Details

analyze139.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.6%	99.4%	0
0%	0.6%	99.4%	1
0%	0.6%	99.4%	2
0.3%	0.3%	99.4%	3
0.3%	0.3%	99.4%	4
0.5%	0.2%	99.4%	5
0.5%	0.2%	99.4%	6
0.6%	0.1%	99.4%	7
0.6%	0.1%	99.4%	8
0.6%	0%	99.4%	9
0.6%	0%	99.4%	10
0.6%	0%	99.4%	11
0.6%	0%	99.4%	12

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample2.6s (18.9%)

Results

2.6s

8256×

body

256

valid

preprocess56.0ms (0.4%)

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)

simplify38.0ms (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)))

eval1.0ms (0%)

Compiler: Compiled 47 to 29 computations (38.3% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.3b

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.6b	(/.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

▶

0.6b

(/.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)

localize81.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.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)

series61.0ms (0.4%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
30.0ms	alpha	@	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
9.0ms	alpha	@	inf	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
6.0ms	alpha	@	0	(.f32 (-.f32 (.f32 alpha alpha) 1) 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))))
2.0ms	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))))

rewrite102.0ms (0.7%)

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)))))

simplify79.0ms (0.6%)

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))

localize71.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)
✓	0.0b	(.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)

series55.0ms (0.4%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
15.0ms	cosTheta	@	0	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))
14.0ms	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 (/.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)))
3.0ms	alpha	@	inf	(.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))

rewrite96.0ms (0.7%)

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	72
1	301	72
2	3983	72

Stop Event

1×	node limit

Counts

4 → 155

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

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

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

760×	`associate-/l*_binary32`
693×	`fma-def_binary32`
398×	`associate-*r/_binary32`
388×	`associate-*l/_binary32`
353×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	3212
1	619	2731
2	2508	2650

Stop Event

1×	node limit

Counts

239 → 225

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

eval915.0ms (6.6%)

Compiler: Compiled 15147 to 8641 computations (43% saved)

prune109.0ms (0.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	409	28	437
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	411	28	439

Error

Counts

439 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	0.6b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
	31.7b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
▶	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.6b	(.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)))))
	10.1b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 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))))
	31.7b	(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (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)))
	1.6b	(*.f32 (/.f32 1/2 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))
	0.6b	(pow.f32 (/.f32 (.f32 (.f32 (PI.f32) 2) (.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (log.f32 alpha))) (fma.f32 alpha alpha -1)) -1)
	1.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
	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))))
	0.6b	(/.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))))
	0.6b	(cbrt.f32 (pow.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))
	0.6b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 1/2 (PI.f32)))) (/.f32 1 (log.f32 alpha)))
	0.6b	(/.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))))
	0.6b	(.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha)))
▶	0.8b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
	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)))))
	0.7b	(.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)))))
▶	31.7b	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
	10.1b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	0.9b	(exp.f32 (log.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)))))
	31.7b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
	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))))
	1.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 alpha (*.f32 alpha cosTheta)) cosTheta))))
	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)))
▶	0.6b	(.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))))

Compiler

Compiled 1212 to 862 computations (28.9% saved)

localize74.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.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))))
✓	3.1b	(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	@	0	(pow.f32 (*.f32 alpha alpha) (PI.f32))
1.0ms	alpha	@	inf	(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite83.0ms (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 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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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cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (fma.f32 alpha alpha -1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (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 (fma.f32 alpha alpha -1) (cbrt.f32 (*.f32 (*.f32 2 (*.f32 (PI.f32) (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) 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simplify66.0ms (0.5%)

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

localize37.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha)))
✓	0.3b	(.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))
✓	0.5b	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))

Compiler

Compiled 35 to 12 computations (65.7% saved)

series43.0ms (0.3%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
10.0ms	alpha	@	-inf	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
9.0ms	cosTheta	@	0	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
8.0ms	alpha	@	0	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
7.0ms	alpha	@	inf	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
1.0ms	alpha	@	0	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha)))

rewrite108.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

550×	`log-prod_binary32`
414×	`exp-prod_binary32`
353×	`pow-prod-down_binary32`
276×	`pow2_binary32`
194×	`pow1/3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	37
1	214	37
2	2843	37

Stop Event

1×	node limit

Counts

3 → 113

Calls

Call 1

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

Outputs

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

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

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

simplify106.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

665×	`fma-def_binary32`
594×	`fma-neg_binary32`
548×	`distribute-rgt-in_binary32`
468×	`distribute-lft-in_binary32`
426×	`distribute-neg-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	888
1	68	888
2	170	888
3	583	888
4	2326	888
5	6537	888

Stop Event

1×	node limit

Counts

185 → 125

Calls

Call 1

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

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

localize66.0ms (0.5%)

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)

series7.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
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))))
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))))

rewrite144.0ms (1%)

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

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((#(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)))))

simplify104.0ms (0.8%)

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

localize209.0ms (1.5%)

Local error

Found 3 expressions with local error:

New

Error

Program

✓

0.0b

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

Compiler

Compiled 58 to 31 computations (46.6% saved)

series50.0ms (0.4%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
35.0ms	alpha	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
2.0ms	alpha	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
2.0ms	alpha	@	0	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
2.0ms	cosTheta	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
2.0ms	cosTheta	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))

rewrite95.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

824×	`log-prod_binary32`
270×	`expm1-udef_binary32`
269×	`log1p-udef_binary32`
231×	`log-div_binary32`
225×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	38
1	314	38
2	4300	38

Stop Event

1×	node limit

Counts

2 → 86

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (*.f32 (cbrt.f32 (exp.f32 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))))) (cbrt.f32 (exp.f32 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))))))) (log.f32 (cbrt.f32 (exp.f32 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (exp.f32 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)))))) (log.f32 (sqrt.f32 (exp.f32 (*.f32 (/.f32 (fma.f32 alpha alpha -1) (-.f32 1 (*.f32 cosTheta cosTheta))) (/.f32 (/.f32 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simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

473×	`associate-/r*_binary32`
468×	`times-frac_binary32`
361×	`cancel-sign-sub-inv_binary32`
331×	`associate-/l*_binary32`
321×	`fma-def_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1672
1	295	1574
2	1113	1411
3	5049	1272

Stop Event

1×	node limit

Counts

134 → 122

Calls

Call 1

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

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32))))
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(-.f32 (.f32 1/2 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32))))) (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(fma.f32 1/2 (/.f32 (/.f32 alpha (/.f32 (-.f32 1 (.f32 cosTheta cosTheta)) alpha)) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (PI.f32)))))
(fma.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (PI.f32))))) (.f32 1/2 (/.f32 1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (log.f32 alpha) (PI.f32))))))
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(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
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(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
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(.f32 (/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (fma.f32 cosTheta cosTheta -1))) (.f32 alpha alpha))
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(fma.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (/.f32 alpha (/.f32 (PI.f32) alpha)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))))
(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
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(fma.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (pow.f32 cosTheta 8)) (fma.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (pow.f32 cosTheta 6)) (fma.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (/.f32 (.f32 alpha alpha) (.f32 (log.f32 alpha) (PI.f32)))) (pow.f32 cosTheta 4)) (/.f32 (.f32 -1/2 (+.f32 (.f32 alpha alpha) -1)) (.f32 (log.f32 alpha) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))))))
(fma.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (.f32 (/.f32 alpha (log.f32 alpha)) (/.f32 alpha (PI.f32)))) (pow.f32 cosTheta 8)) (fma.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (.f32 (/.f32 alpha (log.f32 alpha)) (/.f32 alpha (PI.f32)))) (pow.f32 cosTheta 6)) (fma.f32 -1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (/.f32 1/2 (/.f32 (pow.f32 cosTheta 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (*.f32 (/.f32 alpha (log.f32 alpha)) (/.f32 alpha (PI.f32)))))))))
(fma.f32 1/2 (+.f32 (/.f32 (-.f32 0 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32)))) (pow.f32 cosTheta 4)) (/.f32 (-.f32 0 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32)))) (pow.f32 cosTheta 6))) (fma.f32 -1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (.f32 cosTheta cosTheta) (PI.f32)))) (.f32 (/.f32 1/2 (pow.f32 cosTheta 8)) (-.f32 0 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (PI.f32)))))))
(fma.f32 1/2 (/.f32 (/.f32 (/.f32 (neg.f32 (fma.f32 alpha alpha -1)) (PI.f32)) (log.f32 alpha)) (pow.f32 cosTheta 8)) (fma.f32 -1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 cosTheta cosTheta) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 (/.f32 (/.f32 (neg.f32 (fma.f32 alpha alpha -1)) (PI.f32)) (log.f32 alpha)) (+.f32 (/.f32 1/2 (pow.f32 cosTheta 4)) (/.f32 1/2 (pow.f32 cosTheta 6))))))
(log.f32 alpha)
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2)))
(neg.f32 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 cosTheta (neg.f32 cosTheta)))
(.f32 cosTheta (.f32 (log.f32 alpha) (neg.f32 cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2)))
(neg.f32 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (.f32 cosTheta (neg.f32 cosTheta)))
(.f32 cosTheta (.f32 (log.f32 alpha) (neg.f32 cosTheta)))
(.f32 (.f32 cosTheta cosTheta) (neg.f32 (log.f32 alpha)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(+.f32 (log.f32 alpha) (.f32 -1 (.f32 (log.f32 alpha) (pow.f32 cosTheta 2))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(*.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(*.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(*.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(*.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 alpha))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 (/.f32 1 alpha))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 (/.f32 1 alpha))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 (/.f32 1 alpha))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 -1 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (log.f32 (/.f32 1 alpha))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))
(.f32 (-.f32 1 (pow.f32 cosTheta 2)) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(fma.f32 -1 (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)) (log.f32 alpha))
(-.f32 (log.f32 alpha) (.f32 (log.f32 alpha) (.f32 cosTheta cosTheta)))
(.f32 (log.f32 alpha) (-.f32 1 (.f32 cosTheta cosTheta)))

localize134.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
✓	0.3b	(/.f32 1 (log.f32 alpha))
✓	0.3b	(.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))))
✓	0.5b	(.f32 (/.f32 1/2 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))

Compiler

Compiled 88 to 48 computations (45.5% saved)

series48.0ms (0.4%)

Counts

4 → 80

Calls

21 calls:

Time	Variable		Point	Expression
33.0ms	alpha	@	-inf	(/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
1.0ms	alpha	@	-inf	(.f32 (/.f32 1/2 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	alpha	@	0	(.f32 (/.f32 1/2 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	alpha	@	inf	(.f32 (/.f32 1/2 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
1.0ms	alpha	@	inf	(/.f32 (/.f32 1 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

rewrite92.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

810×	`log-prod_binary32`
295×	`pow1/3_binary32`
284×	`log1p-udef_binary32`
283×	`expm1-udef_binary32`
268×	`pow3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	87
1	333	81
2	4357	81

Stop Event

1×	node limit

Counts

4 → 162

Calls

Call 1

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

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

677×	`distribute-rgt-in_binary32`
473×	`associate-/r*_binary32`
355×	`associate-r_binary32`
264×	`associate-l_binary32`
256×	`*-commutative_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	5678
1	1227	5261
2	5124	5120

Stop Event

1×	node limit

Counts

242 → 285

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

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

eval887.0ms (6.4%)

Compiler: Compiled 35255 to 21145 computations (40% saved)

prune358.0ms (2.6%)

Pruning

41 alts after pruning (38 fresh and 3 done)

	Pruned	Kept	Total
New	1004	30	1034
Fresh	15	8	23
Picked	1	0	1
Done	1	3	4
Total	1021	41	1062

Error

Counts

1062 → 41

Alt Table

Click to see full alt table

Status	Error	Program
	0.6b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
	31.7b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	10.1b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	3.2b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (log1p.f32 (-.f32 (pow.f32 alpha (-.f32 1 (.f32 cosTheta cosTheta))) 1)))
	0.8b	(pow.f32 (.f32 (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)) (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) 2))) -1)
	31.7b	(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
	0.9b	(.f32 (/.f32 1 (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))))
	1.6b	(*.f32 (/.f32 1/2 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))
	10.1b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	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))))
	1.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
	1.5b	(*.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)))
	1.9b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))))
	1.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
	1.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 alpha (*.f32 alpha cosTheta)) cosTheta))))
	0.9b	(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	9.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	31.7b	(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) cosTheta)) (neg.f32 (log.f32 alpha)))
▶	1.6b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	1.7b	(.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 alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	10.1b	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	31.7b	(/.f32 (/.f32 -1/2 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
	1.8b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (PI.f32) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))))
	0.9b	(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
	0.8b	(.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))
✓	0.8b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
	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))))
	1.0b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
▶	10.1b	(/.f32 (/.f32 -1/2 (PI.f32)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 alpha)))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	1.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
	10.1b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
✓	31.7b	(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
	31.7b	(/.f32 (/.f32 (/.f32 1/2 (*.f32 cosTheta cosTheta)) (log.f32 alpha)) (PI.f32))
	31.7b	(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (*.f32 cosTheta cosTheta))
▶	31.7b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
	31.7b	(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta (PI.f32))) cosTheta)

Compiler

Compiled 1432 to 1065 computations (25.6% saved)

localize121.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.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)

series6.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	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	alpha	@	inf	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))

rewrite89.0ms (0.6%)

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

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

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 alpha (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (/.f32 alpha (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (neg.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 (/.f32 alpha (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (/.f32 alpha (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (/.f32 (/.f32 1 (log.f32 alpha)) (*.f32 (*.f32 (PI.f32) 2) (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 (/.f32 (fma.f32 alpha alpha -1) (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 (/.f32 (fma.f32 alpha alpha -1) (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 (/.f32 1 (log.f32 alpha)) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (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 (cbrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (pow.f32 (cbrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (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 (pow.f32 (cbrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) 2) (cbrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (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 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 (/.f32 1 (log.f32 alpha)) (*.f32 (*.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 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (sqrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (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 (/.f32 1 (log.f32 alpha)) (*.f32 (*.f32 (PI.f32) 2) (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 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1) (neg.f32 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 1 (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 (+.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2)) (/.f32 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (/.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 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (*.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) 2)) (/.f32 (fma.f32 alpha alpha -1) (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 1 (sqrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 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(pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) 1) (/.f32 (cbrt.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) 1) (/.f32 (sqrt.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)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (*.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 (+.f32 alpha 1) 1) (/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (*.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)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.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)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) 2)) (cbrt.f32 (/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (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 (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) 2)) (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 (*.f32 (PI.f32) 2) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (+.f32 alpha 1) (pow.f32 (cbrt.f32 (*.f32 (log.f32 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simplify97.0ms (0.7%)

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))))
(-.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))))))))

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

localize36.0ms (0.3%)

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 (log.f32 alpha) (PI.f32))
✓	0.4b	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))

Compiler

Compiled 33 to 10 computations (69.7% saved)

series5.0ms (0%)

Counts

3 → 56

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta	@	inf	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
0.0ms	alpha	@	-inf	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
0.0ms	cosTheta	@	0	(.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32)))
0.0ms	alpha	@	-inf	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
0.0ms	alpha	@	inf	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))

rewrite90.0ms (0.7%)

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	2593	36

Stop Event

1×	node limit

Counts

3 → 105

Calls

Call 1

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

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

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

664×	`fma-def_binary32`
587×	`fma-neg_binary32`
535×	`distribute-lft-out--_binary32`
428×	`distribute-rgt-neg-in_binary32`
394×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	784
1	67	784
2	179	752
3	574	752
4	2156	752
5	5304	752

Stop Event

1×	node limit

Counts

161 → 116

Calls

Call 1

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

localize44.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 alpha))
✓	0.5b	(/.f32 (/.f32 -1/2 (PI.f32)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (log.f32 alpha)))

Compiler

Compiled 40 to 20 computations (50% saved)

series5.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite64.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

648×	`log-prod_binary32`
331×	`pow2_binary32`
231×	`pow1/3_binary32`
225×	`expm1-udef_binary32`
224×	`log1p-udef_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	259	19
2	3516	19

Stop Event

1×	node limit

Counts

1 → 55

Calls

Call 1

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

Outputs

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

simplify62.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

915×	`fma-def_binary32`
596×	`associate-/l*_binary32`
345×	`fma-neg_binary32`
309×	`associate-*l/_binary32`
298×	`cancel-sign-sub-inv_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	720
1	212	714
2	636	708
3	2092	650
4	6366	630

Stop Event

1×	node limit

Counts

79 → 76

Calls

Call 1

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

localize86.0ms (0.6%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 33 to 19 computations (42.4% saved)

series5.0ms (0%)

Counts

3 → 32

Calls

9 calls:

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

rewrite81.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	32
1	211	32
2	2774	32

Stop Event

1×	node limit

Counts

3 → 157

Calls

Call 1

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

Outputs

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

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

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

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

685×	`associate-/r/_binary32`
675×	`associate-l_binary32`
659×	`associate-/l/_binary32`
331×	`fma-def_binary32`
300×	`div-sub_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	42	518
1	106	500
2	263	480
3	710	399
4	2810	381

Stop Event

1×	node limit

Counts

189 → 174

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

localize86.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.4b	(*.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1)))
✓	9.2b	(log1p.f32 (fma.f32 alpha alpha -1))

Compiler

Compiled 77 to 38 computations (50.6% saved)

series37.0ms (0.3%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
13.0ms	alpha	@	inf	(log1p.f32 (fma.f32 alpha alpha -1))
9.0ms	alpha	@	0	(log1p.f32 (fma.f32 alpha alpha -1))
8.0ms	alpha	@	-inf	(log1p.f32 (fma.f32 alpha alpha -1))
3.0ms	alpha	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

rewrite112.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

896×	`prod-diff_binary32`
381×	`fma-def_binary32`
249×	`log1p-udef_binary32`
248×	`expm1-udef_binary32`
243×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	47
1	347	40
2	4834	40

Stop Event

1×	node limit

Counts

3 → 156

Calls

Call 1

Inputs

(log1p.f32 (fma.f32 alpha alpha -1))

(*.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1)))

(/.f32 (-.f32 (*.f32 alpha alpha) 1) (*.f32 (*.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))

Outputs

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

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(log.f32 alpha)) (PI.f32)))))))))

simplify74.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

845×	`times-frac_binary32`
698×	`associate-/r*_binary32`
466×	`associate-/l*_binary32`
346×	`sub-neg_binary32`
335×	`fma-def_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	1806
1	296	1607
2	1210	1511
3	7038	1511

Stop Event

1×	node limit

Counts

204 → 191

Calls

Call 1

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

eval901.0ms (6.5%)

Compiler: Compiled 23974 to 14576 computations (39.2% saved)

prune279.0ms (2%)

Pruning

37 alts after pruning (33 fresh and 4 done)

	Pruned	Kept	Total
New	828	19	847
Fresh	19	14	33
Picked	0	1	1
Done	4	3	7
Total	851	37	888

Error

Counts

888 → 37

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	1.6b	(/.f32 1 (/.f32 (PI.f32) (*.f32 (/.f32 1/2 (log.f32 alpha)) (fma.f32 alpha alpha -1))))
▶	0.6b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
	10.5b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	10.2b	(exp.f32 (log.f32 (/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))) (log.f32 alpha))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))))
	1.6b	(/.f32 (*.f32 (/.f32 1/2 (log.f32 alpha)) (fma.f32 alpha alpha -1)) (PI.f32))
	10.1b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
	0.9b	(.f32 (/.f32 1 (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha)))
	1.6b	(*.f32 (/.f32 1/2 (PI.f32)) (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)))
	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))))
	1.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
	1.7b	(*.f32 (/.f32 -1/2 (log.f32 (/.f32 1 alpha))) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	1.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))))
	10.1b	(.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1/2 (PI.f32)))
	1.5b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (PI.f32) (fma.f32 alpha alpha -1)))
	1.5b	(/.f32 1/2 (*.f32 (/.f32 (PI.f32) (fma.f32 alpha alpha -1)) (log.f32 alpha)))
	1.7b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (PI.f32))))
✓	9.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log1p.f32 (fma.f32 alpha alpha -1))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	1.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 alpha (*.f32 alpha cosTheta)) cosTheta))))
	0.9b	(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.6b	(/.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))))
▶	10.1b	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	10.1b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
	10.5b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
	10.1b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.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))))
▶	1.5b	(/.f32 1/2 (/.f32 (log.f32 alpha) (/.f32 (fma.f32 alpha alpha -1) (PI.f32))))
	0.8b	(.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))
✓	0.8b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
	1.0b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 3) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	10.5b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 -1 (PI.f32)))
▶	10.4b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	0.9b	(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
▶	1.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))

Compiler

Compiled 1220 to 924 computations (24.3% saved)

localize77.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta)) 1) (log.f32 alpha))
✓	0.2b	(.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))
	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 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))

Compiler

Compiled 81 to 43 computations (46.9% saved)

series13.0ms (0.1%)

Counts

3 → 72

Calls

18 calls:

Time	Variable		Point	Expression
3.0ms	cosTheta	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
3.0ms	alpha	@	0	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
1.0ms	alpha	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
1.0ms	alpha	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))
0.0ms	cosTheta	@	0	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1) (log.f32 alpha)))

rewrite93.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

892×	`log-prod_binary32`
424×	`prod-diff_binary32`
284×	`log1p-udef_binary32`
283×	`expm1-udef_binary32`
248×	`fma-def_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	59
1	334	59
2	4572	59

Stop Event

1×	node limit

Counts

3 → 118

Calls

Call 1

Inputs

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

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

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

simplify111.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

754×	`associate-/l*_binary32`
676×	`fma-def_binary32`
394×	`associate-*r/_binary32`
387×	`associate-*l/_binary32`
346×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2993
1	594	2587
2	2453	2506

Stop Event

1×	node limit

Counts

190 → 181

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

localize58.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(/.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)

series4.0ms (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)))

rewrite58.0ms (0.4%)

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)))))))))

simplify205.0ms (1.5%)

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))

localize126.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta)))
	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.3b	(/.f32 -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 60 to 20 computations (66.7% saved)

series36.0ms (0.3%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
26.0ms	cosTheta	@	0	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta)))
2.0ms	alpha	@	0	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	alpha	@	inf	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	inf	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
1.0ms	cosTheta	@	0	(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))

rewrite294.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`log-prod_binary32`
595×	`prod-diff_binary32`
331×	`egg-rr`
260×	`fma-def_binary32`
227×	`pow1/3_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	45
1	290	37
2	3866	37

Stop Event

1×	node limit

Counts

2 → 362

Calls

Call 1

Inputs

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

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

Outputs

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simplify103.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

781×	`fma-neg_binary32`
471×	`associate-*l/_binary32`
447×	`cancel-sign-sub-inv_binary32`
438×	`associate-/l/_binary32`
299×	`associate-*r/_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	1344
1	194	1193
2	671	1173
3	2912	1163

Stop Event

1×	node limit

Counts

410 → 394

Calls

Call 1

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

localize45.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 38 to 21 computations (44.7% saved)

series6.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite139.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

552×	`log-prod_binary32`
439×	`exp-prod_binary32`
286×	`pow-prod-down_binary32`
273×	`pow2_binary32`
208×	`pow-unpow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	214	31
2	2894	31

Stop Event

1×	node limit

Counts

2 → 99

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (log.f32 alpha) (/.f32 (PI.f32) (fma.f32 alpha alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (cbrt.f32 (pow.f32 alpha (/.f32 (PI.f32) (fma.f32 alpha alpha -1)))) 2)) (log.f32 (cbrt.f32 (pow.f32 alpha (/.f32 (PI.f32) (fma.f32 alpha alpha -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (sqrt.f32 (pow.f32 alpha (/.f32 (PI.f32) (fma.f32 alpha alpha -1))))) (log.f32 (sqrt.f32 (pow.f32 alpha (/.f32 (PI.f32) (fma.f32 alpha alpha -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (*.f32 (log.f32 alpha) (/.f32 (PI.f32) (fma.f32 alpha alpha -1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (log.f32 alpha) (/.f32 (PI.f32) (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (PI.f32) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (log.f32 alpha) (/.f32 (PI.f32) (fma.f32 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simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

510×	`distribute-rgt-out_binary32`
493×	`fma-def_binary32`
359×	`times-frac_binary32`
317×	`distribute-rgt-neg-in_binary32`
290×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	782
1	252	728
2	901	631
3	4405	555

Stop Event

1×	node limit

Counts

123 → 128

Calls

Call 1

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

localize107.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))
✓	0.3b	(/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1)))
✓	0.3b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (fma.f32 cosTheta cosTheta 1))))
✓	0.4b	(/.f32 (+.f32 alpha 1) (PI.f32))

Compiler

Compiled 70 to 43 computations (38.6% saved)

series19.0ms (0.1%)

Counts

4 → 84

Calls

21 calls:

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

rewrite110.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`log-prod_binary32`
318×	`log-div_binary32`
291×	`log1p-udef_binary32`
290×	`expm1-udef_binary32`
241×	`log-pow_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	69
1	345	64
2	5096	64

Stop Event

1×	node limit

Counts

4 → 172

Calls

Call 1

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

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

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

775×	`fma-def_binary32`
679×	`associate-/l*_binary32`
477×	`associate-r_binary32`
449×	`associate-l_binary32`
334×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	154	2894
1	515	2648
2	1953	2439

Stop Event

1×	node limit

Counts

256 → 243

Calls

Call 1

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

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

eval665.0ms (4.8%)

Compiler: Compiled 37680 to 22337 computations (40.7% saved)

prune220.0ms (1.6%)

Pruning

38 alts after pruning (33 fresh and 5 done)

	Pruned	Kept	Total
New	1152	16	1168
Fresh	11	17	28
Picked	1	0	1
Done	3	5	8
Total	1167	38	1205

Error

Counts

1205 → 38

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	10.5b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))))
	4.5b	(/.f32 1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 (-.f32 -1 (*.f32 alpha alpha)) (pow.f32 alpha 4))))
	1.6b	(/.f32 (*.f32 (/.f32 1/2 (log.f32 alpha)) (fma.f32 alpha alpha -1)) (PI.f32))
	10.1b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
	0.9b	(.f32 (/.f32 1 (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 (*.f32 (fma.f32 alpha alpha -1) (/.f32 1/2 (PI.f32))) (log.f32 alpha)))
	11.1b	(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
	1.7b	(*.f32 (/.f32 -1/2 (log.f32 (/.f32 1 alpha))) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	10.1b	(.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1/2 (PI.f32)))
	1.5b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (PI.f32) (fma.f32 alpha alpha -1)))
	10.1b	(/.f32 -1 (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	10.4b	(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
	1.7b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 cosTheta cosTheta 1)) (/.f32 (+.f32 alpha -1) (.f32 (*.f32 2 (log.f32 alpha)) (PI.f32))))
	1.7b	(/.f32 (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 2 (fma.f32 cosTheta cosTheta 1)))) (/.f32 (PI.f32) (+.f32 alpha 1)))
	1.6b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
	0.9b	(/.f32 (.f32 (+.f32 alpha 1) (+.f32 alpha -1)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	10.1b	(/.f32 -1 (.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
✓	0.6b	(/.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))))
	10.4b	(/.f32 1/2 (/.f32 (log.f32 alpha) (/.f32 -1 (PI.f32))))
	0.6b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (+.f32 (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) -1)) 1) (log.f32 alpha)))
	1.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (PI.f32) 2)) (log.f32 alpha))
	10.1b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
	10.5b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
	10.1b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.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))))
✓	1.5b	(/.f32 1/2 (/.f32 (log.f32 alpha) (/.f32 (fma.f32 alpha alpha -1) (PI.f32))))
	0.8b	(.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))
	10.4b	(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
✓	0.8b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (.f32 (-.f32 1 (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
	1.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	10.5b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 -1 (PI.f32)))
	5.9b	(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 -1 (*.f32 alpha alpha)))))
✓	10.4b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	0.9b	(.f32 (/.f32 1/2 (log.f32 alpha)) (-.f32 (/.f32 alpha (/.f32 (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)) alpha)) (/.f32 (/.f32 1 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta)))))
	10.5b	(exp.f32 (log.f32 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))))
	1.6b	(.f32 (+.f32 (/.f32 (.f32 alpha alpha) -1) 1) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))

Compiler

Compiled 625 to 483 computations (22.7% saved)

regimes340.0ms (2.5%)

Counts

95 → 1

Calls

Call 1

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

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:

83.0ms	(*.f32 alpha alpha)
80.0ms	alpha
78.0ms	(/.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))))
62.0ms	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 1583 to 841 computations (46.9% saved)

regimes228.0ms (1.7%)

Counts

69 → 1

Calls

Call 1

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

Calls

4 calls:

64.0ms	(/.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))))
58.0ms	(*.f32 alpha alpha)
43.0ms	alpha
38.0ms	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 1007 to 534 computations (47% saved)

regimes101.0ms (0.7%)

Counts

41 → 1

Calls

Call 1

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

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

4 calls:

27.0ms	alpha
20.0ms	(*.f32 alpha alpha)
20.0ms	(*.f32 alpha alpha)
19.0ms	cosTheta

Results

Error	Segments	Branch
0.6b	1	`cosTheta`
0.6b	1	`alpha`
0.6b	1	`(*.f32 alpha alpha)`
0.6b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 556 to 279 computations (49.8% saved)

regimes73.0ms (0.5%)

Counts

40 → 1

Calls

Call 1

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

21.0ms	cosTheta
20.0ms	(*.f32 alpha alpha)
20.0ms	alpha

Results

Error	Segments	Branch
0.8b	1	`cosTheta`
0.8b	1	`alpha`
0.8b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 527 to 263 computations (50.1% saved)

regimes65.0ms (0.5%)

Counts

34 → 1

Calls

Call 1

Inputs
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (/.f32 (log.f32 alpha) (/.f32 -1 (PI.f32))))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 -1 (PI.f32)))
(-.f32 (+.f32 1 (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))) 1)
(/.f32 (/.f32 (/.f32 1/2 (*.f32 cosTheta cosTheta)) (log.f32 alpha)) (PI.f32))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (*.f32 cosTheta cosTheta))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (log.f32 alpha) (PI.f32))))
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta (PI.f32))) cosTheta)
(/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (*.f32 cosTheta cosTheta)) (PI.f32))
(/.f32 (/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (log.f32 alpha))) (PI.f32))
(/.f32 (/.f32 (/.f32 -1/2 cosTheta) (*.f32 (PI.f32) 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 (neg.f32 (log.f32 alpha))) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
(/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 -1 (*.f32 alpha alpha)))))
(/.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)))
(/.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 (PI.f32)) (.f32 (-.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 (.f32 (PI.f32) (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
(.f32 (+.f32 (/.f32 (.f32 alpha alpha) -1) 1) (/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 -1/2 (PI.f32)))
(/.f32 -1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 -1 (.f32 (.f32 (PI.f32) (.f32 1/3 (.f32 6 (log.f32 alpha)))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 -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 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.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	alpha
20.0ms	(*.f32 alpha alpha)
15.0ms	cosTheta

Results

Error	Segments	Branch
0.8b	1	`cosTheta`
0.8b	1	`alpha`
0.8b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 401 to 206 computations (48.6% saved)

regimes64.0ms (0.5%)

Counts

33 → 1

Calls

Call 1

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

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

Calls

3 calls:

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

Results

Error	Segments	Branch
1.6b	1	`cosTheta`
1.6b	1	`alpha`
1.6b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 382 to 197 computations (48.4% saved)

regimes36.0ms (0.3%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

2 calls:

15.0ms	alpha
13.0ms	cosTheta

Results

Error	Segments	Branch
1.6b	1	`cosTheta`
1.6b	1	`alpha`

Compiler

Compiled 286 to 140 computations (51% saved)

regimes31.0ms (0.2%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

2 calls:

13.0ms	alpha
12.0ms	cosTheta

Results

Error	Segments	Branch
5.9b	1	`cosTheta`
5.9b	1	`alpha`

Compiler

Compiled 272 to 132 computations (51.5% saved)

regimes22.0ms (0.2%)

Counts

18 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	cosTheta
9.0ms	alpha

Results

Error	Segments	Branch
10.1b	1	`cosTheta`
10.1b	1	`alpha`

Compiler

Compiled 176 to 86 computations (51.1% saved)

regimes22.0ms (0.2%)

Counts

17 → 1

Calls

Call 1

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

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

Calls

2 calls:

9.0ms	alpha
9.0ms	cosTheta

Results

Error	Segments	Branch
10.4b	1	`cosTheta`
10.4b	1	`alpha`

Compiler

Compiled 164 to 81 computations (50.6% saved)

regimes9.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0.2%)

Threshold costs -0.0b (-0.2%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

2 calls:

4.0ms	cosTheta
3.0ms	alpha

Results

Error	Segments	Branch
10.5b	1	`cosTheta`
10.5b	1	`alpha`

Compiler

Compiled 20 to 14 computations (30% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`*-commutative_binary32`
10×	`+-commutative_binary32`
8×	`sub-neg_binary32`
4×	`neg-sub0_binary32`
4×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	56	269
1	93	269
2	104	269
3	111	269
4	114	269

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

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

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

Compiler

Compiled 194 to 140 computations (27.8% saved)

soundness0.0ms (0%)

end339.0ms (2.5%)

Compiler: Compiled 174 to 92 computations (47.1% saved)