Details

analyze96.0ms (0.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.6%	99.4%	0%	0%	0%	0
0%	0%	0.6%	99.4%	0%	0%	0%	1
0%	0%	0.6%	99.4%	0%	0%	0%	2
50%	0.3%	0.3%	99.4%	0%	0%	0%	3
50%	0.3%	0.3%	99.4%	0%	0%	0%	4
75%	0.5%	0.2%	99.4%	0%	0%	0%	5
75%	0.5%	0.2%	99.4%	0%	0%	0%	6
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	7
87.5%	0.6%	0.1%	99.4%	0%	0%	0%	8
93.8%	0.6%	0%	99.4%	0%	0%	0%	9
93.8%	0.6%	0%	99.4%	0%	0%	0%	10
96.9%	0.6%	0%	99.4%	0%	0%	0%	11
96.9%	0.6%	0%	99.4%	0%	0%	0%	12

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample2.9s (18.8%)

Results

2.9s

8256×

body

256

valid

Bogosity

preprocess78.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

694×	`distribute-rgt-in_binary32`
676×	`distribute-lft-in_binary32`
485×	`associate-/r*_binary32`
348×	`fma-def_binary32`
334×	`distribute-rgt-out_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	66
1	79	62
2	317	62
3	1615	62
4	6872	62
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

(/.f32 (-.f32 (*.f32 cosTheta cosTheta) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 cosTheta cosTheta))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 cosTheta cosTheta) 1) alpha) alpha))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta))))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 (log.f32 alpha) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
(/.f32 (-.f32 (.f32 cosTheta cosTheta) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 cosTheta cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 cosTheta cosTheta) 1) alpha) alpha))))
(/.f32 (fma.f32 cosTheta cosTheta -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 cosTheta cosTheta))) (+.f32 1 (.f32 (fma.f32 cosTheta cosTheta -1) (*.f32 alpha alpha)))))
(/.f32 (/.f32 (/.f32 (fma.f32 cosTheta cosTheta -1) (PI.f32)) (.f32 2 (log.f32 cosTheta))) (fma.f32 alpha (.f32 alpha (fma.f32 cosTheta cosTheta -1)) 1))
(/.f32 (/.f32 (fma.f32 cosTheta cosTheta -1) (fma.f32 (.f32 alpha alpha) (fma.f32 cosTheta cosTheta -1) 1)) (.f32 (PI.f32) (*.f32 (log.f32 cosTheta) 2)))
(/.f32 (/.f32 (fma.f32 cosTheta cosTheta -1) (PI.f32)) (.f32 (.f32 (log.f32 cosTheta) 2) (fma.f32 alpha (*.f32 alpha (fma.f32 cosTheta cosTheta -1)) 1)))

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

596×	`associate-/l*_binary32`
446×	`associate-l_binary32`
378×	`associate-*l/_binary32`
354×	`associate-r_binary32`
351×	`associate-+l+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	166	31
3	822	31
4	4306	31

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta)))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (.f32 (log.f32 alpha) 2)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

eval2.0ms (0%)

Compiler: Compiled 47 to 29 computations (38.3% 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

0.3b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Status

Error

Program

▶

0.5b

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

▶

0.5b

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 49 to 32 computations (34.7% saved)

localize83.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
✓	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 93 to 39 computations (58.1% saved)

series50.0ms (0.3%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
25.0ms	alpha	@	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
7.0ms	alpha	@	inf	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
4.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

rewrite169.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`log-prod_binary32`
572×	`fma-def_binary32`
275×	`fma-neg_binary32`
266×	`log1p-udef_binary32`
265×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	62
1	311	60
2	4669	60

Stop Event

1×	node limit

Counts

4 → 152

Calls

Call 1

Inputs
(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (log.f32 alpha) (PI.f32)) (.f32 (log.f32 alpha) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (PI.f32) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (log.f32 (cbrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (log.f32 (sqrt.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (-.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (.f32 (pow.f32 (.f32 2 (log.f32 alpha)) 3) (pow.f32 (PI.f32) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (PI.f32) (log.f32 alpha) (.f32 (PI.f32) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (log.f32 alpha) (PI.f32) (*.f32 (log.f32 alpha) (PI.f32)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (.f32 alpha alpha) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (neg.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (exp.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) (cbrt.f32 (exp.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) (log.f32 (cbrt.f32 (exp.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) (log.f32 (sqrt.f32 (exp.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (/.f32 (.f32 alpha alpha) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (pow.f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) 2) (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (neg.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))) (fma.f32 alpha alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 (cbrt.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta))) (cbrt.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta))))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta)))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 (pow.f32 alpha 6) -1) (.f32 cosTheta cosTheta)) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) cosTheta) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (exp.f32 cosTheta) (.f32 (fma.f32 alpha alpha -1) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (.f32 (log1p.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (pow.f32 (cbrt.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 2) (cbrt.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (hypot.f32 1 (.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) cosTheta)) (hypot.f32 1 (.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) cosTheta)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (+.f32 1 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 3)) (/.f32 1 (fma.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) -1) 1)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (-.f32 1 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 2)) (/.f32 1 (-.f32 1 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)))) -1)))))

simplify162.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-/l*_binary32`
571×	`fma-def_binary32`
346×	`associate-*l/_binary32`
319×	`distribute-rgt-in_binary32`
309×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3055
1	593	2651
2	2468	2480

Stop Event

1×	node limit

Counts

236 → 212

Calls

Call 1

Inputs
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (+.f32 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 4))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32))))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32)))))) (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(/.f32 -1/2 (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (+.f32 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(*.f32 -1 cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(*.f32 cosTheta (pow.f32 alpha 2))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(*.f32 cosTheta (pow.f32 alpha 2))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(*.f32 -1 (pow.f32 cosTheta 2))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))

Outputs
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(-.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 -1/2 (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2)))))) (.f32 alpha alpha)) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(fma.f32 (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta))))) (.f32 1/2 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 cosTheta (PI.f32))))) (.f32 alpha alpha) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta))))))
(fma.f32 alpha (.f32 alpha (fma.f32 1/2 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 cosTheta (PI.f32))) (/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta))))))) (/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (fma.f32 (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 -1/2 (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2)))))) (.f32 alpha alpha) (neg.f32 (/.f32 (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta)))))) (.f32 -1/2 (/.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2)))))) (/.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (.f32 cosTheta cosTheta) (pow.f32 alpha 4)))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))))
(fma.f32 (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta))))) (.f32 1/2 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 cosTheta (PI.f32))))) (.f32 alpha alpha) (fma.f32 -1 (/.f32 (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta))))) (.f32 1/2 (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 cosTheta (PI.f32))))) (/.f32 (/.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 cosTheta cosTheta)) (pow.f32 alpha 4))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta)))))))
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(+.f32 (/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32)) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (*.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6))))) (-.f32 (/.f32 (/.f32 1 (.f32 2 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) (pow.f32 cosTheta 8))))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8)))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32)) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6))) (log.f32 alpha))) (+.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8)))))))
(*.f32 -1 cosTheta)
(neg.f32 cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 cosTheta (pow.f32 alpha 2))
(.f32 cosTheta (.f32 alpha alpha))
(.f32 alpha (.f32 alpha cosTheta))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 cosTheta (pow.f32 alpha 2))
(.f32 cosTheta (.f32 alpha alpha))
(.f32 alpha (.f32 alpha cosTheta))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(fma.f32 -1 cosTheta (.f32 cosTheta (.f32 alpha alpha)))
(*.f32 cosTheta (fma.f32 alpha alpha -1))
(*.f32 -1 (pow.f32 cosTheta 2))
(neg.f32 (*.f32 cosTheta cosTheta))
(*.f32 cosTheta (neg.f32 cosTheta))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))
(.f32 (.f32 cosTheta cosTheta) (*.f32 alpha alpha))
(.f32 alpha (.f32 alpha (*.f32 cosTheta cosTheta)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))
(fma.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha) (neg.f32 (*.f32 cosTheta cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))

localize105.0ms (0.7%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2))
✓	0.4b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

New

Error

Program

✓

0.1b

(*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))

✓

0.3b

(/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2))

✓

0.4b

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

Compiler

Compiled 70 to 37 computations (47.1% saved)

series58.0ms (0.4%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
23.0ms	cosTheta	@	0	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
13.0ms	alpha	@	0	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
4.0ms	alpha	@	-inf	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
3.0ms	alpha	@	inf	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
3.0ms	alpha	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

rewrite85.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

791×	`log-prod_binary32`
380×	`pow2_binary32`
268×	`pow1/3_binary32`
258×	`log1p-udef_binary32`
257×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	301	60
2	3983	60

Stop Event

1×	node limit

Counts

3 → 128

Calls

Call 1

Inputs
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
(/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2))
(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))

Inputs

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))

(/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2))

(*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (exp.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) 2)) (log.f32 (cbrt.f32 (exp.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) (log.f32 (sqrt.f32 (exp.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) 2) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (fma.f32 alpha alpha -1) (.f32 (/.f32 1/2 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha 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Outputs

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

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

758×	`associate-/l*_binary32`
689×	`fma-def_binary32`
396×	`associate-*r/_binary32`
388×	`associate-*l/_binary32`
346×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	171	2820
1	604	2501
2	2478	2384

Stop Event

1×	node limit

Counts

188 → 187

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 6) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (*.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 alpha) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (*.f32 (log.f32 alpha) (PI.f32)))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(/.f32 -1/2 (PI.f32))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(*.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(*.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (PI.f32))) (.f32 1/2 (/.f32 1 (PI.f32))))
(.f32 (log.f32 alpha) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))
(+.f32 (.f32 (log.f32 alpha) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))) (.f32 (log.f32 alpha) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))
(+.f32 (.f32 (log.f32 alpha) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))) (.f32 (log.f32 alpha) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))
(+.f32 (.f32 (log.f32 alpha) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))) (.f32 (log.f32 alpha) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))))
(+.f32 (.f32 -1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (log.f32 (/.f32 1 alpha)))) (.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))))
(+.f32 (.f32 -1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (log.f32 (/.f32 1 alpha)))) (.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))))
(+.f32 (.f32 -1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (log.f32 (/.f32 1 alpha)))) (.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)))))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)))
(+.f32 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))))
(+.f32 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))))
(+.f32 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))))
(log.f32 alpha)
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (.f32 (.f32 alpha alpha) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2))))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32)))))
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(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
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(.f32 (log.f32 alpha) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
(.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(.f32 (log.f32 alpha) (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
(+.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))))
(.f32 (log.f32 alpha) (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (+.f32 (.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1))) 1))
(.f32 (log.f32 alpha) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))

eval494.0ms (3.2%)

Compiler: Compiled 14192 to 8087 computations (43% saved)

prune387.0ms (2.5%)

Pruning

29 alts after pruning (29 fresh and 0 done)

	Pruned	Kept	Total
New	370	29	399
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	372	29	401

Error

Counts

401 → 29

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(pow.f32 (.f32 (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))) -1)
	0.9b	(pow.f32 (cbrt.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) 3)
	0.8b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (pow.f32 (cbrt.f32 (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))) 3))
	0.9b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
	2.1b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
	31.6b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	11.1b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (/.f32 (.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha 1)))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.2b	(/.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)))) 1) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
	0.5b	(/.f32 (log1p.f32 (expm1.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)))) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
▶	31.6b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
	31.6b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
	11.0b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	0.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) 2) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))))
	0.7b	(.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
▶	0.5b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
▶	0.6b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	2.1b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	0.6b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))

Compiler

Compiled 1298 to 924 computations (28.8% saved)

localize182.0ms (1.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

Compiler

Compiled 94 to 39 computations (58.5% saved)

series7.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(pow.f32 (*.f32 alpha alpha) (PI.f32))
1.0ms	alpha	@	0	(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite88.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

869×	`log-prod_binary32`
545×	`fma-def_binary32`
268×	`fma-neg_binary32`
266×	`log1p-udef_binary32`
265×	`expm1-udef_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	41
1	315	39
2	4636	39

Stop Event

1×	node limit

Counts

2 → 89

Calls

Call 1

Inputs

(pow.f32 (*.f32 alpha alpha) (PI.f32))

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Outputs

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

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

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

949×	`associate-/l*_binary32`
565×	`fma-def_binary32`
342×	`associate-*l/_binary32`
319×	`distribute-rgt-in_binary32`
307×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	174	2469
1	583	2201
2	2505	2014

Stop Event

1×	node limit

Counts

125 → 134

Calls

Call 1

Inputs
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (+.f32 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 4))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32))))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32)))))) (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(/.f32 -1/2 (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (+.f32 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))

Outputs
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(pow.f32 (exp.f32 2) (*.f32 (log.f32 alpha) (PI.f32)))
(pow.f32 (*.f32 alpha alpha) (PI.f32))
(pow.f32 alpha (*.f32 (PI.f32) 2))
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(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6))))) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (.f32 (PI.f32) (pow.f32 cosTheta 4))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6)))))) (+.f32 (/.f32 1 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (.f32 (PI.f32) (pow.f32 cosTheta 4)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (*.f32 (PI.f32) (pow.f32 cosTheta 8)))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (pow.f32 (fma.f32 alpha alpha -1) 3)) (*.f32 (PI.f32) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (+.f32 (+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8))))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha))))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (*.f32 (PI.f32) (pow.f32 cosTheta 4)))))
(-.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6))))) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (.f32 (PI.f32) (pow.f32 cosTheta 4))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6)))))) (+.f32 (/.f32 1 (.f32 (.f32 (.f32 2 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (.f32 (PI.f32) (pow.f32 cosTheta 4)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (*.f32 (PI.f32) (pow.f32 cosTheta 8)))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (pow.f32 (fma.f32 alpha alpha -1) 3)) (*.f32 (PI.f32) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6)))) (+.f32 (+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8))))))

localize37.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
✓	0.4b	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
✓	0.4b	(*.f32 (log.f32 alpha) (PI.f32))

Compiler

Compiled 33 to 10 computations (69.7% saved)

series66.0ms (0.4%)

Counts

3 → 56

Calls

15 calls:

Time	Variable		Point	Expression
27.0ms	alpha	@	inf	(*.f32 (log.f32 alpha) (PI.f32))
10.0ms	cosTheta	@	0	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
9.0ms	alpha	@	-inf	(*.f32 (log.f32 alpha) (PI.f32))
6.0ms	alpha	@	-inf	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
6.0ms	alpha	@	0	(*.f32 (log.f32 alpha) (PI.f32))

rewrite79.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

523×	`log-prod_binary32`
431×	`prod-exp_binary32`
388×	`exp-prod_binary32`
354×	`pow-prod-down_binary32`
263×	`pow2_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	208	36
2	2594	36

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

Inputs
(*.f32 (log.f32 alpha) (PI.f32))
(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))

Outputs

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

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta))) 2)) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)))) (log.f32 (sqrt.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))) 2)) (cbrt.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))) (sqrt.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (-.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (pow.f32 (pow.f32 alpha (PI.f32)) (*.f32 cosTheta cosTheta)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32)))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cbrt.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 cosTheta (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (*.f32 (PI.f32) (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (PI.f32)) 1) (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1) (*.f32 2 (log.f32 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (log.f32 cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1) (*.f32 (log.f32 cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 2 (log.f32 cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1) (*.f32 (*.f32 2 (log.f32 cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 1) (log.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 2) (log.f32 (*.f32 (log.f32 alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (*.f32 2 (log.f32 cosTheta)) 1) (log.f32 (*.f32 (log.f32 alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 2 (log.f32 cosTheta)) (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 2) (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (*.f32 2 (log.f32 cosTheta)) 1) (*.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta)) (*.f32 (log.f32 cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (PI.f32)) 1)))))))

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

simplify93.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary32`
587×	`fma-neg_binary32`
429×	`distribute-rgt-neg-in_binary32`
395×	`distribute-lft-neg-in_binary32`
369×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	784
1	67	784
2	179	752
3	572	752
4	2135	752
5	5324	752

Stop Event

1×	node limit

Counts

161 → 116

Calls

Call 1

Inputs
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))

Outputs
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(neg.f32 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(*.f32 (neg.f32 (log.f32 alpha)) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (log.f32 alpha))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))

localize104.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))

Compiler

Compiled 95 to 50 computations (47.4% saved)

series7.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	alpha	@	0	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
1.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

rewrite100.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

598×	`fma-def_binary32`
297×	`expm1-udef_binary32`
297×	`log1p-udef_binary32`
284×	`fma-neg_binary32`
279×	`pow3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	352	41
2	5147	41

Stop Event

1×	node limit

Counts

2 → 91

Calls

Call 1

Inputs

(*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Outputs

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simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

726×	`associate-/l*_binary32`
539×	`fma-def_binary32`
472×	`*-commutative_binary32`
391×	`associate-*r/_binary32`
388×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	155	2196
1	542	2027
2	2247	1986

Stop Event

1×	node limit

Counts

127 → 135

Calls

Call 1

Inputs
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 6) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (*.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 alpha) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (*.f32 (log.f32 alpha) (PI.f32)))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))

Outputs
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(.f32 2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (.f32 2 (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(.f32 2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (.f32 2 (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(.f32 2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (.f32 2 (PI.f32)))
(.f32 2 (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(.f32 2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (.f32 2 (PI.f32)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
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(.f32 1/2 (fma.f32 (.f32 alpha alpha) (fma.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 1 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))) (/.f32 -1 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))))
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(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
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(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(+.f32 (.f32 (/.f32 -1/2 (log.f32 alpha)) (+.f32 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (/.f32 cosTheta (/.f32 (PI.f32) cosTheta))) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 4) (/.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (/.f32 (pow.f32 cosTheta 4) (PI.f32))) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4))))))
(-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (-.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))) (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(-.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))) (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))))
(+.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (fma.f32 alpha alpha -1) 3)))))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (+.f32 (+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 8) (pow.f32 (fma.f32 alpha alpha -1) 3)))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4))))))
(-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (-.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))) (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(-.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))) (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))))
(+.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (-.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (fma.f32 alpha alpha -1) 3)))))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 (fma.f32 alpha alpha -1) (PI.f32)) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (+.f32 (+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 8) (pow.f32 (fma.f32 alpha alpha -1) 3)))))))

localize70.0ms (0.5%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.1b

(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

✓

0.3b

(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))

✓

0.5b

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

Compiler

Compiled 70 to 37 computations (47.1% saved)

series11.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	0	(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
1.0ms	alpha	@	inf	(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
1.0ms	cosTheta	@	inf	(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
1.0ms	alpha	@	0	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	cosTheta	@	0	(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

rewrite148.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

778×	`log-prod_binary32`
284×	`pow1/3_binary32`
272×	`log1p-udef_binary32`
271×	`expm1-udef_binary32`
262×	`log-div_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	312	60
2	4200	60

Stop Event

1×	node limit

Counts

3 → 155

Calls

Call 1

Inputs

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))

(/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (*.f32 1/2 (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))) (cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (log.f32 (cbrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) (log.f32 (sqrt.f32 (pow.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (*.f32 1/2 (fma.f32 alpha alpha -1)) (*.f32 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (log.f32 alpha))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 alpha alpha -1) (/.f32 (*.f32 (log.f32 alpha) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 1/2 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (fma.f32 alpha alpha -1) (/.f32 (log.f32 alpha) (/.f32 1/2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1/2 (*.f32 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 1/2 (PI.f32)) (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> 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simplify152.0ms (1%)

Algorithm

1×	egg-herbie

Rules

838×	`fma-def_binary32`
609×	`associate-*l/_binary32`
413×	`distribute-rgt-in_binary32`
400×	`distribute-lft-in_binary32`
288×	`associate-/l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	237	3672
1	807	3368
2	3355	3313

Stop Event

1×	node limit

Counts

215 → 237

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(/.f32 -1 (log.f32 alpha))
(-.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (/.f32 1 (log.f32 alpha)))
(-.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (/.f32 1 (log.f32 alpha)))
(-.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (/.f32 1 (log.f32 alpha)))
(*.f32 -1 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 1 alpha))))
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(/.f32 (pow.f32 alpha 2) (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))))
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(-.f32 (/.f32 (pow.f32 alpha 2) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha))))) (/.f32 1 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha))))))
(/.f32 1/2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))
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(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 4)) (.f32 (pow.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) 3) (PI.f32))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 6) (pow.f32 alpha 6)) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 4) (PI.f32)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 4)) (.f32 (pow.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) 3) (PI.f32)))))))
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(/.f32 1/2 (PI.f32))
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(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
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(/.f32 1/2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (.f32 (pow.f32 cosTheta 8) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))))

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (.f32 (.f32 alpha alpha) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))) (/.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2))))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32)))))
(fma.f32 (.f32 1/2 (.f32 alpha alpha)) (+.f32 (/.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
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(fma.f32 -1/2 (/.f32 (/.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (pow.f32 cosTheta 4)) (.f32 (PI.f32) (pow.f32 alpha 4))) (fma.f32 1/2 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 alpha 6)))) (/.f32 1/2 (.f32 cosTheta (.f32 cosTheta (.f32 alpha (*.f32 alpha (PI.f32))))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 3) (.f32 (pow.f32 cosTheta 8) (.f32 (pow.f32 alpha 8) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 4) (PI.f32))))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (pow.f32 cosTheta 6) (*.f32 (pow.f32 alpha 6) (PI.f32))))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (.f32 alpha alpha)))) (fma.f32 -1/2 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 3) (.f32 (pow.f32 cosTheta 8) (.f32 (PI.f32) (pow.f32 alpha 8)))) (fma.f32 -1/2 (/.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 alpha 4)))) (.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 alpha 6))))))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 alpha alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (fma.f32 -1/2 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 3) (.f32 (pow.f32 cosTheta 8) (.f32 (PI.f32) (pow.f32 alpha 8)))) (fma.f32 -1/2 (/.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)))) (.f32 1/2 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2) (.f32 (pow.f32 alpha 6) (*.f32 (PI.f32) (pow.f32 cosTheta 6))))))))
(fma.f32 -1/2 (+.f32 (/.f32 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 3) (.f32 (PI.f32) (pow.f32 alpha 8))) (pow.f32 cosTheta 8)) (/.f32 (/.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (pow.f32 cosTheta 4)) (.f32 (PI.f32) (pow.f32 alpha 4)))) (fma.f32 1/2 (/.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 alpha 6)))) (/.f32 1/2 (.f32 cosTheta (.f32 cosTheta (.f32 alpha (*.f32 alpha (PI.f32))))))))
(/.f32 1/2 (PI.f32))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (PI.f32))) (*.f32 1/2 (/.f32 1 (PI.f32))))
(fma.f32 -1/2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) -1)) (PI.f32)) (/.f32 1/2 (PI.f32)))
(fma.f32 -1/2 (.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (.f32 cosTheta cosTheta)) (/.f32 1/2 (PI.f32)))
(fma.f32 -1/2 (.f32 (.f32 (/.f32 cosTheta (PI.f32)) cosTheta) (fma.f32 alpha alpha -1)) (/.f32 1/2 (PI.f32)))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)) (PI.f32))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (PI.f32))) (*.f32 1/2 (/.f32 1 (PI.f32)))))
(fma.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (/.f32 (PI.f32) (pow.f32 cosTheta 4))) (fma.f32 -1/2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32)) (/.f32 1/2 (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 -1/2 (.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (*.f32 cosTheta cosTheta)) (/.f32 1/2 (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 -1/2 (.f32 (*.f32 (/.f32 cosTheta (PI.f32)) cosTheta) (fma.f32 alpha alpha -1)) (/.f32 1/2 (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6)) (PI.f32))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)) (PI.f32))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (PI.f32))) (*.f32 1/2 (/.f32 1 (PI.f32))))))
(fma.f32 -1/2 (/.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (/.f32 (PI.f32) (pow.f32 cosTheta 6))) (fma.f32 1/2 (/.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (/.f32 (PI.f32) (pow.f32 cosTheta 4))) (fma.f32 -1/2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) -1)) (PI.f32)) (/.f32 1/2 (PI.f32)))))
(fma.f32 -1/2 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (/.f32 (PI.f32) (pow.f32 cosTheta 6))) (fma.f32 1/2 (.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (PI.f32)) (pow.f32 cosTheta 4)) (fma.f32 -1/2 (.f32 (/.f32 (fma.f32 alpha alpha -1) (PI.f32)) (*.f32 cosTheta cosTheta)) (/.f32 1/2 (PI.f32)))))
(fma.f32 -1/2 (/.f32 (pow.f32 cosTheta 6) (/.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 3))) (fma.f32 1/2 (.f32 (/.f32 (pow.f32 cosTheta 4) (PI.f32)) (pow.f32 (fma.f32 alpha alpha -1) 2)) (fma.f32 -1/2 (.f32 (*.f32 (/.f32 cosTheta (PI.f32)) cosTheta) (fma.f32 alpha alpha -1)) (/.f32 1/2 (PI.f32)))))
(/.f32 1/2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32)))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 alpha alpha -1))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 2))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (*.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))) (-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2)))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (-.f32 (/.f32 (/.f32 1/2 (pow.f32 (fma.f32 alpha alpha -1) 3)) (.f32 (PI.f32) (pow.f32 cosTheta 6))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2))))))
(+.f32 (+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2))))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 3)))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (.f32 (pow.f32 cosTheta 8) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))) (-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 4))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (-.f32 (/.f32 (/.f32 1/2 (pow.f32 (fma.f32 alpha alpha -1) 3)) (.f32 (PI.f32) (pow.f32 cosTheta 6))) (+.f32 (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 (/.f32 1/2 (*.f32 (PI.f32) (pow.f32 cosTheta 8))) (pow.f32 (fma.f32 alpha alpha -1) 4)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 1/2 (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 3)))) (-.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 8) (pow.f32 (fma.f32 alpha alpha -1) 4)))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))))
(/.f32 1/2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32)))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (fma.f32 alpha alpha -1))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 2))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (*.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))) (-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2)))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (-.f32 (/.f32 (/.f32 1/2 (pow.f32 (fma.f32 alpha alpha -1) 3)) (.f32 (PI.f32) (pow.f32 cosTheta 6))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2))))))
(+.f32 (+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (/.f32 -1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2))))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 3)))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (.f32 (pow.f32 cosTheta 8) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))) (-.f32 (/.f32 1/2 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (PI.f32))) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 4))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (PI.f32) (fma.f32 alpha alpha -1)))) (-.f32 (/.f32 (/.f32 1/2 (pow.f32 (fma.f32 alpha alpha -1) 3)) (.f32 (PI.f32) (pow.f32 cosTheta 6))) (+.f32 (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 (/.f32 1/2 (*.f32 (PI.f32) (pow.f32 cosTheta 8))) (pow.f32 (fma.f32 alpha alpha -1) 4)))))
(+.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (fma.f32 alpha alpha -1))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 1/2 (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 3)))) (-.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 8) (pow.f32 (fma.f32 alpha alpha -1) 4)))) (/.f32 1/2 (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (pow.f32 (fma.f32 alpha alpha -1) 2)))))))

localize95.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
✓	0.1b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
✓	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

Compiler

Compiled 82 to 34 computations (58.5% saved)

series116.0ms (0.8%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
35.0ms	alpha	@	inf	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
32.0ms	alpha	@	0	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
26.0ms	alpha	@	inf	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
12.0ms	alpha	@	0	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
5.0ms	alpha	@	inf	(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))

rewrite144.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

741×	`log-prod_binary32`
378×	`pow2_binary32`
343×	`pow-unpow_binary32`
261×	`pow1/3_binary32`
252×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	58
1	308	58
2	3968	58

Stop Event

1×	node limit

Counts

3 → 150

Calls

Call 1

Inputs

(/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))

Outputs

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

simplify186.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

596×	`fma-def_binary32`
392×	`associate-*l/_binary32`
386×	`associate-*r/_binary32`
319×	`distribute-rgt-in_binary32`
307×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	187	2762
1	626	2520
2	2630	2322

Stop Event

1×	node limit

Counts

198 → 207

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (+.f32 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 6) (pow.f32 cosTheta 4))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 -1 (/.f32 (.f32 (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32))))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32)))))) (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(/.f32 -1/2 (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(-.f32 (/.f32 1/2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))) (+.f32 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))) (.f32 -1 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))))
(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (log.f32 alpha)) (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)))
(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (log.f32 alpha)) (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)))
(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
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(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
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(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(fma.f32 -1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
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(*.f32 -1/2 (/.f32 (/.f32 alpha (/.f32 (log.f32 (/.f32 -1 alpha)) alpha)) (PI.f32)))
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(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
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(/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha))))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(-.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) (pow.f32 cosTheta 4)) (PI.f32)))))
(-.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6))))) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (pow.f32 cosTheta 4)) (PI.f32))))))
(-.f32 (+.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (pow.f32 cosTheta 6)))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (*.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (log.f32 alpha))) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (PI.f32) (pow.f32 cosTheta 6))))) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 cosTheta cosTheta)) (.f32 2 (log.f32 alpha)))) (+.f32 (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (pow.f32 cosTheta 4)) (PI.f32)))) (/.f32 1 (.f32 (.f32 2 (log.f32 alpha)) (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (*.f32 (PI.f32) (pow.f32 cosTheta 8))))))))
(+.f32 (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (PI.f32) (pow.f32 cosTheta 6))) (-.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (fma.f32 alpha alpha -1))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (PI.f32) (pow.f32 cosTheta 8)))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (log.f32 alpha))) (-.f32 (-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6))) (log.f32 alpha))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8))))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))) -2)
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))) -2)
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))) -2)
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))) -2)
(.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2))

eval1.3s (8.6%)

Compiler: Compiled 32396 to 19083 computations (41.1% saved)

prune324.0ms (2.1%)

Pruning

37 alts after pruning (35 fresh and 2 done)

	Pruned	Kept	Total
New	960	26	986
Fresh	15	9	24
Picked	1	0	1
Done	2	2	4
Total	978	37	1015

Error

Counts

1015 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	0.9b	(pow.f32 (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) 3)
	0.5b	(/.f32 (fma.f32 alpha alpha -1) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 1 (.f32 2 (log.f32 (pow.f32 alpha (PI.f32)))))))
	0.9b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
	2.1b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
▶	0.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
	31.6b	(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
	31.6b	(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
	31.6b	(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
	31.6b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
	11.1b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 1/2 (.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))
	31.6b	(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
✓	31.6b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
▶	31.6b	(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
	11.0b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
▶	11.0b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	0.5b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (PI.f32))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.9b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
▶	2.2b	(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
▶	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	2.1b	(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
	2.1b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	0.7b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	1.1b	(.f32 (log.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))

Compiler

Compiled 1402 to 1025 computations (26.9% saved)

localize74.0ms (0.5%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.1b

(*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2))

0.3b

(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))

✓

0.4b

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))

Compiler

Compiled 70 to 37 computations (47.1% saved)

series8.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	0	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
1.0ms	alpha	@	inf	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2))
1.0ms	alpha	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
1.0ms	cosTheta	@	0	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2))
1.0ms	alpha	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))

rewrite82.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

790×	`log-prod_binary32`
380×	`pow2_binary32`
268×	`pow1/3_binary32`
258×	`log1p-udef_binary32`
257×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	50
1	301	50
2	3937	50

Stop Event

1×	node limit

Counts

2 → 87

Calls

Call 1

Inputs

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))

(*.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2))

Outputs

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simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

727×	`associate-/l*_binary32`
600×	`fma-def_binary32`
397×	`associate-*r/_binary32`
386×	`associate-*l/_binary32`
331×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	157	2707
1	557	2432
2	2313	2265

Stop Event

1×	node limit

Counts

135 → 137

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 6) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (*.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 alpha) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (*.f32 (log.f32 alpha) (PI.f32)))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(.f32 2 (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
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(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(*.f32 2 (PI.f32))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
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(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
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(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 3))))) (/.f32 -1/2 (.f32 (.f32 (.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (pow.f32 cosTheta 4)) (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
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(-.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))))
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(-.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))))
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(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 -1/2 (.f32 (.f32 (*.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (pow.f32 cosTheta 4)) (PI.f32)))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))))
(-.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (.f32 cosTheta cosTheta) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))) (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (+.f32 (.f32 alpha alpha) -1)))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (-.f32 (-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 1/2 (.f32 (.f32 (pow.f32 cosTheta 8) (pow.f32 (fma.f32 alpha alpha -1) 3)) (.f32 (log.f32 alpha) (PI.f32))))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 4)) (*.f32 (log.f32 alpha) (fma.f32 alpha alpha -1))))))
(+.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (-.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 6)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 1/2 (.f32 (.f32 (PI.f32) (pow.f32 cosTheta 8)) (.f32 (log.f32 alpha) (pow.f32 (fma.f32 alpha alpha -1) 3))))) (/.f32 -1/2 (.f32 (.f32 (.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (pow.f32 cosTheta 4)) (PI.f32)))))
(.f32 2 (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))
(.f32 2 (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32)))
(.f32 2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(.f32 2 (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 2 (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (.f32 (*.f32 2 alpha) alpha))
(.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (.f32 2 (*.f32 alpha alpha)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(.f32 2 (.f32 (pow.f32 alpha 2) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 2 (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (.f32 (*.f32 2 alpha) alpha))
(.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (.f32 2 (*.f32 alpha alpha)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 2 (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
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(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(*.f32 2 (PI.f32))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (.f32 2 (+.f32 (.f32 alpha alpha) -1)) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 2 (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (fma.f32 alpha alpha -1)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)) (.f32 2 (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (.f32 2 (+.f32 (.f32 alpha alpha) -1)) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 2 (.f32 (.f32 cosTheta (.f32 cosTheta (PI.f32))) (fma.f32 alpha alpha -1)))
(.f32 (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)) (.f32 2 (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))
(+.f32 (.f32 2 (PI.f32)) (.f32 2 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(.f32 2 (+.f32 (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)) (.f32 (.f32 alpha alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))))
(.f32 2 (.f32 (PI.f32) (+.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (.f32 (.f32 (.f32 alpha alpha) cosTheta) cosTheta))))
(.f32 2 (.f32 (fma.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1) 1) (PI.f32)))

localize44.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
✓	0.3b	(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
✓	0.3b	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))

Compiler

Compiled 35 to 10 computations (71.4% saved)

series7.0ms (0%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	0	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
1.0ms	alpha	@	-inf	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
1.0ms	cosTheta	@	inf	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
1.0ms	alpha	@	inf	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
1.0ms	cosTheta	@	0	(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))

rewrite79.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

522×	`log-prod_binary32`
428×	`prod-exp_binary32`
394×	`exp-prod_binary32`
351×	`pow-prod-down_binary32`
263×	`pow2_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	38
1	208	38
2	2588	38

Stop Event

1×	node limit

Counts

3 → 107

Calls

Call 1

Inputs
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta))) 2)) (log.f32 (cbrt.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)))) (log.f32 (sqrt.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 2)) (cbrt.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))) (sqrt.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (-.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (pow.f32 alpha (*.f32 cosTheta cosTheta)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (pow.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha))) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 cosTheta (sqrt.f32 (log.f32 alpha)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (log.f32 alpha)) 1) (*.f32 2 (log.f32 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (log.f32 alpha)) (*.f32 (log.f32 cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (log.f32 alpha)) 1) (*.f32 (log.f32 cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (log.f32 alpha)) (*.f32 (*.f32 2 (log.f32 cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (log.f32 alpha)) 1) (*.f32 (*.f32 2 (log.f32 cosTheta)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 1) (log.f32 (*.f32 (log.f32 alpha) cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 2) (log.f32 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (*.f32 2 (log.f32 cosTheta)) 1) (log.f32 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 2 (log.f32 cosTheta)) (*.f32 (log.f32 (log.f32 alpha)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 2) (*.f32 (log.f32 (log.f32 alpha)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (*.f32 2 (log.f32 cosTheta)) 1) (*.f32 (log.f32 (log.f32 alpha)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) cosTheta)) (*.f32 (log.f32 cosTheta) 1)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32)))) 2)) (log.f32 (cbrt.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))))) (log.f32 (sqrt.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 6) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 1) (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))) 2)) (cbrt.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (exp.f32 (sqrt.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))) (sqrt.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 4))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (-.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 6))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (pow.f32 (pow.f32 alpha cosTheta) (*.f32 cosTheta (PI.f32))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (pow.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta) 6)) 1/3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 (sqrt.f32 (*.f32 (log.f32 alpha) (PI.f32))) cosTheta)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (*.f32 (log.f32 (*.f32 (*.f32 (*.f32 (log.f32 alpha) (PI.f32)) cosTheta) cosTheta)) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 cosTheta) 2) (log.f32 (*.f32 (log.f32 alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (*.f32 2 (log.f32 cosTheta)) 1) (log.f32 (*.f32 (log.f32 alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1) (log.f32 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (PI.f32)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1) (*.f32 (log.f32 (PI.f32)) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (PI.f32)) 1) (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (PI.f32)) (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (*.f32 (log.f32 (PI.f32)) 1) (*.f32 (log.f32 (*.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (log.f32 cosTheta) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (+.f32 (log.f32 (*.f32 (log.f32 alpha) (PI.f32))) (*.f32 (*.f32 2 (log.f32 cosTheta)) 1)))))))

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

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

767×	`fma-def_binary32`
695×	`fma-neg_binary32`
521×	`distribute-rgt-in_binary32`
438×	`distribute-lft-in_binary32`
423×	`associate-l_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	912
1	66	912
2	183	912
3	668	912
4	2541	912
5	6629	912

Stop Event

1×	node limit

Counts

179 → 119

Calls

Call 1

Inputs
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))

Outputs
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (pow.f32 cosTheta 2)))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(*.f32 (log.f32 alpha) (pow.f32 cosTheta 2))
(.f32 (log.f32 alpha) (.f32 cosTheta cosTheta))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
(.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
(.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
(.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32))))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
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(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32))))
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(.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))
(.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32)))
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(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
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(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
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(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 cosTheta cosTheta)) (log.f32 alpha))
(/.f32 1/2 (.f32 cosTheta (.f32 (log.f32 alpha) (*.f32 cosTheta (PI.f32)))))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))

localize50.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f32 1 (*.f32 cosTheta cosTheta))
✓	0.1b	(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
✓	0.2b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
✓	0.4b	(.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))

Compiler

Compiled 47 to 22 computations (53.2% saved)

series14.0ms (0.1%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	0	(.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
1.0ms	alpha	@	-inf	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
1.0ms	alpha	@	0	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
1.0ms	alpha	@	0	(.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
1.0ms	alpha	@	inf	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))

rewrite93.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

592×	`log-prod_binary32`
382×	`pow-prod-down_binary32`
317×	`pow2_binary32`
222×	`pow1/3_binary32`
217×	`expm1-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	54
1	253	54
2	3194	54

Stop Event

1×	node limit

Counts

4 → 139

Calls

Call 1

Inputs
(.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(-.f32 1 (*.f32 cosTheta cosTheta))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) 1) (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 cosTheta (neg.f32 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))) 2)) (log.f32 (cbrt.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))) (log.f32 (sqrt.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 1 (pow.f32 cosTheta 6))) (+.f32 1 (fma.f32 cosTheta cosTheta (pow.f32 cosTheta 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (-.f32 1 (pow.f32 cosTheta 4))) (fma.f32 cosTheta cosTheta 1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (-.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (-.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (PI.f32) (log.f32 alpha) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (log.f32 alpha) (PI.f32) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (.f32 (PI.f32) (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (PI.f32) (log.f32 alpha)) 1 (.f32 (.f32 (PI.f32) (log.f32 alpha)) (.f32 cosTheta (neg.f32 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (.f32 (PI.f32) (log.f32 alpha))) 2) (cbrt.f32 (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (.f32 (PI.f32) (log.f32 alpha))) (sqrt.f32 (.f32 (PI.f32) (log.f32 alpha))) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (PI.f32) (pow.f32 (cbrt.f32 (log.f32 alpha)) 2)) (cbrt.f32 (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (PI.f32) (sqrt.f32 (log.f32 alpha))) (sqrt.f32 (log.f32 alpha)) (.f32 (.f32 cosTheta (neg.f32 cosTheta)) (.f32 (PI.f32) (log.f32 alpha))))))))
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(cbrt.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)) (cbrt.f32 (-.f32 1 (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta cosTheta))) (sqrt.f32 (-.f32 1 (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 1 (pow.f32 cosTheta 6)) (/.f32 1 (+.f32 1 (fma.f32 cosTheta cosTheta (pow.f32 cosTheta 4)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 1 (pow.f32 cosTheta 4)) (/.f32 1 (fma.f32 cosTheta cosTheta 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 1 (fma.f32 cosTheta cosTheta (pow.f32 cosTheta 4))) (-.f32 1 (pow.f32 cosTheta 6))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 cosTheta cosTheta 1) (-.f32 1 (pow.f32 cosTheta 4))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (pow.f32 cosTheta 6)) (+.f32 1 (fma.f32 cosTheta 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(#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (-.f32 1 (.f32 cosTheta cosTheta))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (-.f32 1 (.f32 cosTheta cosTheta))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 1 (fma.f32 cosTheta cosTheta (pow.f32 cosTheta 4))) (-.f32 1 (pow.f32 cosTheta 6))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (fma.f32 cosTheta cosTheta 1) (-.f32 1 (pow.f32 cosTheta 4))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (-.f32 1 (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (-.f32 1 (.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (-.f32 1 (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (-.f32 1 (.f32 cosTheta cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log1p.f32 (.f32 cosTheta (neg.f32 cosTheta))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log1p.f32 (.f32 cosTheta (neg.f32 cosTheta))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (.f32 cosTheta (neg.f32 cosTheta)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 cosTheta (neg.f32 cosTheta) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (cbrt.f32 cosTheta) cosTheta) (neg.f32 (pow.f32 (cbrt.f32 cosTheta) 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (neg.f32 cosTheta) cosTheta 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 (.f32 cosTheta (neg.f32 cosTheta))) 2) (cbrt.f32 (.f32 cosTheta (neg.f32 cosTheta))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (.f32 cosTheta (neg.f32 cosTheta))) (sqrt.f32 (.f32 cosTheta (neg.f32 cosTheta))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 -1 (.f32 cosTheta cosTheta) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (neg.f32 (.f32 (cbrt.f32 cosTheta) cosTheta)) (pow.f32 (cbrt.f32 cosTheta) 2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (neg.f32 cosTheta) 1) cosTheta 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (neg.f32 cosTheta) (pow.f32 (cbrt.f32 cosTheta) 2)) (cbrt.f32 cosTheta) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (.f32 (neg.f32 cosTheta) (sqrt.f32 cosTheta)) (sqrt.f32 cosTheta) 1)))))

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

784×	`div-sub_binary32`
744×	`fma-neg_binary32`
672×	`associate-/l*_binary32`
313×	`associate-*l/_binary32`
271×	`*-commutative_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	85	1446
1	250	1440
2	796	1434
3	2720	1360
4	7144	1356

Stop Event

1×	node limit

Counts

223 → 182

Calls

Call 1

Inputs
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(*.f32 (log.f32 alpha) (PI.f32))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
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(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
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(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 (log.f32 alpha) (PI.f32)))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(/.f32 1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
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(/.f32 1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
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(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
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(-.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 alpha) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (+.f32 (.f32 -1/2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (pow.f32 cosTheta 6) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (pow.f32 cosTheta 4) (.f32 (log.f32 alpha) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
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(*.f32 (log.f32 alpha) (-.f32 1 (pow.f32 cosTheta 2)))
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(*.f32 (log.f32 alpha) (-.f32 1 (pow.f32 cosTheta 2)))
(*.f32 (log.f32 alpha) (-.f32 1 (pow.f32 cosTheta 2)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 (/.f32 1 alpha))))
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(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(log.f32 alpha)
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
1
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(*.f32 -1 (pow.f32 cosTheta 2))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(*.f32 -1 (pow.f32 cosTheta 2))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))

Outputs
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (log.f32 alpha) (PI.f32))
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(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
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(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32)))
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(.f32 (log.f32 alpha) (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
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(.f32 (.f32 cosTheta (log.f32 alpha)) (neg.f32 (*.f32 cosTheta (PI.f32))))
(.f32 (log.f32 alpha) (.f32 cosTheta (*.f32 (PI.f32) (neg.f32 cosTheta))))
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(neg.f32 (.f32 (log.f32 alpha) (.f32 (*.f32 cosTheta cosTheta) (PI.f32))))
(.f32 (log.f32 alpha) (neg.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32)))))
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(.f32 (.f32 cosTheta (log.f32 alpha)) (neg.f32 (*.f32 cosTheta (PI.f32))))
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(/.f32 -1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 (log.f32 alpha) (PI.f32))))
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(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
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1
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localize76.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))
✓	0.5b	(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

Compiler

Compiled 33 to 19 computations (42.4% saved)

series4.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

2.0ms

alpha

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

1.0ms

alpha

-inf

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

1.0ms

alpha

inf

(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

rewrite62.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`log-prod_binary32`
398×	`exp-prod_binary32`
336×	`pow-prod-down_binary32`
273×	`pow2_binary32`
193×	`pow1/3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	211	17
2	2763	17

Stop Event

1×	node limit

Counts

1 → 72

Calls

Call 1

Inputs
(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

Outputs

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

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

643×	`associate-/r/_binary32`
641×	`associate-l_binary32`
617×	`associate-/l/_binary32`
315×	`fma-def_binary32`
293×	`div-sub_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	298
1	98	280
2	253	276
3	682	213
4	2691	195

Stop Event

1×	node limit

Counts

84 → 80

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(*.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))))
(/.f32 alpha (/.f32 (log.f32 alpha) (/.f32 alpha (/.f32 (PI.f32) 1/2))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(*.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))))
(/.f32 alpha (/.f32 (log.f32 alpha) (/.f32 alpha (/.f32 (PI.f32) 1/2))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))

localize157.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
✓	0.3b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.4b	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
✓	0.4b	(/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

series17.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
3.0ms	alpha	@	-inf	(/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
2.0ms	alpha	@	-inf	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	cosTheta	@	inf	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	cosTheta	@	0	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	cosTheta	@	inf	(/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

rewrite98.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

325×	`log1p-udef_binary32`
324×	`expm1-udef_binary32`
319×	`log-div_binary32`
273×	`log-pow_binary32`
242×	`prod-diff_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	70
1	385	65
2	5562	65

Stop Event

1×	node limit

Counts

3 → 141

Calls

Call 1

Inputs

(/.f32 (+.f32 alpha 1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2)))

(*.f32 (/.f32 (+.f32 alpha 1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))

(/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

Outputs

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

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

simplify98.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

926×	`distribute-rgt-in_binary32`
892×	`distribute-lft-in_binary32`
283×	`associate-/r*_binary32`
195×	`associate-r_binary32`
164×	`times-frac_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	4418
1	881	3842
2	3648	3727

Stop Event

1×	node limit

Counts

201 → 227

Calls

Call 1

Inputs
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(+.f32 (.f32 -1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))))
(+.f32 (.f32 -1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (-.f32 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (.f32 (log.f32 alpha) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1)))) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (*.f32 (log.f32 alpha) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1)))) (.f32 (log.f32 alpha) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (-.f32 alpha 1)))) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (.f32 (log.f32 alpha) (PI.f32)))))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 (log.f32 alpha) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))))))
(/.f32 -1 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))))
(-.f32 (/.f32 alpha (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (/.f32 1 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))
(-.f32 (+.f32 (/.f32 (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (/.f32 alpha (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))) (/.f32 1 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))
(-.f32 (+.f32 (/.f32 alpha (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (+.f32 (.f32 -1 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 3)) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)))) (/.f32 1 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2)))))
(/.f32 1 (*.f32 alpha (pow.f32 cosTheta 2)))
(-.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha)) (/.f32 1 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 3))) (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha))) (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 3))) (/.f32 1 (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 4))) (+.f32 (/.f32 1 (.f32 (pow.f32 alpha 3) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha)))) (+.f32 (/.f32 1 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 2))) (+.f32 (/.f32 1 (.f32 (pow.f32 alpha 3) (pow.f32 cosTheta 4))) (/.f32 1 (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2))))))
(/.f32 1 (*.f32 alpha (pow.f32 cosTheta 2)))
(-.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha)) (/.f32 1 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 3))) (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha))) (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 3))) (/.f32 1 (.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)))))
(-.f32 (+.f32 (.f32 -1 (/.f32 (-.f32 (/.f32 1 (pow.f32 cosTheta 2)) (/.f32 1 (pow.f32 cosTheta 4))) (pow.f32 alpha 4))) (+.f32 (/.f32 1 (.f32 (pow.f32 alpha 3) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 cosTheta 2) alpha)))) (+.f32 (/.f32 1 (.f32 (pow.f32 alpha 3) (pow.f32 cosTheta 4))) (/.f32 1 (*.f32 (pow.f32 alpha 2) (pow.f32 cosTheta 2)))))
(-.f32 alpha 1)
(-.f32 (+.f32 (.f32 -1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) alpha) 1)
(-.f32 (+.f32 (.f32 -1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (+.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1))) alpha)) 1)
(-.f32 (+.f32 (.f32 -1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (-.f32 alpha 1)))) (+.f32 (.f32 -1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (+.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1))) alpha))) 1)
(/.f32 (-.f32 alpha 1) (*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6)))))))
(/.f32 (-.f32 alpha 1) (*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6)))))))

Outputs
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(fma.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(fma.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(fma.f32 1/2 (/.f32 alpha (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
(fma.f32 1/2 (/.f32 (/.f32 alpha (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)))
(.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(/.f32 (.f32 -1/2 alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha))))
(.f32 -1/2 (/.f32 alpha (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(.f32 -1/2 (/.f32 alpha (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (/.f32 (.f32 -1/2 alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))) (/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (/.f32 (.f32 -1/2 alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))) (/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))
(-.f32 (.f32 -1/2 (/.f32 alpha (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (/.f32 (.f32 -1/2 alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (/.f32 alpha (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))) (/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (PI.f32)))))
(.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(*.f32 1/2 (/.f32 (/.f32 alpha (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))) (PI.f32)))
(.f32 1/2 (/.f32 alpha (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))) (PI.f32)) (/.f32 1/2 (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (/.f32 alpha (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))) (PI.f32)) (/.f32 1/2 (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (/.f32 alpha (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 1/2 (/.f32 alpha (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))) (PI.f32)) (/.f32 1/2 (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (/.f32 alpha (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 (.f32 1/2 (.f32 alpha alpha)) (-.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))))) (/.f32 (neg.f32 (.f32 cosTheta cosTheta)) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) 2)))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta)))))))
(fma.f32 (.f32 (.f32 1/2 alpha) alpha) (+.f32 (/.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (/.f32 cosTheta (.f32 (log.f32 alpha) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))) (/.f32 cosTheta (PI.f32)))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(fma.f32 (.f32 alpha alpha) (.f32 (+.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta)))) (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) 1/2) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
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(-.f32 alpha 1)
(+.f32 alpha -1)
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(+.f32 -1 (-.f32 alpha (.f32 (.f32 cosTheta cosTheta) (*.f32 (+.f32 alpha -1) (fma.f32 alpha alpha -1)))))
(.f32 (+.f32 (.f32 cosTheta (neg.f32 (*.f32 cosTheta (fma.f32 alpha alpha -1)))) 1) (+.f32 alpha -1))
(-.f32 (+.f32 (.f32 -1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (+.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1))) alpha)) 1)
(+.f32 (fma.f32 -1 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (+.f32 alpha -1)) (fma.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (.f32 (pow.f32 cosTheta 4) (+.f32 alpha -1)) alpha)) -1)
(+.f32 -1 (-.f32 (fma.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)) (+.f32 alpha -1) alpha) (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 alpha -1) (fma.f32 alpha alpha -1)))))
(+.f32 -1 (+.f32 alpha (.f32 (+.f32 alpha -1) (+.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)) (.f32 cosTheta (neg.f32 (.f32 cosTheta (fma.f32 alpha alpha -1))))))))
(-.f32 (+.f32 (.f32 -1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 6) (-.f32 alpha 1)))) (+.f32 (.f32 -1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 2) (-.f32 alpha 1)))) (+.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 4) (-.f32 alpha 1))) alpha))) 1)
(+.f32 (fma.f32 -1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (+.f32 alpha -1) (pow.f32 cosTheta 6))) (fma.f32 -1 (.f32 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1)) (+.f32 alpha -1)) (fma.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2) (*.f32 (pow.f32 cosTheta 4) (+.f32 alpha -1)) alpha))) -1)
(+.f32 -1 (-.f32 (-.f32 (fma.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)) (+.f32 alpha -1) alpha) (.f32 (.f32 cosTheta cosTheta) (.f32 (+.f32 alpha -1) (fma.f32 alpha alpha -1)))) (.f32 (+.f32 alpha -1) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))))
(+.f32 -1 (-.f32 (fma.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)) (+.f32 alpha -1) alpha) (.f32 (+.f32 alpha -1) (+.f32 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)) (.f32 (*.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1))))))
(/.f32 (-.f32 alpha 1) (*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) -1)))
(/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))
(/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (-.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))))
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(+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 alpha (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6)))))))
(-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))))
(+.f32 (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 -1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6)))))))
(-.f32 (+.f32 (+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 alpha (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6))))) (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 4) (pow.f32 cosTheta 8)))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (+.f32 (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 4) (pow.f32 cosTheta 8))) (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (+.f32 (/.f32 1 (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (fma.f32 alpha alpha -1) 4)) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 4) (pow.f32 cosTheta 8))) (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (+.f32 (/.f32 1 (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (fma.f32 alpha alpha -1) 4)) (pow.f32 cosTheta 8))))))
(/.f32 (-.f32 alpha 1) (*.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)))
(/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (+.f32 (*.f32 alpha alpha) -1)))
(/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))
(/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))
(+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (-.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))))
(-.f32 (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))))))
(+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 alpha (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6)))))))
(-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))))
(+.f32 (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))) (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2)))) (/.f32 -1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))))
(-.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (+.f32 (/.f32 alpha (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4)))))) (+.f32 (/.f32 1 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 4))) (+.f32 (/.f32 alpha (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 8))) (/.f32 1 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 6)))))))
(-.f32 (+.f32 (+.f32 (/.f32 alpha (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (/.f32 alpha (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6))))) (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 4) (pow.f32 cosTheta 8)))) (+.f32 (/.f32 1 (.f32 (.f32 cosTheta cosTheta) (+.f32 (.f32 alpha alpha) -1))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (+.f32 (.f32 alpha alpha) -1) 2))) (+.f32 (/.f32 1 (.f32 (pow.f32 (+.f32 (.f32 alpha alpha) -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 4) (pow.f32 cosTheta 8))) (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1))))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (+.f32 (/.f32 1 (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (fma.f32 alpha alpha -1) 4)) (pow.f32 cosTheta 8))))))
(+.f32 (/.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 4) (pow.f32 cosTheta 8))) (-.f32 (+.f32 (+.f32 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (/.f32 alpha (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6)))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 cosTheta cosTheta) (fma.f32 alpha alpha -1)))) (+.f32 (/.f32 alpha (.f32 (pow.f32 cosTheta 4) (pow.f32 (fma.f32 alpha alpha -1) 2))) (+.f32 (/.f32 1 (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))) (/.f32 (/.f32 alpha (pow.f32 (fma.f32 alpha alpha -1) 4)) (pow.f32 cosTheta 8))))))

eval595.0ms (3.9%)

Compiler: Compiled 22357 to 13327 computations (40.4% saved)

prune221.0ms (1.4%)

Pruning

33 alts after pruning (30 fresh and 3 done)

	Pruned	Kept	Total
New	842	20	862
Fresh	20	10	30
Picked	0	1	1
Done	4	2	6
Total	866	33	899

Error

Counts

899 → 33

Alt Table

Click to see full alt table

Status	Error	Program
▶	2.1b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
	0.7b	(/.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (+.f32 alpha -1)))
	11.0b	(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
	11.1b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	11.8b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	2.1b	(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
	2.2b	(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
	2.1b	(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
	2.1b	(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
▶	11.8b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
✓	11.0b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	11.0b	(/.f32 -1/2 (log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
	2.3b	(*.f32 (pow.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) 2) (/.f32 1/2 (PI.f32)))
	0.9b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
✓	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	2.2b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
	1.0b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (+.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1 (-.f32 1 (*.f32 cosTheta cosTheta)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	2.1b	(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
	2.1b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	11.8b	(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
	2.2b	(.f32 (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (.f32 alpha alpha) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
	2.2b	(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 1/2 (PI.f32)))
	0.6b	(.f32 (.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (+.f32 alpha 1) 2)) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	2.6b	(*.f32 (log.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
	2.2b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))

Compiler

Compiled 1132 to 852 computations (24.7% saved)

localize99.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.2b	(log.f32 (/.f32 1 alpha))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))

Compiler

Compiled 109 to 65 computations (40.4% saved)

series24.0ms (0.2%)

Counts

3 → 40

Calls

12 calls:

Time	Variable		Point	Expression
9.0ms	alpha	@	-inf	(*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))
6.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
1.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

rewrite104.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

613×	`fma-def_binary32`
321×	`log1p-udef_binary32`
320×	`expm1-udef_binary32`
295×	`fma-neg_binary32`
271×	`log-pow_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	17	49
1	379	47
2	5492	47

Stop Event

1×	node limit

Counts

3 → 127

Calls

Call 1

Inputs

(*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 -2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (*.f32 (*.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

(log.f32 (/.f32 1 alpha))

Outputs

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

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

simplify65.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

886×	`associate-/l*_binary32`
595×	`fma-def_binary32`
430×	`associate-*l/_binary32`
427×	`associate-*r/_binary32`
360×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	2007
1	528	1862
2	2561	1804

Stop Event

1×	node limit

Counts

167 → 169

Calls

Call 1

Inputs
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (+.f32 (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))) (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (+.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 4) (.f32 (pow.f32 cosTheta 6) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 6) (.f32 (pow.f32 cosTheta 8) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 alpha 2) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 -1/2 (.f32 (pow.f32 cosTheta 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 6) (.f32 (pow.f32 alpha 4) (.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))))
(-.f32 (+.f32 (.f32 -1/2 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (pow.f32 cosTheta 6) (.f32 (pow.f32 alpha 4) (.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))))) (+.f32 (.f32 1/2 (/.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (.f32 (pow.f32 cosTheta 8) (.f32 (pow.f32 alpha 6) (.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))))
(.f32 -1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 -1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (pow.f32 cosTheta 2)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (+.f32 (.f32 -1/2 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 4) (pow.f32 cosTheta 6)) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (pow.f32 cosTheta 4)) (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (.f32 (pow.f32 cosTheta 8) (PI.f32))))))) (+.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (*.f32 (pow.f32 cosTheta 6) (PI.f32))))))))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))

Outputs
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))
(*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))
(*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))
(*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 alpha) (PI.f32)))
(*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))
(*.f32 (log.f32 alpha) (neg.f32 (PI.f32)))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
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(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))

localize29.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	0.4b	(*.f32 (log.f32 alpha) (PI.f32))

Compiler

Compiled 17 to 8 computations (52.9% saved)

series2.0ms (0%)

Counts

1 → 8

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	-inf	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
1.0ms	alpha	@	0	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
1.0ms	alpha	@	inf	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

rewrite678.0ms (4.4%)

Algorithm

1×	batch-egg-rewrite

Rules

690×	`pow1_binary32`
640×	`add-log-exp_binary32`
639×	`log1p-expm1-u_binary32`
639×	`expm1-log1p-u_binary32`
628×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	145	10
2	1751	10

Stop Event

1×	node limit

Counts

1 → 21

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

Outputs

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

simplify189.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

3549×	`fma-neg_binary32`
793×	`fma-def_binary32`
390×	`associate--r-_binary32`
339×	`unsub-neg_binary32`
311×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	96
1	34	96
2	57	80
3	115	80
4	236	80
5	600	80
6	2071	80
7	3458	80
8	4004	80
9	4055	80
10	4073	80
11	4075	80
12	6013	80
13	6635	80
14	6901	80
15	6988	80
16	7002	80
17	7006	80
18	7143	80
19	7151	80

Stop Event

1×	node limit

Counts

29 → 24

Calls

Call 1

Inputs
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))

Outputs
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 1/2 (*.f32 (neg.f32 (log.f32 alpha)) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))

localize65.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f32 (*.f32 alpha alpha) 1)
✓	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 68 to 22 computations (67.6% saved)

series9.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
2.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))

rewrite113.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary32`
377×	`fma-def_binary32`
242×	`log1p-udef_binary32`
241×	`expm1-udef_binary32`
234×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	39
1	312	35
2	4728	35

Stop Event

1×	node limit

Counts

3 → 188

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(log.f32 (*.f32 alpha alpha))
(-.f32 (*.f32 alpha alpha) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (fma.f32 (neg.f32 (sqrt.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))))) (sqrt.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (*.f32 alpha alpha) (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 1 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (*.f32 (cbrt.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (cbrt.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))))) (cbrt.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (sqrt.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (sqrt.f32 (*.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha 1) (/.f32 alpha (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 (cbrt.f32 (pow.f32 alpha 4)) 1) (/.f32 (pow.f32 (cbrt.f32 alpha) 2) (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 1 (PI.f32)) (/.f32 (*.f32 alpha alpha) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 (cbrt.f32 (pow.f32 alpha 4)) (PI.f32)) (/.f32 (pow.f32 (cbrt.f32 alpha) 2) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta cosTheta 1)) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 alpha) (log.f32 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 2 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (cbrt.f32 (pow.f32 alpha 4))) (*.f32 2 (log.f32 (cbrt.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (log.f32 alpha) 1) (*.f32 (log.f32 alpha) 1))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 2 (log.f32 alpha)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (*.f32 2 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (log.f32 alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (*.f32 2 (log.f32 alpha))) (cbrt.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 2)) (cbrt.f32 (*.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (*.f32 2 (log.f32 alpha))) (sqrt.f32 (*.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (log.f32 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 3 (*.f32 2 (log.f32 (cbrt.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/3 (*.f32 6 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 (log.f32 alpha) 3) (pow.f32 (log.f32 alpha) 3)) (fma.f32 (log.f32 alpha) (log.f32 alpha) (-.f32 (*.f32 (log.f32 alpha) (log.f32 alpha)) (*.f32 (log.f32 alpha) (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 (log.f32 alpha) (log.f32 alpha)) (*.f32 (log.f32 alpha) (log.f32 alpha))) (log.f32 (/.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 2 (log.f32 alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (*.f32 2 (log.f32 alpha))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (*.f32 2 (log.f32 alpha))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (*.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (fma.f32 alpha alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (*.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (*.f32 2 (log.f32 alpha))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (log.f32 alpha) (log.f32 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (log.f32 alpha) 1 (*.f32 (log.f32 alpha) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 (cbrt.f32 (log.f32 alpha)) (cbrt.f32 (log.f32 alpha))) (cbrt.f32 (log.f32 alpha)) (log.f32 alpha))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 (log.f32 alpha)) (sqrt.f32 (log.f32 alpha)) (log.f32 alpha))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 alpha alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -1 (*.f32 alpha alpha))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (fma.f32 alpha alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 alpha alpha -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (cbrt.f32 (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (sqrt.f32 (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (pow.f32 alpha 6) -1) (/.f32 1 (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (pow.f32 alpha 4) -1) (/.f32 1 (fma.f32 alpha alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 alpha 1) (+.f32 alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 alpha -1) (+.f32 alpha 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1)) (+.f32 (pow.f32 alpha 6) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 1 (/.f32 (fma.f32 alpha alpha 1) (+.f32 (pow.f32 alpha 4) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 alpha 6) -1) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 alpha 6) -1) (+.f32 (pow.f32 alpha 4) (-.f32 1 (*.f32 (*.f32 alpha alpha) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (pow.f32 alpha 4) -1) (fma.f32 alpha alpha 1))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 alpha 6) -1)) (neg.f32 (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (neg.f32 (+.f32 (pow.f32 alpha 4) -1)) (neg.f32 (fma.f32 alpha alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (fma.f32 alpha alpha -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (fma.f32 alpha alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (fma.f32 alpha alpha -1) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (*.f32 2 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (*.f32 (log.f32 alpha) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (*.f32 (log.f32 (fma.f32 alpha alpha -1)) 1))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 alpha alpha -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 alpha alpha) 1 -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 1 (*.f32 alpha alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 alpha) 2) (cbrt.f32 (pow.f32 alpha 4)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (pow.f32 (cbrt.f32 alpha) 2) (*.f32 (cbrt.f32 alpha) alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (pow.f32 alpha 4)) (pow.f32 (cbrt.f32 alpha) 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (cbrt.f32 (pow.f32 alpha 4)) (*.f32 (pow.f32 (cbrt.f32 alpha) 2) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (sqrt.f32 alpha) (*.f32 (sqrt.f32 alpha) alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 alpha (sqrt.f32 alpha)) (sqrt.f32 alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x fma.f32 (*.f32 alpha (pow.f32 (cbrt.f32 alpha) 2)) (cbrt.f32 alpha) -1)))))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

717×	`times-frac_binary32`
644×	`associate-/r*_binary32`
410×	`associate-/l*_binary32`
377×	`distribute-neg-frac_binary32`
346×	`sub-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	97	1746
1	285	1529
2	1139	1433
3	6545	1433

Stop Event

1×	node limit

Counts

236 → 224

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 6)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 8) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 8) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(*.f32 2 (log.f32 alpha))
(*.f32 2 (log.f32 alpha))
(*.f32 2 (log.f32 alpha))
(*.f32 2 (log.f32 alpha))
(*.f32 -2 (log.f32 (/.f32 1 alpha)))
(*.f32 -2 (log.f32 (/.f32 1 alpha)))
(*.f32 -2 (log.f32 (/.f32 1 alpha)))
(*.f32 -2 (log.f32 (/.f32 1 alpha)))
(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
-1
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)
(pow.f32 alpha 2)
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)
(pow.f32 alpha 2)
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)
(-.f32 (pow.f32 alpha 2) 1)

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (log.f32 alpha) alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
(.f32 1/2 (fma.f32 (/.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 alpha (log.f32 alpha)) (/.f32 (/.f32 -1 (PI.f32)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))))
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(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (log.f32 alpha) alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
(.f32 1/2 (fma.f32 (/.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 alpha (log.f32 alpha)) (/.f32 (/.f32 -1 (PI.f32)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))))
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(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (log.f32 alpha) alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
(.f32 1/2 (fma.f32 (/.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 alpha (log.f32 alpha)) (/.f32 (/.f32 -1 (PI.f32)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(/.f32 (.f32 -1/2 (.f32 alpha alpha)) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(.f32 -1/2 (/.f32 (/.f32 (.f32 alpha alpha) (-.f32 1 (.f32 cosTheta cosTheta))) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))))
(.f32 (/.f32 (/.f32 alpha (neg.f32 (log.f32 alpha))) (-.f32 1 (.f32 cosTheta cosTheta))) (*.f32 (/.f32 alpha (PI.f32)) -1/2))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
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(fma.f32 -1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 (/.f32 -1 alpha))))) (/.f32 1/2 (.f32 (PI.f32) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 (/.f32 -1 alpha))))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (/.f32 alpha (PI.f32)) (log.f32 (/.f32 -1 alpha)))) (/.f32 (/.f32 1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (log.f32 (/.f32 -1 alpha))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
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(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
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(/.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (*.f32 (log.f32 alpha) (PI.f32)))
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(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
(*.f32 (log.f32 (/.f32 -1 alpha)) -2)
(*.f32 -2 (log.f32 (/.f32 -1 alpha)))
(*.f32 (log.f32 (/.f32 -1 alpha)) -2)
-1
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(pow.f32 alpha 2)
(*.f32 alpha alpha)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(pow.f32 alpha 2)
(*.f32 alpha alpha)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)
(-.f32 (pow.f32 alpha 2) 1)
(+.f32 (*.f32 alpha alpha) -1)
(fma.f32 alpha alpha -1)

localize102.0ms (0.7%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))
✓	0.4b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))

Compiler

Compiled 33 to 19 computations (42.4% saved)

series1.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time

Variable

Point

Expression

0.0ms

alpha

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))

0.0ms

alpha

-inf

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))

0.0ms

alpha

inf

(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))

rewrite66.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

557×	`log-prod_binary32`
438×	`exp-prod_binary32`
315×	`pow-prod-down_binary32`
269×	`pow2_binary32`
190×	`pow1/3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	207	17
2	2811	17

Stop Event

1×	node limit

Counts

1 → 64

Calls

Call 1

Inputs
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))

Outputs

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

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

643×	`associate-/r/_binary32`
641×	`associate-l_binary32`
617×	`associate-/l/_binary32`
315×	`fma-def_binary32`
293×	`div-sub_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	298
1	98	280
2	253	276
3	682	213
4	2691	195

Stop Event

1×	node limit

Counts

76 → 72

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(*.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))))
(/.f32 alpha (/.f32 (log.f32 alpha) (/.f32 alpha (/.f32 (PI.f32) 1/2))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (*.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))))
(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(*.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))))
(/.f32 alpha (/.f32 (log.f32 alpha) (/.f32 alpha (/.f32 (PI.f32) 1/2))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 alpha))) (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (log.f32 alpha)) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))

localize93.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	3.0b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

Compiler

Compiled 69 to 22 computations (68.1% saved)

series4.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
0.0ms	cosTheta	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
0.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

rewrite137.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

721×	`prod-diff_binary32`
351×	`fma-def_binary32`
242×	`log1p-udef_binary32`
241×	`expm1-udef_binary32`
228×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	28
1	316	24
2	4695	24

Stop Event

1×	node limit

Counts

1 → 105

Calls

Call 1

Inputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

Outputs

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cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (/.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta 1)) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 1 (fma.f32 cosTheta cosTheta 1)) (/.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 1 (cbrt.f32 (pow.f32 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))) 2))) (/.f32 (*.f32 alpha alpha) (cbrt.f32 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 1 (*.f32 (sqrt.f32 (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (hypot.f32 1 cosTheta))) (/.f32 (*.f32 alpha alpha) (*.f32 (sqrt.f32 (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (hypot.f32 1 cosTheta))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha 1) (/.f32 alpha (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 (cbrt.f32 (pow.f32 alpha 4)) 1) (/.f32 (cbrt.f32 (*.f32 alpha alpha)) (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha (*.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))) (/.f32 alpha (fma.f32 cosTheta cosTheta 1)) (neg.f32 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1))) (fma.f32 (neg.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))) 1 (*.f32 (/.f32 1 (*.f32 (PI.f32) (*.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fma.f32 (/.f32 alpha (fma.f32 cosTheta cosTheta 1)) (/.f32 alpha (*.f32 (PI.f32) (*.f32 2 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simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

933×	`fma-neg_binary32`
609×	`times-frac_binary32`
593×	`associate-/r*_binary32`
361×	`associate-/l*_binary32`
345×	`sub-neg_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	93	1590
1	279	1391
2	1087	1295
3	5927	1295

Stop Event

1×	node limit

Counts

129 → 133

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))))
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(/.f32 (-.f32 (pow.f32 alpha 2) 1) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))
(-.f32 (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(-.f32 (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (+.f32 (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))) (/.f32 (.f32 (-.f32 (pow.f32 alpha 2) 1) (pow.f32 cosTheta 6)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
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(.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 2) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32)))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 4) (PI.f32))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 8) (PI.f32)))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (.f32 -1 (/.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))))))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (PI.f32)))) (+.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))) (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (pow.f32 alpha 2)) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(fma.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (.f32 cosTheta cosTheta))) (PI.f32)))) (neg.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))) (PI.f32))))))
(fma.f32 1/2 (.f32 (/.f32 alpha (.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))) (/.f32 alpha (PI.f32))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
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(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
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(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 (/.f32 alpha (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))))
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(fma.f32 -1/2 (/.f32 (/.f32 (.f32 alpha alpha) (-.f32 1 (.f32 cosTheta cosTheta))) (neg.f32 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 1/2 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (neg.f32 (.f32 (PI.f32) (log.f32 alpha))))))
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(fma.f32 -1/2 (.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (/.f32 alpha (PI.f32)) (log.f32 (/.f32 -1 alpha)))) (/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))) (log.f32 (/.f32 -1 alpha))))
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(fma.f32 -1/2 (.f32 (/.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))) (/.f32 alpha (log.f32 (/.f32 -1 alpha)))) (/.f32 1/2 (.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) (log.f32 (/.f32 -1 alpha)))))
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(+.f32 (fma.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (/.f32 1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (pow.f32 cosTheta 6)))) (+.f32 (/.f32 1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (pow.f32 cosTheta 8))) (-.f32 (/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (pow.f32 cosTheta 4)) (fma.f32 (/.f32 alpha (.f32 (log.f32 alpha) 2)) (/.f32 alpha (.f32 (PI.f32) (pow.f32 cosTheta 4))) (.f32 (/.f32 alpha (*.f32 (log.f32 alpha) 2)) (+.f32 (/.f32 (/.f32 alpha (PI.f32)) (pow.f32 cosTheta 6)) (/.f32 (/.f32 alpha (PI.f32)) (pow.f32 cosTheta 8))))))))

eval693.0ms (4.5%)

Compiler: Compiled 30145 to 18058 computations (40.1% saved)

prune207.0ms (1.3%)

Pruning

40 alts after pruning (33 fresh and 7 done)

	Pruned	Kept	Total
New	857	21	878
Fresh	13	12	25
Picked	0	1	1
Done	1	6	7
Total	871	40	911

Error

Counts

911 → 40

Alt Table

Click to see full alt table

Status	Error	Program
✓	2.1b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
	1.0b	(/.f32 (/.f32 (+.f32 (pow.f32 alpha 6) -1) (+.f32 (pow.f32 alpha 4) (-.f32 1 (.f32 (.f32 alpha alpha) -1)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.9b	(/.f32 (/.f32 (+.f32 (pow.f32 alpha 4) -1) (fma.f32 alpha alpha 1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.7b	(/.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (+.f32 alpha -1)))
	11.0b	(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
	11.1b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	11.8b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	11.8b	(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.0b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 3 (.f32 2 (log.f32 (cbrt.f32 alpha))))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	1.0b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (pow.f32 (sqrt.f32 (neg.f32 (log.f32 alpha))) 2) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (expm1.f32 (log1p.f32 (neg.f32 (log.f32 alpha)))) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (log1p.f32 (-.f32 (pow.f32 (/.f32 1 alpha) (PI.f32)) 1))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	2.1b	(/.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (.f32 (PI.f32) 2))
	2.1b	(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
	1.0b	(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	2.2b	(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
	2.1b	(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
	2.1b	(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
	11.8b	(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
✓	11.8b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
✓	11.0b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	11.8b	(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
	12.3b	(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
	0.9b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
	2.1b	(*.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))
	2.3b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))
✓	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	2.2b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	2.3b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
	2.1b	(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
	2.1b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	11.8b	(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
	2.2b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))

Compiler

Compiled 734 to 560 computations (23.7% saved)

regimes562.0ms (3.7%)

Counts

98 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (+.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1 (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))
(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
(/.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (.f32 (PI.f32) 2))
(.f32 (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (.f32 alpha alpha) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 3 (.f32 2 (log.f32 (cbrt.f32 alpha))))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (log1p.f32 (-.f32 (pow.f32 (/.f32 1 alpha) (PI.f32)) 1))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (+.f32 alpha -1)))
(/.f32 (/.f32 (+.f32 (pow.f32 alpha 4) -1) (fma.f32 alpha alpha 1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(.f32 (.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (+.f32 alpha 1) 2)) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (expm1.f32 (log1p.f32 (neg.f32 (log.f32 alpha)))) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (pow.f32 (sqrt.f32 (neg.f32 (log.f32 alpha))) 2) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (/.f32 (.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha 1)))))
(/.f32 (/.f32 (+.f32 (pow.f32 alpha 6) -1) (+.f32 (pow.f32 alpha 4) (-.f32 1 (.f32 (.f32 alpha alpha) -1)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (log.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(*.f32 (pow.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) 2) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
(/.f32 1/2 (.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (PI.f32))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) 2) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))))
(.f32 (/.f32 (+.f32 alpha 1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
(/.f32 (fma.f32 alpha alpha -1) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 1 (.f32 2 (log.f32 (pow.f32 alpha (PI.f32)))))))
(pow.f32 (.f32 (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) 2)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))) -1)
(.f32 (log.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (log1p.f32 (expm1.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)))) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (pow.f32 (cbrt.f32 (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha))) 3))
(pow.f32 (cbrt.f32 (.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) 3)
(pow.f32 (cbrt.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))) 3)
(/.f32 (-.f32 (exp.f32 (log1p.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)))) 1) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (log.f32 alpha)))
(.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))

Outputs
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))

Calls

5 calls:

293.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
72.0ms	cosTheta
55.0ms	alpha
52.0ms	(*.f32 alpha alpha)
46.0ms	(*.f32 alpha alpha)

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))`
0.5b	1	`(*.f32 alpha alpha)`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 1775 to 949 computations (46.5% saved)

regimes332.0ms (2.2%)

Counts

79 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (+.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1 (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))
(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
(/.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (.f32 (PI.f32) 2))
(.f32 (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (.f32 alpha alpha) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 3 (.f32 2 (log.f32 (cbrt.f32 alpha))))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (log1p.f32 (-.f32 (pow.f32 (/.f32 1 alpha) (PI.f32)) 1))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (+.f32 alpha -1)))
(/.f32 (/.f32 (+.f32 (pow.f32 alpha 4) -1) (fma.f32 alpha alpha 1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(.f32 (.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (+.f32 alpha 1) 2)) (/.f32 (+.f32 alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (expm1.f32 (log1p.f32 (neg.f32 (log.f32 alpha)))) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (pow.f32 (sqrt.f32 (neg.f32 (log.f32 alpha))) 2) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (/.f32 (.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 cosTheta cosTheta)) (fma.f32 alpha alpha 1)))))
(/.f32 (/.f32 (+.f32 (pow.f32 alpha 6) -1) (+.f32 (pow.f32 alpha 4) (-.f32 1 (.f32 (.f32 alpha alpha) -1)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(*.f32 (log.f32 (exp.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(*.f32 (pow.f32 (sqrt.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) 2) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))
(/.f32 1/2 (.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))

Calls

4 calls:

76.0ms	alpha
70.0ms	cosTheta
56.0ms	(*.f32 alpha alpha)
56.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 1314 to 702 computations (46.6% saved)

regimes198.0ms (1.3%)

Counts

60 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (+.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1 (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))
(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
(/.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (.f32 (PI.f32) 2))
(.f32 (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (.f32 alpha alpha) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 3 (.f32 2 (log.f32 (cbrt.f32 alpha))))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))

Calls

5 calls:

41.0ms	alpha
38.0ms	cosTheta
33.0ms	(*.f32 alpha alpha)
33.0ms	(*.f32 alpha alpha)
30.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))`
0.5b	1	`(*.f32 alpha alpha)`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 863 to 455 computations (47.3% saved)

regimes265.0ms (1.7%)

Counts

59 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (+.f32 (/.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1 (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (fma.f32 alpha alpha -1))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 1/2 (*.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (PI.f32)))
(/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 (fma.f32 alpha alpha -1) 2) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))
(/.f32 1 (/.f32 (PI.f32) (/.f32 (*.f32 (fma.f32 alpha alpha -1) 1/2) (log.f32 alpha))))
(/.f32 1 (/.f32 (log.f32 alpha) (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32)))))
(/.f32 (.f32 (fma.f32 alpha alpha -1) (/.f32 1 (log.f32 alpha))) (.f32 (PI.f32) 2))
(.f32 (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (.f32 alpha alpha) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (PI.f32)))
(.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 1/2 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 3 (.f32 2 (log.f32 (cbrt.f32 alpha))))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Calls

5 calls:

85.0ms	cosTheta
63.0ms	alpha
38.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
31.0ms	(*.f32 alpha alpha)
28.0ms	(*.f32 alpha alpha)

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))`
0.5b	1	`(*.f32 alpha alpha)`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 839 to 441 computations (47.4% saved)

regimes110.0ms (0.7%)

Counts

32 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Calls

4 calls:

46.0ms	alpha
18.0ms	(*.f32 alpha alpha)
18.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
17.0ms	cosTheta

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 435 to 216 computations (50.3% saved)

regimes64.0ms (0.4%)

Counts

31 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))

Calls

3 calls:

20.0ms	(*.f32 alpha alpha)
18.0ms	alpha
17.0ms	cosTheta

Results

Error	Segments	Branch
0.9b	1	`cosTheta`
0.9b	1	`alpha`
0.9b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 385 to 190 computations (50.6% saved)

regimes79.0ms (0.5%)

Counts

26 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))

Outputs
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))

Calls

3 calls:

38.0ms	(*.f32 alpha alpha)
16.0ms	alpha
16.0ms	cosTheta

Results

Error	Segments	Branch
0.9b	1	`cosTheta`
0.9b	1	`alpha`
0.9b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 284 to 140 computations (50.7% saved)

regimes76.0ms (0.5%)

Counts

25 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (-.f32 alpha 1))

Outputs
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))

Calls

2 calls:

55.0ms	alpha
15.0ms	cosTheta

Results

Error	Segments	Branch
2.2b	1	`cosTheta`
2.2b	1	`alpha`

Compiler

Compiled 260 to 126 computations (51.5% saved)

regimes33.0ms (0.2%)

Counts

23 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))

Outputs
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))

Calls

2 calls:

14.0ms	alpha
13.0ms	cosTheta

Results

Error	Segments	Branch
11.0b	1	`cosTheta`
11.0b	1	`alpha`

Compiler

Compiled 232 to 109 computations (53% saved)

regimes31.0ms (0.2%)

Counts

22 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))

Outputs
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))

Calls

2 calls:

13.0ms	alpha
12.0ms	cosTheta

Results

Error	Segments	Branch
11.0b	1	`cosTheta`
11.0b	1	`alpha`

Compiler

Compiled 220 to 104 computations (52.7% saved)

regimes26.0ms (0.2%)

Counts

19 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(*.f32 (/.f32 -1/2 (log.f32 alpha)) (/.f32 1 (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 -1 (log.f32 alpha)) (*.f32 (PI.f32) 2))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta cosTheta))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta (*.f32 cosTheta (PI.f32))) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (*.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 (/.f32 -1/2 (.f32 cosTheta (.f32 cosTheta (PI.f32)))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (neg.f32 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))

Outputs
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))

Calls

2 calls:

11.0ms	alpha
10.0ms	cosTheta

Results

Error	Segments	Branch
11.8b	1	`cosTheta`
11.8b	1	`alpha`

Compiler

Compiled 184 to 87 computations (52.7% saved)

regimes44.0ms (0.3%)

Accuracy

Total -0.0b remaining (-0.2%)

Threshold costs -0.0b (-0.2%)

Counts

3 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

Calls

2 calls:

4.0ms	alpha
4.0ms	cosTheta

Results

Error	Segments	Branch
11.8b	1	`cosTheta`
11.8b	1	`alpha`

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary32`
7×	`+-commutative_binary32`
5×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	318
1	93	318
2	99	318
3	102	318
4	103	318

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

Outputs
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (*.f32 (PI.f32) 2)))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) -1))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) -1)))) (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (log.f32 (pow.f32 alpha (.f32 (PI.f32) 2)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) -1)))) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 (.f32 alpha alpha) -1)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (-.f32 1 (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (-.f32 1 (*.f32 cosTheta cosTheta))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

Compiler

Compiled 229 to 163 computations (28.8% saved)

soundness82.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

596×	`associate-/l*_binary32`
446×	`associate-l_binary32`
378×	`associate-*l/_binary32`
354×	`associate-r_binary32`
351×	`associate-+l+_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	166	31
3	822	31
4	4306	31

Stop Event

1×	node limit

Compiler

Compiled 404 to 274 computations (32.2% saved)

end125.0ms (0.8%)

Compiler: Compiled 207 to 110 computations (46.9% saved)