Details

analyze719.0ms (5.3%)

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 (28.7%)

Results

3.8s	8256×	body	256	valid
88.0ms	129×	body	256	invalid

preprocess71.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	unsound
1×	node limit

Calls

Call 1

Inputs
0
1
2
3
4

Outputs
0
1
0
2
3
2
4

Call 2

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

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

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

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

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

eval2.0ms (0%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

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

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)))))

▶

0.1b

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

Compiler

Compiled 55 to 39 computations (29.1% saved)

localize116.0ms (0.8%)

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))
✓	7.6b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	8.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 138 to 57 computations (58.7% saved)

series77.0ms (0.6%)

Counts

4 → 120

Calls

48 calls:

Time	Variable		Point	Expression
28.0ms	sinTheta_i	@	inf	(-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) 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))))
8.0ms	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))))
2.0ms	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))))

rewrite156.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 203

Calls

Call 1

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

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

simplify132.0ms (1%)

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))

localize143.0ms (1%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 90 to 42 computations (53.3% saved)

series40.0ms (0.3%)

Counts

4 → 180

Calls

54 calls:

Time	Variable		Point	Expression
4.0ms	sinTheta_i	@	0	(-.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	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	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	(*.f32 (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))

rewrite155.0ms (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)
(exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))
(-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))
(*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 6931/10000 (.f32 cosTheta_i (/.f32 cosTheta_O v)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 1) 6931/10000)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2) (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 3) 332956652491/1000000000000) (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) (-.f32 48038761/100000000 (.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 (.f32 cosTheta_i (/.f32 cosTheta_O v)) (.f32 cosTheta_i (/.f32 cosTheta_O v)) -48038761/100000000) (fma.f32 cosTheta_i (/.f32 cosTheta_O v) -6931/10000))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (neg.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (/.f32 1 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)) (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))) (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000)) (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (exp.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000))) (neg.f32 (exp.f32 (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (E.f32) (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2)) (cbrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))) (sqrt.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v))))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 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simplify164.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

376 → 276

Calls

Call 1

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

eval422.0ms (3.1%)

Compiler: Compiled 16139 to 8857 computations (45.1% saved)

prune161.0ms (1.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	497	7	504
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	499	7	506

Error

0.0b

Counts

506 → 7

Alt Table

Click to see full alt table

Status	Error	Program
▶	30.5b	(*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))
▶	0.5b	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
	0.1b	(.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (/.f32 1 v))) (/.f32 1/2 v))
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v)))
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (exp.f32 (-.f32 (fma.f32 cosTheta_i (/.f32 cosTheta_O v) 6931/10000) (fma.f32 sinTheta_i (/.f32 sinTheta_O v) (/.f32 1 v)))) (/.f32 1/2 v))) 3)
▶	28.8b	(.f32 (exp.f32 (.f32 sinTheta_i (neg.f32 (/.f32 sinTheta_O v)))) (/.f32 1/2 v))
▶	30.5b	(*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))

Compiler

Compiled 252 to 194 computations (23% saved)

localize102.0ms (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)))
✓	0.1b	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
✓	0.1b	(-.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) v))) (/.f32 1 v))
	8.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 84 to 46 computations (45.2% saved)

series14.0ms (0.1%)

Counts

3 → 52

Calls

27 calls:

Time	Variable		Point	Expression
3.0ms	cosTheta_i	@	-inf	(+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 (*.f32 cosTheta_i cosTheta_O) 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	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_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)))
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)))

rewrite130.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 228

Calls

Call 1

Inputs

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

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

(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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((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))))) (exp.f32 (/.f32 -1 v)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))))) (/.f32 1 (exp.f32 (/.f32 1 v))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (exp.f32 6931/10000) (exp.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (fma.f32 (/.f32 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simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

624×	`associate-/l*_binary32`
544×	`associate-r_binary32`
448×	`associate-l_binary32`
385×	`associate-/r*_binary32`
236×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	108	1627
1	313	1469
2	1174	1324
3	6828	1289

Stop Event

1×	node limit

Counts

280 → 272

Calls

Call 1

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

localize26.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 20 to 17 computations (15% saved)

series3.0ms (0%)

Counts

2 → 0

Calls

6 calls:

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

rewrite65.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

704×	`pow1_binary32`
658×	`add-log-exp_binary32`
658×	`log1p-expm1-u_binary32`
658×	`expm1-log1p-u_binary32`
646×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	145	15
2	1749	15

Stop Event

1×	node limit

Counts

2 → 51

Calls

Call 1

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

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

51 → 51

Calls

Call 1

Inputs

Outputs

localize23.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 19 to 16 computations (15.8% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

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

rewrite52.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`pow1_binary32`
625×	`add-log-exp_binary32`
625×	`log1p-expm1-u_binary32`
625×	`expm1-log1p-u_binary32`
614×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	9
1	146	9
2	1700	9

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

35 → 24

Calls

Call 1

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

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

localize39.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 43 to 15 computations (65.1% saved)

series13.0ms (0.1%)

Counts

3 → 108

Calls

27 calls:

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

rewrite101.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

3 → 211

Calls

Call 1

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

Outputs

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simplify114.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

319 → 231

Calls

Call 1

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

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

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 54 to 22 computations (59.3% saved)

series42.0ms (0.3%)

Counts

4 → 72

Calls

42 calls:

Time	Variable		Point	Expression
19.0ms	v	@	-inf	(/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v)
3.0ms	cosTheta_O	@	inf	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
1.0ms	cosTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
1.0ms	sinTheta_i	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))
1.0ms	cosTheta_O	@	0	(exp.f32 (/.f32 (-.f32 (.f32 cosTheta_i cosTheta_O) (+.f32 1 (.f32 sinTheta_i sinTheta_O))) v))

rewrite94.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

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

Stop Event

1×	node limit

Counts

4 → 128

Calls

Call 1

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

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

simplify110.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	node limit

Counts

200 → 165

Calls

Call 1

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

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

eval338.0ms (2.5%)

Compiler: Compiled 16346 to 9681 computations (40.8% saved)

prune141.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	778	9	787
Fresh	2	0	2
Picked	1	0	1
Done	4	0	4
Total	785	9	794

Error

0.0b

Counts

794 → 9

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(pow.f32 (cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))) 3)
	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
	28.3b	(exp.f32 (*.f32 (/.f32 sinTheta_i v) (neg.f32 sinTheta_O)))
▶	0.5b	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))
▶	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	0.1b	(pow.f32 (E.f32) (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v))))
	1.9b	(*.f32 (exp.f32 (+.f32 6931/10000 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))))) (exp.f32 (/.f32 -1 v)))
▶	28.4b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	30.0b	1

Compiler

Compiled 276 to 220 computations (20.3% saved)

localize90.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 106 to 68 computations (35.8% saved)

series37.0ms (0.3%)

Counts

4 → 144

Calls

36 calls:

Time	Variable		Point	Expression
7.0ms	v	@	-inf	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
3.0ms	v	@	inf	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
3.0ms	cosTheta_i	@	0	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
2.0ms	cosTheta_i	@	inf	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))
2.0ms	cosTheta_O	@	0	(cbrt.f32 (exp.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (-.f32 6931/10000 (/.f32 1 v)))))

rewrite124.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary32`
365×	`fma-def_binary32`
298×	`expm1-udef_binary32`
298×	`log1p-udef_binary32`
249×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	85
1	345	85
2	4487	85

Stop Event

1×	node limit

Counts

4 → 146

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 6931/10000 (-.f32 (/.f32 1 v) (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) 6931/10000) (/.f32 1 v))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 -1 v))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) 2) (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 -1 v)))) (/.f32 (pow.f32 (+.f32 6931/10000 (/.f32 -1 v)) 2) (-.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) (+.f32 6931/10000 (/.f32 -1 v)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (+.f32 (fma.f32 (/.f32 cosTheta_i v) cosTheta_O (log.f32 (/.f32 1/2 v))) 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simplify319.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

622×	`distribute-rgt-in_binary32`
611×	`distribute-lft-in_binary32`
281×	`associate-r_binary32`
246×	`distribute-rgt-neg-in_binary32`
245×	`unswap-sqr_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	308	6612
1	994	5895
2	3779	5450

Stop Event

1×	node limit

Counts

290 → 230

Calls

Call 1

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

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

localize21.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.0b	(exp.f32 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	8.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 22 to 8 computations (63.6% saved)

series4.0ms (0%)

Counts

1 → 16

Calls

9 calls:

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

rewrite50.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 20

Calls

Call 1

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

Outputs

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

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

36 → 27

Calls

Call 1

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

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

localize28.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 32 to 16 computations (50% saved)

series39.0ms (0.3%)

Counts

2 → 40

Calls

18 calls:

Time	Variable		Point	Expression
31.0ms	cosTheta_i	@	0	(/.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	cosTheta_i	@	inf	(/.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	v	@	inf	(exp.f32 (/.f32 (-.f32 (*.f32 cosTheta_i cosTheta_O) 1) v))

rewrite73.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

2 → 179

Calls

Call 1

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

Outputs

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

simplify61.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 4 (0.0ms)

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

Stop Event

1×	node limit

Counts

219 → 197

Calls

Call 1

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

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

localize82.0ms (0.6%)

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)))
✓	0.1b	(-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))

Compiler

Compiled 46 to 37 computations (19.6% saved)

series66.0ms (0.5%)

Counts

4 → 44

Calls

12 calls:

Time	Variable		Point	Expression
40.0ms	v	@	-inf	(+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))
17.0ms	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)))

rewrite152.0ms (1.1%)

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

simplify54.0ms (0.4%)

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))

localize75.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 71 to 44 computations (38% saved)

series5.0ms (0%)

Counts

2 → 39

Calls

12 calls:

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

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

731×	`prod-diff_binary32`
365×	`fma-def_binary32`
302×	`expm1-udef_binary32`
302×	`log1p-udef_binary32`
256×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	31
1	357	31
2	4663	31

Stop Event

1×	node limit

Counts

2 → 60

Calls

Call 1

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

Outputs

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

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

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

994×	`times-frac_binary32`
615×	`associate-/l*_binary32`
525×	`associate-r_binary32`
436×	`associate-l_binary32`
383×	`associate-/r*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	94	1548
1	280	1466
2	1041	1360
3	7732	1355

Stop Event

1×	node limit

Counts

99 → 89

Calls

Call 1

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

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

eval769.0ms (5.6%)

Compiler: Compiled 26467 to 19065 computations (28% saved)

prune221.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	1058	6	1064
Fresh	3	1	4
Picked	1	0	1
Done	3	1	4
Total	1065	8	1073

Error

0.0b

Counts

1073 → 8

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
▶	30.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	30.0b	1
▶	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
▶	0.5b	(exp.f32 (/.f32 -1 v))
▶	0.0b	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 3)
▶	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 202 to 176 computations (12.9% saved)

localize71.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 73 to 60 computations (17.8% saved)

series7.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

3.0ms

-inf

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

2.0ms

inf

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

2.0ms

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

rewrite62.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

691×	`prod-diff_binary32`
520×	`log-prod_binary32`
316×	`pow2_binary32`
315×	`fma-def_binary32`
220×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	262	19
2	3452	19

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

582×	`associate-r_binary32`
569×	`associate-l_binary32`
463×	`fma-neg_binary32`
334×	`times-frac_binary32`
310×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	136	1559
1	416	1338
2	1289	1126
3	7367	1114

Stop Event

1×	node limit

Counts

35 → 41

Calls

Call 1

Inputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3)
(+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3) (.f32 -1/3 (.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/9) (/.f32 1 v))))
(+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))) (.f32 1/3 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 17) 1) 1/9))) (pow.f32 v 2)))) (.f32 -1/3 (.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/9) (/.f32 1 v)))))
(+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))) (.f32 1/3 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 17) 1) 1/9))) (pow.f32 v 2)))) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 2)) 1/3) (/.f32 (-.f32 (.f32 -1/6 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))) (+.f32 (.f32 -1/27 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/3)) (.f32 -2/3 (.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 4) 1) 1/9) (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))) (.f32 1/3 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 17) 1) 1/9))))))) (pow.f32 v 3)))) (.f32 -1/3 (.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/9) (/.f32 1 v))))))
(pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/3)
(+.f32 (.f32 -1/3 (.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) v) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/9))) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/3))
(+.f32 (.f32 -1/3 (.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) v) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/9))) (+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/3) (.f32 1/3 (.f32 (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (*.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/9) (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 7) 1/3)))) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/3)))))
(+.f32 (.f32 -1/3 (.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) v) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/9))) (+.f32 (.f32 -1/3 (.f32 (/.f32 (-.f32 (.f32 1/6 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (+.f32 (.f32 1/27 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/3) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 3))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/9) (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 4) 1/3) (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 4)) 1/9) (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 7) 1/3))))))))) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/3))) (+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/3) (.f32 1/3 (.f32 (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/9) (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 7) 1/3)))) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/3))))))

Outputs
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (-.f32 (log.f32 (/.f32 1/2 v)) (/.f32 1 v)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (+.f32 (log.f32 (/.f32 1/2 v)) (/.f32 -1 v)))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))))
(pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3)
(cbrt.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2)))))
(cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))))
(cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000)))
(cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v)))
(+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3) (.f32 -1/3 (.f32 (pow.f32 (*.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/9) (/.f32 1 v))))
(+.f32 (cbrt.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2))))) (.f32 -1/3 (.f32 (/.f32 1 v) (*.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1/18) (pow.f32 (pow.f32 (exp.f32 (+.f32 (neg.f32 (log.f32 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1/18)))))
(fma.f32 -1/3 (/.f32 (*.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 7) 1/18) (pow.f32 (pow.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v)))) 7) 1/18)) v) (cbrt.f32 (exp.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))))))
(fma.f32 -1/3 (/.f32 (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 7) 1/18) (/.f32 v (pow.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 7) 1/18))) (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 6931/10000))))
(fma.f32 -1/3 (/.f32 (pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 7) 1/18) (/.f32 v (pow.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 7) 1/18))) (cbrt.f32 (*.f32 1/2 (/.f32 (exp.f32 6931/10000) v))))
(+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 1/3) (+.f32 (.f32 1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 2)) 1/3) (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2))))) (.f32 1/3 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 17) 1) 1/9))) (pow.f32 v 2)))) (.f32 -1/3 (.f32 (pow.f32 (.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 1 v)) (+.f32 6931/10000 (log.f32 1/2)))) 7) 1) 1/9) (/.f32 1 v)))))
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(fma.f32 1/3 (/.f32 (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))) (/.f32 v (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2))) v))) (fma.f32 -1/3 (.f32 (.f32 (/.f32 (/.f32 -1 v) v) (.f32 (exp.f32 6931/10000) -1/2)) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2)) 1/18))) (cbrt.f32 (.f32 (/.f32 -1 v) (*.f32 (exp.f32 6931/10000) -1/2)))))
(fma.f32 1/3 (/.f32 (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18))) (/.f32 v (/.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2))) v))) (fma.f32 -1/3 (.f32 (.f32 (/.f32 (/.f32 -1 v) v) (.f32 (exp.f32 6931/10000) -1/2)) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2)) 1/18))) (cbrt.f32 (.f32 (/.f32 -1 v) (*.f32 (exp.f32 6931/10000) -1/2)))))
(+.f32 (.f32 -1/3 (.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) v) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/9))) (+.f32 (.f32 -1/3 (.f32 (/.f32 (-.f32 (.f32 1/6 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (+.f32 (.f32 1/27 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/3) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 3))) (.f32 2/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/9) (.f32 (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 4) 1/3) (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000)))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 4)) 1/9) (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 7) 1/3))))))))) (pow.f32 v 3)) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/3))) (+.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/3) (.f32 1/3 (.f32 (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (.f32 (pow.f32 (/.f32 (pow.f32 1 4) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/9) (pow.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 7) 1/3)))) (pow.f32 v 2)) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 (log.f32 -1/2) 6931/10000))) 2)) 1/3))))))
(fma.f32 -1/3 (.f32 (/.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) v) (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/18))) (fma.f32 -1/3 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2))) (/.f32 (-.f32 (.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 1/6) (fma.f32 1/27 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2))) (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 3)) (.f32 2/3 (.f32 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/18)) (.f32 (cbrt.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18)) (cbrt.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 7)))))))))) (pow.f32 v 3))) (+.f32 (cbrt.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (.f32 (/.f32 (-.f32 (.f32 1/2 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2))))) (.f32 1/3 (.f32 (.f32 (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18)) (cbrt.f32 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 7))))) (.f32 v v)) (cbrt.f32 (/.f32 1 (pow.f32 (exp.f32 (+.f32 (log.f32 (/.f32 -1 v)) (+.f32 6931/10000 (log.f32 -1/2)))) 2))))))))
(fma.f32 -1/3 (.f32 (/.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) v) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 2)) 1/18))) (fma.f32 -1/3 (/.f32 (-.f32 (.f32 (.f32 1/6 (/.f32 -1 v)) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) (fma.f32 2/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 4)) (.f32 (fma.f32 1/2 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 7)))))) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 8)) 1/18)))) (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 2))) (.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 3) 1/27)))) (/.f32 (pow.f32 v 3) (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 2))))) (fma.f32 1/3 (.f32 (/.f32 (fma.f32 1/2 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) (.f32 -1/3 (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 4)) 1/18) (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 7)))))) (.f32 v v)) (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2)))) 2)))) (cbrt.f32 (.f32 (/.f32 -1 v) (exp.f32 (+.f32 6931/10000 (log.f32 -1/2))))))))
(+.f32 (fma.f32 -1/3 (.f32 (.f32 (/.f32 (/.f32 -1 v) v) (.f32 (exp.f32 6931/10000) -1/2)) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2)) 1/18))) (cbrt.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)))) (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2))) (+.f32 (.f32 -1/3 (/.f32 (+.f32 (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/12) (.f32 (.f32 -1/27 (.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 6931/10000)) 3) -1/8)) (cbrt.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 2))))) (.f32 (.f32 -2/3 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4))) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 8)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 8)) 1/18) (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))))))) (pow.f32 v 3))) (.f32 1/3 (/.f32 (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 1/2 v) (exp.f32 6931/10000)) 4)) 1/18))) (.f32 v v))))))
(+.f32 (fma.f32 -1/3 (.f32 (.f32 (/.f32 (/.f32 -1 v) v) (.f32 (exp.f32 6931/10000) -1/2)) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2)) 1/18) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2)) 1/18))) (cbrt.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)))) (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2))) (+.f32 (.f32 -1/3 (/.f32 (fma.f32 -1 (.f32 (/.f32 (exp.f32 6931/10000) v) -1/12) (fma.f32 -1/27 (.f32 (cbrt.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 2))) (.f32 (pow.f32 (.f32 (/.f32 -1 v) (exp.f32 6931/10000)) 3) -1/8)) (.f32 (.f32 -2/3 (cbrt.f32 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4))) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 8)) 1/18) (.f32 (pow.f32 (/.f32 1 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 8)) 1/18) (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18)))))))) (pow.f32 v 3))) (.f32 1/3 (/.f32 (fma.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/4) (.f32 (.f32 -1/3 (.f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 -1 v) (.f32 (exp.f32 6931/10000) -1/2)) 7)) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18))) (pow.f32 (/.f32 1 (pow.f32 (.f32 1/2 (/.f32 (exp.f32 6931/10000) v)) 4)) 1/18))) (*.f32 v v))))))

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f32 cosTheta_i cosTheta_O)
✓	0.0b	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
	8.4b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)

Compiler

Compiled 24 to 10 computations (58.3% saved)

series170.0ms (1.2%)

Counts

1 → 9

Calls

9 calls:

Time	Variable		Point	Expression
168.0ms	cosTheta_O	@	0	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_O	@	inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_i	@	0	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	v	@	-inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))
0.0ms	cosTheta_O	@	-inf	(+.f32 1 (/.f32 (*.f32 cosTheta_i cosTheta_O) v))

rewrite107.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 31

Calls

Call 1

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

Outputs

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

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×

saturated

Counts

40 → 34

Calls

Call 1

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

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

localize14.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

Compiler

Compiled 14 to 11 computations (21.4% saved)

series1.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite63.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

1 → 23

Calls

Call 1

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

Outputs

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

simplify43.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	node limit

Counts

31 → 30

Calls

Call 1

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

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

localize165.0ms (1.2%)

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	(+.f32 6931/10000 (/.f32 -1 v))
✓	0.1b	(exp.f32 (+.f32 6931/10000 (/.f32 -1 v)))

Compiler

Compiled 36 to 29 computations (19.4% saved)

series4.0ms (0%)

Counts

3 → 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))))
1.0ms	v	@	inf	(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)))

rewrite93.0ms (0.7%)

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

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 5 (0.0ms)

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

Stop Event

1×	node limit

Counts

169 → 156

Calls

Call 1

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

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

localize124.0ms (0.9%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 48 to 38 computations (20.8% saved)

series2.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

1.0ms

-inf

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

1.0ms

inf

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

0.0ms

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

rewrite82.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	17
1	274	17
2	3627	17

Stop Event

1×	node limit

Counts

1 → 27

Calls

Call 1

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

Outputs

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

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

785×	`fma-def_binary32`
709×	`associate-/r*_binary32`
705×	`associate-*l/_binary32`
498×	`associate-l_binary32`
438×	`associate-*r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	52	468
1	140	380
2	416	274
3	1886	248

Stop Event

1×	node limit

Counts

39 → 41

Calls

Call 1

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

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

eval742.0ms (5.4%)

Compiler: Compiled 18988 to 15325 computations (19.3% saved)

prune224.0ms (1.6%)

Pruning

12 alts after pruning (7 fresh and 5 done)

	Pruned	Kept	Total
New	872	6	878
Fresh	1	1	2
Picked	0	1	1
Done	1	4	5
Total	874	12	886

Error

0.0b

Counts

886 → 12

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.0b	(exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))
	30.0b	1
✓	0.0b	(pow.f32 (cbrt.f32 (exp.f32 (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))) 3)
	0.1b	(pow.f32 (exp.f32 (*.f32 (+.f32 (log.f32 (/.f32 1/2 v)) (-.f32 6931/10000 (/.f32 1 v))) 1/3)) 3)
	0.5b	(*.f32 (/.f32 1/2 v) (exp.f32 (/.f32 -1 v)))
	0.5b	(+.f32 1 (expm1.f32 (/.f32 -1 v)))
✓	0.1b	(*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))
✓	0.5b	(exp.f32 (/.f32 -1 v))
	24.4b	(*.f32 cosTheta_i (/.f32 cosTheta_O v))
	18.0b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
	0.1b	(pow.f32 (cbrt.f32 (*.f32 (/.f32 1/2 v) (exp.f32 (+.f32 6931/10000 (/.f32 -1 v))))) 3)
✓	0.1b	(pow.f32 (E.f32) (-.f32 (+.f32 6931/10000 (log.f32 (/.f32 1/2 v))) (/.f32 1 v)))

Compiler

Compiled 164 to 142 computations (13.4% saved)

regimes230.0ms (1.7%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

12 calls:

48.0ms	cosTheta_O
45.0ms	v
33.0ms	sinTheta_O
15.0ms	cosTheta_i
15.0ms	sinTheta_i

Results

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

Compiler

Compiled 512 to 353 computations (31.1% saved)

regimes129.0ms (0.9%)

Counts

28 → 1

Calls

Call 1

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

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

Calls

11 calls:

15.0ms	sinTheta_i
15.0ms	cosTheta_i
14.0ms	cosTheta_O
14.0ms	sinTheta_O
12.0ms	(+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v))))

Results

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

Compiler

Compiled 462 to 321 computations (30.5% saved)

regimes180.0ms (1.3%)

Counts

25 → 1

Calls

Call 1

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

Calls

9 calls:

48.0ms	cosTheta_O
41.0ms	v
17.0ms	sinTheta_i
16.0ms	sinTheta_O
14.0ms	cosTheta_i

Results

Error	Segments	Branch
0.0b	1	`cosTheta_i`
0.0b	1	`cosTheta_O`
0.0b	1	`sinTheta_i`
0.0b	1	`sinTheta_O`
0.0b	1	`v`
0.0b	1	`(exp.f32 (+.f32 (+.f32 (-.f32 (-.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v) (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (/.f32 1 v)) 6931/10000) (log.f32 (/.f32 1 (*.f32 2 v)))))`
0.0b	1	`(+.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 355 to 244 computations (31.3% saved)

regimes132.0ms (1%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

7 calls:

24.0ms	cosTheta_O
24.0ms	cosTheta_i
22.0ms	sinTheta_i
22.0ms	sinTheta_O
15.0ms	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 198 to 132 computations (33.3% saved)

regimes122.0ms (0.9%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

7 calls:

21.0ms	v
20.0ms	sinTheta_O
19.0ms	sinTheta_i
15.0ms	(*.f32 cosTheta_i cosTheta_O)
14.0ms	(*.f32 sinTheta_i sinTheta_O)

Results

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

Compiler

Compiled 170 to 113 computations (33.5% saved)

regimes50.0ms (0.4%)

Counts

13 → 1

Calls

Call 1

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

6 calls:

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

Results

Error	Segments	Branch
0.5b	1	`cosTheta_i`
0.5b	1	`cosTheta_O`
0.5b	1	`sinTheta_i`
0.5b	1	`sinTheta_O`
0.5b	1	`v`
0.5b	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 113 to 77 computations (31.9% saved)

regimes48.0ms (0.4%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

6 calls:

10.0ms	(*.f32 cosTheta_i cosTheta_O)
8.0ms	sinTheta_O
7.0ms	cosTheta_O
7.0ms	sinTheta_i
7.0ms	v

Results

Error	Segments	Branch
0.5b	1	`cosTheta_i`
0.5b	1	`cosTheta_O`
0.5b	1	`sinTheta_i`
0.5b	1	`sinTheta_O`
0.5b	1	`v`
0.5b	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 97 to 67 computations (30.9% saved)

regimes31.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

6 calls:

6.0ms	sinTheta_O
5.0ms	cosTheta_i
5.0ms	v
4.0ms	cosTheta_O
4.0ms	sinTheta_i

Results

Error	Segments	Branch
18.0b	1	`cosTheta_i`
18.0b	1	`cosTheta_O`
18.0b	1	`sinTheta_i`
18.0b	1	`sinTheta_O`
18.0b	1	`v`
18.0b	1	`(*.f32 cosTheta_i cosTheta_O)`

Compiler

Compiled 62 to 44 computations (29% saved)

regimes20.0ms (0.1%)

Counts

3 → 1

Calls

Call 1

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

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

Calls

5 calls:

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

Results

Error	Segments	Branch
24.4b	1	`cosTheta_i`
24.4b	1	`cosTheta_O`
24.4b	1	`sinTheta_i`
24.4b	1	`sinTheta_O`
24.4b	1	`v`

Compiler

Compiled 42 to 34 computations (19% saved)

regimes19.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

2 → 1

Calls

Call 1

Inputs
1
1

Outputs
1

Calls

5 calls:

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

Results

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

Compiler

Compiled 37 to 32 computations (13.5% saved)

simplify15.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`+-commutative_binary32`
11×	`*-commutative_binary32`
9×	`sub-neg_binary32`
5×	`neg-sub0_binary32`
5×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	154
1	66	154
2	79	154
3	91	154
4	99	154
5	104	154
6	106	154

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

Compiler

Compiled 152 to 124 computations (18.4% saved)

soundness0.0ms (0%)

end74.0ms (0.5%)

Remove

(sort sinTheta_i sinTheta_O)

(sort cosTheta_i cosTheta_O)

Compiler

Compiled 203 to 153 computations (24.6% saved)