32 (fma.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) (.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2)) -4/3) (.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3)) -19/6)) (fma.f32 (.f32 (.f32 2/3 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3)))) (fma.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3)) 9/2 (.f32 (.f32 -1/3 (cbrt.f32 (exp.f32 (neg.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))) (pow.f32 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3))) 2)))) (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 5))) (/.f32 1/27 (/.f32 (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2) (.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3)) 3) -27))))))) (fma.f32 1/3 (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 2)) (fma.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3)) 9/2 (.f32 (.f32 -1/3 (cbrt.f32 (exp.f32 (neg.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v)))))) (pow.f32 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))) 3))) 2)))) (exp.f32 (+.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (/.f32 -1 v))))))
(fma.f32 1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 2))) (.f32 sinTheta_O (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3))))) (fma.f32 1/3 (/.f32 (pow.f32 sinTheta_O 3) (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 2) (-.f32 (fma.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) (.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 2)) -4/3) (.f32 (.f32 (/.f32 (pow.f32 sinTheta_i 3) (pow.f32 v 3)) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3)) -19/6)) (fma.f32 (.f32 (.f32 2/3 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3)))) (fma.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3)) 9/2 (.f32 (.f32 -1/3 (cbrt.f32 (exp.f32 (-.f32 -6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))))) (pow.f32 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3))) 2)))) (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 5))) (/.f32 1/27 (/.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 2) (.f32 (pow.f32 (.f32 (/.f32 sinTheta_i v) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3)) 3) -27))))))) (fma.f32 1/3 (.f32 (/.f32 (.f32 sinTheta_O sinTheta_O) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 2)) (fma.f32 (.f32 (/.f32 (.f32 sinTheta_i sinTheta_i) (.f32 v v)) (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3)) 9/2 (.f32 (.f32 -1/3 (cbrt.f32 (exp.f32 (-.f32 -6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))))) (pow.f32 (/.f32 (.f32 sinTheta_i -3) (/.f32 v (pow.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))) 3))) 2)))) (exp.f32 (+.f32 6931/10000 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) (/.f32 -1 v)))))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))

eval1.0s (5.4%)

Compiler: Compiled 37036 to 23011 computations (37.9% saved)

prune645.0ms (3.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	1175	11	1186
Fresh	3	0	3
Picked	1	0	1
Done	4	0	4
Total	1183	11	1194

Error

0.0b

Counts

1194 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	0.2b	(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
	30.6b	(.f32 (+.f32 (.f32 -1 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) 1) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (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)))) 3/2) 1/3) (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)))) 3/2) 1/3)) (/.f32 1/2 v))
▶	0.3b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
▶	0.0b	(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
	28.7b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.0b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	0.2b	(*.f32 (pow.f32 (pow.f32 (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) 3) 1/3) (/.f32 1/2 v))
▶	30.5b	(/.f32 1/2 v)
▶	28.7b	(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))

Compiler

Compiled 474 to 358 computations (24.5% saved)

localize210.0ms (1.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(cbrt.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
✓	0.1b	(exp.f32 (cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2)))
✓	0.2b	(pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2)
✓	14.1b	(cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))

Compiler

Compiled 160 to 104 computations (35% saved)

series55.0ms (0.3%)

Counts

4 → 89

Calls

36 calls:

Time	Variable		Point	Expression
5.0ms	v	@	-inf	(exp.f32 (cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2)))
5.0ms	v	@	-inf	(cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))
3.0ms	cosTheta_i	@	0	(cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))
3.0ms	v	@	inf	(exp.f32 (cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2)))
3.0ms	v	@	inf	(cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))

rewrite124.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary32`
387×	`fma-def_binary32`
331×	`expm1-udef_binary32`
331×	`log1p-udef_binary32`
207×	`fma-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	105
1	405	105
2	5051	105

Stop Event

1×	node limit

Counts

4 → 109

Calls

Call 1

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

Outputs
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simplify202.0ms (1%)

Algorithm

1×	egg-herbie

Rules

569×	`associate-r_binary32`
433×	`associate-l_binary32`
411×	`unswap-sqr_binary32`
402×	`*-commutative_binary32`
376×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	471	11338
1	1585	10522
2	5994	10115

Stop Event

1×	node limit

Counts

198 → 220

Calls

Call 1

Inputs
(pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3)
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))))
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (+.f32 (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))) (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)))))) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3)))))
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (+.f32 (.f32 -1/3 (.f32 (.f32 (pow.f32 cosTheta_i 3) (+.f32 (.f32 8/27 (.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/3))) (+.f32 (.f32 2/3 (.f32 (pow.f32 (/.f32 1 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/9) (/.f32 (.f32 (-.f32 (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2))))) cosTheta_O) v))) (.f32 2/3 (.f32 (pow.f32 (/.f32 1 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/9) (/.f32 (.f32 cosTheta_O (-.f32 (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)))))) v)))))) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3))) (+.f32 (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))) (.f32 1/3 (.f32 (.f32 (pow.f32 cosTheta_i 2) (-.f32 (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_O 2) (pow.f32 v 2)))))) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3))))))
(pow.f32 (pow.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))) 2) 1/3)
(+.f32 (.f32 2/3 (.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) v) (pow.f32 (.f32 1 (pow.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))) 5)) 1/9))) (pow.f32 (pow.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))) 2) 1/3))
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(pow.f32 (pow.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))) 2) 1/3)
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(pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3)
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))))
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3) (.f32 (-.f32 (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2))))) (pow.f32 cosTheta_O 2)))) (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9)))))
(+.f32 (.f32 -1/3 (.f32 (.f32 (+.f32 (.f32 8/27 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/3))) (.f32 4/3 (.f32 (pow.f32 (/.f32 1 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/9) (/.f32 (.f32 cosTheta_i (-.f32 (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2)))))) v)))) (pow.f32 cosTheta_O 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3))) (+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 4)) 1/3) (.f32 (-.f32 (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2)) (.f32 4/3 (.f32 (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 16)) 1/9) (/.f32 (pow.f32 cosTheta_i 2) (pow.f32 v 2))))) (pow.f32 cosTheta_O 2)))) (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))))))
(pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)
(+.f32 (.f32 2 (/.f32 (.f32 cosTheta_i (*.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) cosTheta_O)) v)) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2))
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(/.f32 (*.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))
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(/.f32 (*.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2))
(+.f32 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2)) (.f32 2 (/.f32 (.f32 cosTheta_i (.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) cosTheta_O)) v)))
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(/.f32 (pow.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2))
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(+.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2)) (+.f32 (pow.f32 (+.f32 (.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))) 2) (.f32 2 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (+.f32 (.f32 -1 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2)))) v))))
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(+.f32 (/.f32 (pow.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) 2) (pow.f32 v 2)) (+.f32 (.f32 2 (/.f32 (.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) 1) (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) v)) (pow.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))) 2)))
(pow.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)) 2)
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(+.f32 (.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/9))) (+.f32 (.f32 -1/9 (.f32 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 7)) 1/9))) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3)))
(+.f32 (.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/9))) (+.f32 (.f32 -1/9 (.f32 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 7)) 1/9))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3) (.f32 (+.f32 (.f32 -2/9 (.f32 (pow.f32 (pow.f32 1 4) 1/9) (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3)))) (.f32 1/27 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3)))) (pow.f32 cosTheta_O 3)))) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3))))

Outputs
(pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3)
(cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2))
(cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2))
(+.f32 (pow.f32 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2) 1/3) (.f32 2/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 5)) 1/9))))
(+.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) (.f32 (.f32 2/3 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 5) 1/18) (pow.f32 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 5) 1/18))))
(fma.f32 2/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (*.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18))) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)))
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(+.f32 (fma.f32 2/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18))) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2))) (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 4))) (.f32 (.f32 1/3 (.f32 cosTheta_i cosTheta_i)) (.f32 (+.f32 (.f32 (.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18)) -4/3) 1) (*.f32 (/.f32 cosTheta_O v) (/.f32 cosTheta_O v))))))
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(+.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) (fma.f32 -1/3 (.f32 (fma.f32 8/27 (.f32 (/.f32 (pow.f32 cosTheta_O 3) (pow.f32 v 3)) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5))) (.f32 (.f32 (.f32 (pow.f32 (/.f32 1 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) 1/18) (pow.f32 (/.f32 1 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) 1/18)) (.f32 (/.f32 cosTheta_O v) (+.f32 (.f32 (/.f32 cosTheta_O v) (/.f32 cosTheta_O v)) (.f32 (.f32 (.f32 (.f32 (/.f32 cosTheta_O v) (/.f32 cosTheta_O v)) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18)) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18)) -4/3)))) 4/3)) (.f32 (pow.f32 cosTheta_i 3) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 4))))) (fma.f32 1/3 (.f32 (.f32 cosTheta_i cosTheta_i) (.f32 (+.f32 (.f32 (/.f32 cosTheta_O v) (/.f32 cosTheta_O v)) (.f32 (.f32 (.f32 (.f32 (/.f32 cosTheta_O v) (/.f32 cosTheta_O v)) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18)) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 16) 1/18)) -4/3)) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 4))))) (.f32 (.f32 (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18) (pow.f32 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 5) 1/18)) (.f32 2/3 (.f32 (/.f32 cosTheta_i v) cosTheta_O))))))
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(pow.f32 (pow.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))) 2) 1/3)
(cbrt.f32 (pow.f32 (fma.f32 -1 (log.f32 v) (+.f32 6931/10000 (log.f32 1/2))) 2))
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(+.f32 (fma.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)) 1/18) (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))))) (fma.f32 1/3 (.f32 (/.f32 (fma.f32 -2/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 6)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 6)) 1/18) (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3))) (.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3) (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2))) 1/27))) (pow.f32 v 3)) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)))) (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))))) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 4)) 1/18)) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 4)) 1/18)) (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) (.f32 v v)) -1/9))))
(+.f32 (fma.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)) 1/18) (/.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) v))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))))) (fma.f32 1/3 (.f32 (/.f32 (.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 3) (+.f32 (.f32 1/27 (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)))) (.f32 -2/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 6)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 6)) 1/18))))) (pow.f32 v 3)) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 2)))) (.f32 (.f32 (.f32 (cbrt.f32 (/.f32 1 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))))) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 4)) 1/18)) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 -1 v)) (log.f32 -1/2))) 4)) 1/18)) (.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta_i cosTheta_O)) 2) (*.f32 v v)) -1/9))))
(pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3)
(cbrt.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))
(cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))
(+.f32 (.f32 1/3 (.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/9))) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3))
(fma.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (*.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(fma.f32 1/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (*.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(+.f32 (.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/9))) (+.f32 (.f32 -1/9 (.f32 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 7)) 1/9))) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3)))
(fma.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (.f32 cosTheta_O cosTheta_O))) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 7)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 7)) 1/18))) (cbrt.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))))))
(fma.f32 1/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O cosTheta_O)))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))
(fma.f32 1/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))))))
(+.f32 (.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/9))) (+.f32 (.f32 -1/9 (.f32 (/.f32 (.f32 (pow.f32 cosTheta_i 2) (pow.f32 cosTheta_O 2)) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 7)) 1/9))) (+.f32 (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3) (.f32 (+.f32 (.f32 -2/9 (.f32 (pow.f32 (pow.f32 1 4) 1/9) (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3)))) (.f32 1/27 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 2)) 1/3)))) (pow.f32 cosTheta_O 3)))) (pow.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)) 1/3))))
(fma.f32 1/3 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (/.f32 (.f32 cosTheta_i cosTheta_i) (/.f32 (.f32 v v) (.f32 cosTheta_O cosTheta_O))) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 7)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 7)) 1/18))) (fma.f32 -1/3 (.f32 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2))) (+.f32 (.f32 -2/9 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2))))) (.f32 (.f32 1/27 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3))) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v))) 2)))))) (pow.f32 cosTheta_O 3)) (cbrt.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))))
(fma.f32 1/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (.f32 (/.f32 cosTheta_i v) (/.f32 cosTheta_i v)) (.f32 cosTheta_O cosTheta_O)))) (fma.f32 -1/3 (.f32 (.f32 (.f32 (/.f32 (pow.f32 cosTheta_i 3) (pow.f32 v 3)) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)))) -5/27) (.f32 (pow.f32 cosTheta_O 3) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2))))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))
(fma.f32 1/3 (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)) 1/18))) (fma.f32 -1/9 (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 7)) 1/18) (.f32 (.f32 (/.f32 cosTheta_i v) cosTheta_O) (.f32 (/.f32 cosTheta_i v) cosTheta_O)))) (fma.f32 -1/3 (.f32 (.f32 (.f32 (pow.f32 (/.f32 cosTheta_i v) 3) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2)))) -5/27) (.f32 (pow.f32 cosTheta_O 3) (cbrt.f32 (/.f32 1 (pow.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v))) 2))))) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))))

localize10.0ms (0%)

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

localize56.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 22 to 8 computations (63.6% saved)

series6.0ms (0%)

Counts

2 → 72

Calls

18 calls:

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

rewrite72.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

848×	`pow1_binary32`
785×	`add-log-exp_binary32`
785×	`log1p-expm1-u_binary32`
785×	`expm1-log1p-u_binary32`
766×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	16
2	2093	16

Stop Event

1×	node limit

Counts

2 → 65

Calls

Call 1

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

Outputs

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

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

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

137 → 74

Calls

Call 1

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

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

localize42.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 32 to 16 computations (50% saved)

series11.0ms (0.1%)

Counts

1 → 16

Calls

9 calls:

Time	Variable		Point	Expression
7.0ms	cosTheta_O	@	0	(exp.f32 (/.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))
0.0ms	cosTheta_O	@	inf	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

rewrite224.0ms (1.2%)

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	10
1	188	10
2	2504	10

Stop Event

1×	node limit

Counts

1 → 67

Calls

Call 1

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

Outputs

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

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	51	512
1	156	512
2	522	464
3	3429	416
4	4972	400

Stop Event

1×	node limit

Counts

83 → 81

Calls

Call 1

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

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

localize92.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 46 to 37 computations (19.6% saved)

series163.0ms (0.8%)

Counts

4 → 44

Calls

12 calls:

Time	Variable		Point	Expression
100.0ms	v	@	-inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
53.0ms	v	@	0	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
6.0ms	v	@	inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
1.0ms	v	@	inf	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
1.0ms	v	@	-inf	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

rewrite144.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 295

Calls

Call 1

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

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

simplify68.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

339 → 321

Calls

Call 1

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

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

eval956.0ms (4.9%)

Compiler: Compiled 27719 to 21125 computations (23.8% saved)

prune136.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	690	6	696
Fresh	2	4	6
Picked	0	1	1
Done	4	0	4
Total	696	11	707

Error

0.0b

Counts

707 → 11

Alt Table

Click to see full alt table

Status	Error	Program
	0.0b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	0.0b	(pow.f32 (/.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (exp.f32 (/.f32 1/2 v))) 2)
▶	0.2b	(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
▶	0.0b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	0.1b	(.f32 (.f32 (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)))) 3/2) 1/3) (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)))) 3/2) 1/3)) (/.f32 1/2 v))
	0.1b	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))
▶	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	30.0b	1
▶	0.2b	(*.f32 (pow.f32 (pow.f32 (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) 3) 1/3) (/.f32 1/2 v))
	0.3b	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 438 to 350 computations (20.1% saved)

localize110.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(exp.f32 (/.f32 1/2 v))
✓	0.1b	(/.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (exp.f32 (/.f32 1/2 v)))
✓	0.2b	(sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
✓	0.4b	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))

Compiler

Compiled 57 to 48 computations (15.8% saved)

series19.0ms (0.1%)

Counts

4 → 20

Calls

12 calls:

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

rewrite107.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

484×	`log-prod_binary32`
375×	`exp-prod_binary32`
310×	`prod-exp_binary32`
283×	`pow-prod-down_binary32`
254×	`pow2_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	45
1	208	45
2	2577	43

Stop Event

1×	node limit

Counts

4 → 196

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (/.f32 v (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 6931/10000) (.f32 v 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 v (.f32 1/2 (exp.f32 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 1/2 (exp.f32 6931/10000)) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (.f32 1/2 (exp.f32 6931/10000))) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (.f32 1/2 (exp.f32 6931/10000)) 1) v)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (.f32 1/2 (exp.f32 6931/10000)) (pow.f32 (cbrt.f32 v) 2)) (cbrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (.f32 1/2 (exp.f32 6931/10000)) (sqrt.f32 v)) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 -1/2 (exp.f32 6931/10000)) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (exp.f32 6931/10000) -1/2) (neg.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3/2) 2/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/5000) (.f32 1/4 (pow.f32 v -2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 20793/10000) (pow.f32 (/.f32 1/2 v) 3)) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/6) 6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/30000) (cbrt.f32 (/.f32 1/2 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 v (.f32 1/2 (exp.f32 6931/10000))) -1)))) (#(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 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 sqrt.f32 (.f32 (exp.f32 6931/5000) (.f32 1/4 (pow.f32 v -2))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) (exp.f32 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (exp.f32 20793/10000) (pow.f32 (/.f32 1/2 v) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/5000 (log.f32 (.f32 1/4 (pow.f32 v -2)))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/30000 (log.f32 (cbrt.f32 (/.f32 1/2 v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (+.f32 6931/10000 (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) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/10000 (.f32 (log.f32 (/.f32 1/2 v)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2) (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1) (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1) (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2) (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1) (*.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1/2 v))) (exp.f32 6931/20000))) 2)) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1/2 v))) (exp.f32 6931/20000)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1/2 v))) (exp.f32 6931/20000)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1/2 v))) (exp.f32 6931/20000)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/6) (.f32 (exp.f32 6931/30000) (cbrt.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 6931/30000) (cbrt.f32 (/.f32 1/2 v))) (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/6))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/4) (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/4))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 6931/20000))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (sqrt.f32 (.f32 1/2 (exp.f32 6931/10000))) (sqrt.f32 v))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1/2) (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3/2) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/5000) (.f32 1/4 (pow.f32 v -2))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 20793/10000) (pow.f32 (/.f32 1/2 v) 3)) 1/6)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/6) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (exp.f32 6931/30000) (cbrt.f32 (/.f32 1/2 v))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 1/4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))) 2)) (cbrt.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))))) (sqrt.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 (sqrt.f32 (/.f32 1/2 v))) (exp.f32 6931/20000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 3/2 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/3 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 1/4 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) 1/2) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (.f32 (+.f32 6931/20000 (log.f32 (sqrt.f32 (/.f32 1/2 v)))) 1) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000)))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (exp.f32 6931/20000) (sqrt.f32 (/.f32 1/2 v))) (exp.f32 (neg.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 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((x pow.f32 (pow.f32 (exp.f32 (cbrt.f32 (.f32 1/4 (pow.f32 v -2)))) (sqrt.f32 (cbrt.f32 (/.f32 1/2 v)))) (sqrt.f32 (cbrt.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (exp.f32 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (/.f32 1/2 v)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (/.f32 1/2 v))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (exp.f32 (/.f32 1/2 v))))))))

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1243×	`associate-*r/_binary32`
558×	`fma-def_binary32`
536×	`unswap-sqr_binary32`
400×	`associate-/r/_binary32`
384×	`sqr-pow_binary32`

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	24	206
1	59	206
2	117	206
3	239	206
4	565	206
5	2086	202
6	4026	198
7	4314	194
8	4626	194
9	4998	194
10	5457	194
11	7773	194

Stop Event

1×	node limit

Counts

216 → 205

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))
1
(+.f32 1 (*.f32 1/2 (/.f32 1 v)))
(+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (.f32 1/2 (/.f32 1 v))))
(+.f32 (.f32 1/48 (/.f32 1 (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))
1
(+.f32 1 (*.f32 1/2 (/.f32 1 v)))
(+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (.f32 1/2 (/.f32 1 v))))
(+.f32 (.f32 1/48 (/.f32 1 (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))

Outputs
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (exp.f32 6931/10000) (/.f32 1/2 v))
1
(+.f32 1 (*.f32 1/2 (/.f32 1 v)))
(+.f32 1 (/.f32 1/2 v))
(+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (.f32 1/2 (/.f32 1 v))))
(+.f32 1 (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))))
(fma.f32 (/.f32 1 v) (+.f32 1/2 (/.f32 1/8 v)) 1)
(+.f32 (.f32 1/48 (/.f32 1 (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))
(+.f32 (+.f32 (/.f32 1/48 (pow.f32 v 3)) 1) (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))))
(+.f32 (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))) (+.f32 1 (/.f32 1/48 (pow.f32 v 3))))
(+.f32 1 (+.f32 (/.f32 1/8 (*.f32 v v)) (+.f32 (/.f32 1/2 v) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 1 (+.f32 (/.f32 1/2 v) (+.f32 (/.f32 1/8 (*.f32 v v)) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 (/.f32 1/2 v) (+.f32 1 (+.f32 (/.f32 1/8 (*.f32 v v)) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 1 (fma.f32 (/.f32 1 (*.f32 v v)) (+.f32 1/8 (/.f32 1/48 v)) (/.f32 1/2 v)))
(+.f32 1 (fma.f32 (/.f32 1 v) (+.f32 1/2 (/.f32 1/8 v)) (/.f32 1/48 (pow.f32 v 3))))
(fma.f32 (/.f32 1 v) (fma.f32 (/.f32 1 v) (+.f32 1/8 (/.f32 1/48 v)) 1/2) 1)
1
(+.f32 1 (*.f32 1/2 (/.f32 1 v)))
(+.f32 1 (/.f32 1/2 v))
(+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (.f32 1/2 (/.f32 1 v))))
(+.f32 1 (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))))
(fma.f32 (/.f32 1 v) (+.f32 1/2 (/.f32 1/8 v)) 1)
(+.f32 (.f32 1/48 (/.f32 1 (pow.f32 v 3))) (+.f32 1 (+.f32 (.f32 1/8 (/.f32 1 (pow.f32 v 2))) (*.f32 1/2 (/.f32 1 v)))))
(+.f32 (+.f32 (/.f32 1/48 (pow.f32 v 3)) 1) (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))))
(+.f32 (+.f32 (/.f32 1/2 v) (/.f32 1/8 (*.f32 v v))) (+.f32 1 (/.f32 1/48 (pow.f32 v 3))))
(+.f32 1 (+.f32 (/.f32 1/8 (*.f32 v v)) (+.f32 (/.f32 1/2 v) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 1 (+.f32 (/.f32 1/2 v) (+.f32 (/.f32 1/8 (*.f32 v v)) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 (/.f32 1/2 v) (+.f32 1 (+.f32 (/.f32 1/8 (*.f32 v v)) (/.f32 1/48 (pow.f32 v 3)))))
(+.f32 1 (fma.f32 (/.f32 1 (*.f32 v v)) (+.f32 1/8 (/.f32 1/48 v)) (/.f32 1/2 v)))
(+.f32 1 (fma.f32 (/.f32 1 v) (+.f32 1/2 (/.f32 1/8 v)) (/.f32 1/48 (pow.f32 v 3))))
(fma.f32 (/.f32 1 v) (fma.f32 (/.f32 1 v) (+.f32 1/8 (/.f32 1/48 v)) 1/2) 1)

localize21.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	8.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 24 to 10 computations (58.3% saved)

series3.0ms (0%)

Counts

1 → 9

Calls

9 calls:

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

rewrite86.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

40 → 34

Calls

Call 1

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

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

localize74.0ms (0.4%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 36 to 29 computations (19.4% saved)

series4.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite107.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 133

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 48038761/100000000 (+.f32 6931/10000 (/.f32 1 v))) (/.f32 (pow.f32 v -2) (+.f32 6931/10000 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 6931/10000 (/.f32 -1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 6931/10000 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2)) (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 3 (*.f32 1/3 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000) (/.f32 1 (+.f32 48038761/100000000 (-.f32 (pow.f32 v -2) (/.f32 -6931/10000 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (/.f32 1 (+.f32 6931/10000 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/3 (*.f32 3 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (*.f32 1/2 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 48038761/100000000 (-.f32 (pow.f32 v -2) (/.f32 -6931/10000 v))) (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 6931/10000 (/.f32 1 v)) (-.f32 48038761/100000000 (pow.f32 v -2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000) (+.f32 48038761/100000000 (-.f32 (pow.f32 v -2) (/.f32 -6931/10000 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000) (+.f32 (pow.f32 v -2) (-.f32 48038761/100000000 (/.f32 -6931/10000 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 48038761/100000000 (pow.f32 v -2)) (+.f32 6931/10000 (/.f32 1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000)) (neg.f32 (+.f32 48038761/100000000 (-.f32 (pow.f32 v -2) (/.f32 -6931/10000 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (-.f32 48038761/100000000 (pow.f32 v -2))) (neg.f32 (+.f32 6931/10000 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (pow.f32 v -2) 48038761/100000000) (-.f32 (/.f32 -1 v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (+.f32 6931/10000 (/.f32 -1 v))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log.f32 (+.f32 6931/10000 (/.f32 -1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 48038761/100000000 (-.f32 (pow.f32 v -2) (/.f32 -6931/10000 v))) (fma.f32 -1 (pow.f32 v -3) 332956652491/1000000000000)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 6931/10000 (/.f32 1 v)) (-.f32 48038761/100000000 (pow.f32 v -2))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v)))) 2)) (cbrt.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v))))) (sqrt.f32 (log.f32 (+.f32 6931/10000 (/.f32 -1 v)))))))) 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simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

169 → 156

Calls

Call 1

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

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

localize100.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
✓	0.0b	(+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))
✓	0.2b	(pow.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3)
✓	0.3b	(*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))

Compiler

Compiled 85 to 60 computations (29.4% saved)

series79.0ms (0.4%)

Counts

4 → 104

Calls

36 calls:

Time	Variable		Point	Expression
40.0ms	cosTheta_i	@	-inf	(exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))
5.0ms	cosTheta_i	@	0	(pow.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3)
4.0ms	v	@	0	(pow.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3)
3.0ms	v	@	inf	(pow.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3)
3.0ms	cosTheta_O	@	0	(pow.f32 (exp.f32 (*.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3)

rewrite106.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

614×	`log-prod_binary32`
357×	`pow2_binary32`
248×	`expm1-udef_binary32`
248×	`log1p-udef_binary32`
244×	`pow1/3_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	59
1	303	54
2	3642	50

Stop Event

1×	node limit

Counts

4 → 217

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 20793/10000 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 20793/10000 (.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)) 20793/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 1/2 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)) (.f32 1/2 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (fma.f32 3 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v) 20793/10000))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 2 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (exp.f32 3) 6931/10000)) (log.f32 (pow.f32 (exp.f32 3) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (exp.f32 3) (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) (log.f32 (pow.f32 (exp.f32 3) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2) 1)) (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2) (cbrt.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v))) 2)))) (.f32 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simplify189.0ms (1%)

Algorithm

1×	egg-herbie

Rules

514×	`distribute-rgt-in_binary32`
499×	`distribute-lft-in_binary32`
383×	`cancel-sign-sub-inv_binary32`
234×	`associate-r_binary32`
227×	`associate-/r/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3897
1	820	3532
2	3028	3235

Stop Event

1×	node limit

Counts

321 → 277

Calls

Call 1

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

localize301.0ms (1.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
	0.1b	(fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)
✓	0.2b	(pow.f32 (pow.f32 (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) 3) 1/3)
✓	0.6b	(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)))))

Compiler

Compiled 179 to 95 computations (46.9% saved)

series214.0ms (1.1%)

Counts

2 → 120

Calls

30 calls:

Time	Variable		Point	Expression
24.0ms	v	@	inf	(pow.f32 (pow.f32 (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) 3) 1/3)
23.0ms	cosTheta_i	@	0	(pow.f32 (pow.f32 (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) 3) 1/3)
22.0ms	sinTheta_O	@	0	(pow.f32 (pow.f32 (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) 3) 1/3)
21.0ms	sinTheta_i	@	0	(pow.f32 (pow.f32 (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) 3) 1/3)
20.0ms	cosTheta_O	@	0	(pow.f32 (pow.f32 (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) 3) 1/3)

rewrite97.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`prod-diff_binary32`
337×	`expm1-udef_binary32`
337×	`log1p-udef_binary32`
321×	`fma-def_binary32`
296×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	458	48
2	5132	48

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

Inputs

(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)))))

(pow.f32 (pow.f32 (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) 3) 1/3)

Outputs

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

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

simplify538.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

705×	`distribute-lft-in_binary32`
705×	`distribute-rgt-in_binary32`
552×	`*-commutative_binary32`
260×	`associate-r_binary32`
243×	`times-frac_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1005	49836
1	4030	46890

Stop Event

1×	node limit

Counts

171 → 133

Calls

Call 1

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

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

eval2.7s (14%)

Compiler: Compiled 88056 to 60634 computations (31.1% saved)

prune401.0ms (2.1%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	998	10	1008
Fresh	2	3	5
Picked	1	0	1
Done	2	3	5
Total	1003	16	1019

Error

0.0b

Counts

1019 → 16

Alt Table

Click to see full alt table

Status	Error	Program
	0.3b	(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	0.2b	(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 9) 1/3) (/.f32 1/2 v))
	0.2b	(.f32 (pow.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3))) 1/3) (/.f32 1/2 v))
	30.0b	(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
	25.3b	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	0.1b	(pow.f32 (pow.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000))) 3) 1/3) 2)
✓	0.0b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	30.0b	(+.f32 1 (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 v))))
	0.0b	(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
	0.1b	(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))
✓	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	30.0b	1
	0.0b	(pow.f32 (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/20000 (neg.f32 (/.f32 1/2 v))))) 2)
	18.8b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	0.3b	(exp.f32 (/.f32 -1 v))

Compiler

Compiled 251 to 213 computations (15.1% saved)

regimes224.0ms (1.2%)

Counts

37 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 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 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))
(.f32 (pow.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3))) 1/3) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(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)))))
(pow.f32 (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/20000 (neg.f32 (/.f32 1/2 v))))) 2)
(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))
(pow.f32 (/.f32 (sqrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))) (exp.f32 (/.f32 1/2 v))) 2)
(pow.f32 (pow.f32 (pow.f32 (/.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (-.f32 (/.f32 1/2 v) 6931/20000))) 3) 1/3) 2)
(*.f32 (pow.f32 (pow.f32 (cbrt.f32 (exp.f32 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 9) 1/3) (/.f32 1/2 v))
(*.f32 (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) (/.f32 1/2 v))
(*.f32 (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) (/.f32 1/2 v))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))) 2)) (cbrt.f32 (+.f32 (+.f32 6931/10000 (/.f32 -1 v)) (log.f32 (/.f32 1/2 v)))))
(pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))) 2)) (cbrt.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(*.f32 (pow.f32 (pow.f32 (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) 3) 1/3) (/.f32 1/2 v))
(pow.f32 (exp.f32 (cbrt.f32 (pow.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))) 2))) (cbrt.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
(.f32 (.f32 (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)))) 3/2) 1/3) (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)))) 3/2) 1/3)) (/.f32 1/2 v))

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

Calls

11 calls:

48.0ms	(+.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))))
35.0ms	(*.f32 cosTheta_i cosTheta_O)
19.0ms	sinTheta_O
18.0ms	sinTheta_i
17.0ms	cosTheta_O

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.0b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.0b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.0b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 701 to 483 computations (31.1% saved)

regimes257.0ms (1.3%)

Counts

27 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))
(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
(+.f32 1 (*.f32 cosTheta_i (/.f32 1 (/.f32 v cosTheta_O))))
(+.f32 1 (.f32 cosTheta_O (.f32 cosTheta_i (/.f32 1 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 (*.f32 cosTheta_i cosTheta_O) v))
(exp.f32 (/.f32 cosTheta_i (/.f32 v cosTheta_O)))
(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))
(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
(.f32 (exp.f32 (.f32 (/.f32 sinTheta_O v) (neg.f32 sinTheta_i))) (/.f32 1/2 v))
(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
(.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) (/.f32 1 (exp.f32 (/.f32 1 v))))
(.f32 (pow.f32 (exp.f32 (+.f32 20793/10000 (.f32 (/.f32 -1 v) 3))) 1/3) (/.f32 1/2 v))
(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
(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)))))
(pow.f32 (*.f32 (sqrt.f32 (/.f32 1/2 v)) (exp.f32 (+.f32 6931/20000 (neg.f32 (/.f32 1/2 v))))) 2)
(.f32 (pow.f32 (exp.f32 (.f32 3 (+.f32 6931/10000 (/.f32 (fma.f32 cosTheta_i cosTheta_O -1) v)))) 1/3) (/.f32 1/2 v))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

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

Calls

11 calls:

108.0ms	sinTheta_i
50.0ms	(+.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))))
15.0ms	cosTheta_i
14.0ms	sinTheta_O
12.0ms	cosTheta_O

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.0b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.0b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.0b	1	`(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))`
0.0b	1	`(*.f32 cosTheta_i cosTheta_O)`
0.0b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 445 to 303 computations (31.9% saved)

regimes89.0ms (0.5%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

7 calls:

29.0ms	sinTheta_O
10.0ms	cosTheta_O
10.0ms	sinTheta_i
10.0ms	cosTheta_i
9.0ms	v

Results

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

Compiler

Compiled 196 to 127 computations (35.2% saved)

regimes265.0ms (1.4%)

Counts

15 → 1

Calls

Call 1

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

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

Calls

7 calls:

180.0ms	cosTheta_i
43.0ms	sinTheta_O
10.0ms	sinTheta_i
8.0ms	cosTheta_O
7.0ms	v

Results

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

Compiler

Compiled 147 to 98 computations (33.3% saved)

regimes58.0ms (0.3%)

Counts

13 → 1

Calls

Call 1

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

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

Calls

7 calls:

10.0ms	sinTheta_i
9.0ms	cosTheta_O
8.0ms	v
8.0ms	cosTheta_i
7.0ms	sinTheta_O

Results

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

Compiler

Compiled 131 to 88 computations (32.8% saved)

regimes41.0ms (0.2%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

7 calls:

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

Results

Error	Segments	Branch
18.8b	1	`cosTheta_i`
18.8b	1	`cosTheta_O`
18.8b	1	`sinTheta_i`
18.8b	1	`sinTheta_O`
18.8b	1	`v`
18.8b	1	`(*.f32 cosTheta_i cosTheta_O)`
18.8b	1	`(*.f32 sinTheta_i sinTheta_O)`

Compiler

Compiled 103 to 72 computations (30.1% saved)

regimes63.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)
(*.f32 cosTheta_i (/.f32 cosTheta_O v))

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

Calls

5 calls:

47.0ms	sinTheta_O
4.0ms	cosTheta_i
4.0ms	cosTheta_O
4.0ms	v
4.0ms	sinTheta_i

Results

Error	Segments	Branch
25.3b	1	`cosTheta_i`
25.3b	1	`cosTheta_O`
25.3b	1	`sinTheta_i`
25.3b	1	`sinTheta_O`
25.3b	1	`v`

Compiler

Compiled 44 to 35 computations (20.5% saved)

regimes19.0ms (0.1%)

Accuracy

Total -0.6b remaining (-1.9%)

Threshold costs -0.6b (-1.9%)

Counts

2 → 1

Calls

Call 1

Inputs
1
(/.f32 1/2 v)

Outputs
1

Calls

5 calls:

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

Results

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

Compiler

Compiled 39 to 33 computations (15.4% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary32`
4×	`+-commutative_binary32`
2×	`sub-neg_binary32`
1×	`distribute-neg-frac_binary32`
1×	`unsub-neg_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	87
1	42	87
2	47	87
3	50	87
4	51	87

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 98 to 83 computations (15.3% saved)

soundness0.0ms (0%)

end160.0ms (0.8%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 139 to 116 computations (16.5% saved)