Details

analyze121.0ms (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)

sample2.2s (18.3%)

Results

2.1s

8256×

body

256

valid

preprocess44.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

712×	`distribute-rgt-in_binary32`
694×	`distribute-lft-in_binary32`
486×	`associate-/r*_binary32`
348×	`fma-def_binary32`
325×	`associate-/l*_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	66
1	79	62
2	317	62
3	1615	62
4	6827	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 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (.f32 (PI.f32) (*.f32 2 (log.f32 alpha))))
(/.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 (fma.f32 alpha alpha -1) (.f32 (PI.f32) (.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 (log.f32 alpha) (.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
(/.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 (fma.f32 cosTheta cosTheta -1) (.f32 (.f32 2 (log.f32 cosTheta)) (.f32 (PI.f32) (fma.f32 alpha (.f32 alpha (fma.f32 cosTheta cosTheta -1)) 1))))
(/.f32 (/.f32 (fma.f32 cosTheta cosTheta -1) (.f32 2 (.f32 (PI.f32) (log.f32 cosTheta)))) (fma.f32 (*.f32 alpha alpha) (fma.f32 cosTheta cosTheta -1) 1))
(/.f32 (fma.f32 cosTheta cosTheta -1) (.f32 (PI.f32) (.f32 (.f32 (log.f32 cosTheta) 2) (fma.f32 alpha (.f32 alpha (fma.f32 cosTheta cosTheta -1)) 1))))
(/.f32 (/.f32 (fma.f32 cosTheta cosTheta -1) (.f32 (.f32 (PI.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)

simplify29.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

598×	`associate-/l*_binary32`
435×	`associate-l_binary32`
382×	`associate-*l/_binary32`
360×	`distribute-rgt-in_binary32`
359×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	166	31
3	823	31
4	4240	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 (PI.f32) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

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

0.5b

Counts

3 → 2

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

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))))

▶

0.5b

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

Compiler

Compiled 49 to 32 computations (34.7% saved)

localize48.0ms (0.4%)

Local error

Found 8 expressions with local error:

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

series105.0ms (0.9%)

Counts

4 → 72

Calls

18 calls:

Time	Variable		Point	Expression
41.0ms	alpha	@	-inf	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
30.0ms	alpha	@	0	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
11.0ms	alpha	@	inf	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))
8.0ms	alpha	@	-inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
2.0ms	alpha	@	inf	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))

rewrite92.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	70
1	301	70
2	3902	70

Stop Event

1×	node limit

Counts

4 → 146

Calls

Call 1

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

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

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

790×	`associate-/l*_binary32`
625×	`fma-def_binary32`
428×	`associate-*r/_binary32`
417×	`associate-*l/_binary32`
348×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2939
1	609	2612
2	2448	2571

Stop Event

1×	node limit

Counts

218 → 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 (+.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) (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 -1/2 (.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 (*.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 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 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 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 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 -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 1/2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 1/2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 1/2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (PI.f32))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(.f32 -1/2 (/.f32 (.f32 alpha alpha) (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(fma.f32 -1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (log.f32 alpha) (neg.f32 (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)))))
(fma.f32 -1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (log.f32 alpha) (neg.f32 (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)))))
(fma.f32 -1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (*.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (PI.f32) (neg.f32 (log.f32 alpha)))))
(fma.f32 -1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (neg.f32 (log.f32 alpha)))) (/.f32 1/2 (.f32 (log.f32 alpha) (neg.f32 (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 alpha alpha) (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 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 1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))) (/.f32 1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 -1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(.f32 1/2 (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))) (/.f32 -1 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 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 1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))) (/.f32 1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 -1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(.f32 1/2 (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))) (/.f32 -1 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 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 1/2 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))) (/.f32 1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))))
(fma.f32 1/2 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))) (/.f32 -1/2 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))))))
(.f32 1/2 (fma.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))) (/.f32 -1 (.f32 (PI.f32) (-.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (+.f32 1 (neg.f32 (*.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta)))
(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
(-.f32 (.f32 1/2 (.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 (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 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) (/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (-.f32 1 (.f32 cosTheta cosTheta))))
(fma.f32 (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 1/2 (.f32 alpha alpha)) (/.f32 -1/2 (.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 (.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 (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 (/.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))))) (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 (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))) (pow.f32 alpha 4))) (/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta)))))
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(.f32 (.f32 cosTheta alpha) (*.f32 cosTheta alpha))
(.f32 (.f32 alpha cosTheta) (*.f32 alpha 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)
(*.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2))
(.f32 (.f32 alpha alpha) (*.f32 cosTheta cosTheta))
(.f32 (.f32 cosTheta alpha) (*.f32 cosTheta alpha))
(.f32 (.f32 alpha cosTheta) (*.f32 alpha 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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 (.f32 cosTheta cosTheta) (fma.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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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 (.f32 cosTheta cosTheta) (fma.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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 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)
(fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)

localize80.0ms (0.7%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(log.f32 (*.f32 alpha alpha))
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
	0.0b	(.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))
	0.0b	(+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))
✓	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)))

series45.0ms (0.4%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
19.0ms	alpha	@	inf	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
9.0ms	alpha	@	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
4.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

rewrite100.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`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	4649	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 log1p.f32 (-.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 1))))) (#(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 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 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 +.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))) (cbrt.f32 (pow.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 (cbrt.f32 (pow.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 (cbrt.f32 (pow.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 log1p.f32 (expm1.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))))))) (#(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 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)))) (#(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))))))

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

930×	`associate-/l*_binary32`
573×	`fma-def_binary32`
348×	`associate-*l/_binary32`
329×	`distribute-rgt-in_binary32`
315×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	3055
1	593	2651
2	2467	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 (.f32 -2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 -2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 -2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (.f32 -2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -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 (.f32 (log.f32 alpha) (PI.f32)) (-.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 (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))))) (.f32 alpha alpha) (/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta))))))
(fma.f32 (fma.f32 1/2 (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))) (/.f32 1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))))) (.f32 alpha alpha) (/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.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 (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))))) (.f32 alpha alpha) (fma.f32 -1 (.f32 (/.f32 (+.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (.f32 cosTheta cosTheta))))) (.f32 1/2 (.f32 (/.f32 cosTheta (log.f32 alpha)) (/.f32 cosTheta (.f32 (PI.f32) (pow.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2)))))) (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 cosTheta (.f32 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 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (+.f32 (/.f32 1/2 (.f32 (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 2) (pow.f32 cosTheta 6))) (log.f32 alpha))) (/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1))))))
(-.f32 (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 2) (.f32 (pow.f32 cosTheta 6) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (-.f32 (pow.f32 alpha 2) 1) (.f32 (pow.f32 cosTheta 4) (PI.f32))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 (-.f32 (pow.f32 alpha 2) 1) 3) (*.f32 (pow.f32 cosTheta 8) (PI.f32)))))))
(-.f32 (+.f32 (/.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 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 (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 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta)) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8)))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (-.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 (PI.f32) (.f32 (pow.f32 cosTheta 4) (fma.f32 alpha alpha -1)))) (/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (*.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 8)))))))
(*.f32 -1 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 alpha cosTheta) (*.f32 alpha 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 alpha cosTheta) (*.f32 alpha 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))

eval343.0ms (2.9%)

Compiler: Compiled 14915 to 8461 computations (43.3% saved)

prune112.0ms (1%)

Pruning

24 alts after pruning (23 fresh and 1 done)

	Pruned	Kept	Total
New	401	23	424
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	402	24	426

Error

Counts

426 → 24

Alt Table

Click to see full alt table

Status	Error	Program
	23.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log1p.f32 (-.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.8b	(/.f32 (fma.f32 alpha alpha -1) (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
✓	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))))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
	0.6b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.6b	(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) 2)) (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
	0.6b	(/.f32 (.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2)) (log.f32 alpha)) 1) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
▶	0.4b	(/.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))))
	0.7b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (log.f32 (exp.f32 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))
	0.5b	(.f32 (fma.f32 alpha alpha -1) (/.f32 1 (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))
	0.6b	(/.f32 (.f32 (/.f32 1 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))
	0.5b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))
	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))))
▶	31.6b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	10.3b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
	31.6b	(/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
	10.3b	(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
	0.6b	(pow.f32 (/.f32 (PI.f32) (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) -1)
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	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))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	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)))

Compiler

Compiled 1066 to 756 computations (29.1% saved)

localize76.0ms (0.6%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
	0.0b	(log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
	0.0b	(.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))
	0.0b	(+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))
	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))

series8.0ms (0.1%)

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))

rewrite86.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

870×	`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	4622	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

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simplify139.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

947×	`associate-/l*_binary32`
565×	`fma-def_binary32`
347×	`associate-*l/_binary32`
329×	`distribute-rgt-in_binary32`
313×	`distribute-lft-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

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

Stop Event

1×	node limit

Counts

125 → 134

Calls

Call 1

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

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

localize27.0ms (0.2%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(.f32 (PI.f32) (.f32 cosTheta cosTheta))
	0.2b	(/.f32 1/2 (log.f32 alpha))
	0.2b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
	0.0b	(log.f32 alpha)
✓	0.0b	(log.f32 alpha)
✓	0.2b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
✓	0.2b	(/.f32 1/2 (log.f32 alpha))
✓	0.3b	(.f32 (PI.f32) (.f32 cosTheta cosTheta))

series24.0ms (0.2%)

Counts

4 → 52

Calls

15 calls:

Time	Variable		Point	Expression
12.0ms	cosTheta	@	0	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
4.0ms	alpha	@	-inf	(log.f32 alpha)
1.0ms	alpha	@	0	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
1.0ms	cosTheta	@	inf	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
1.0ms	alpha	@	-inf	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))

rewrite76.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

585×	`log-prod_binary32`
451×	`exp-prod_binary32`
357×	`pow-prod-down_binary32`
277×	`pow2_binary32`
195×	`pow1/3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	33
1	214	33
2	2940	33

Stop Event

1×	node limit

Counts

4 → 157

Calls

Call 1

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

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

simplify92.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

782×	`fma-def_binary32`
563×	`fma-neg_binary32`
536×	`distribute-lft-out--_binary32`
412×	`distribute-rgt-neg-in_binary32`
359×	`distribute-lft-neg-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	600
1	57	568
2	135	552
3	466	552
4	1907	552
5	5243	552

Stop Event

1×	node limit

Counts

209 → 169

Calls

Call 1

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

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

localize111.0ms (0.9%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
	0.0b	(.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))
	0.0b	(+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))
	0.0b	(log.f32 alpha)
	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))

series4.0ms (0%)

Counts

1 → 24

Calls

6 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))))
0.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
0.0ms	cosTheta	@	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))))

rewrite77.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	33
1	352	31
2	5111	31

Stop Event

1×	node limit

Counts

1 → 76

Calls

Call 1

Inputs
(/.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 (/.f32 (/.f32 (*.f32 alpha alpha) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (neg.f32 (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (fma.f32 alpha alpha -1) (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) (*.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (pow.f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) 2) (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (*.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))) (sqrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (*.f32 (*.f32 (log.f32 alpha) (*.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 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (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 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (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 (pow.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) 2) 1) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (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 2 (*.f32 (PI.f32) (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 2 (*.f32 (PI.f32) (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 2 (*.f32 (PI.f32) (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) (log.f32 alpha)) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (*.f32 2 (*.f32 (PI.f32) (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)) (log.f32 alpha)) (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (*.f32 2 (*.f32 (PI.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 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 (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)) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (*.f32 (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 1 (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (/.f32 (fma.f32 alpha 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) (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 1 (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (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 2 (*.f32 (PI.f32) (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) (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))) 2)) (cbrt.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (*.f32 (log.f32 alpha) (*.f32 (PI.f32) 2))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (/.f32 (sqrt.f32 (fma.f32 alpha alpha -1)) (pow.f32 (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (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 2 (*.f32 (PI.f32) (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 alpha) (*.f32 2 (*.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))))) 2)) (/.f32 (+.f32 alpha -1) (cbrt.f32 (*.f32 (log.f32 alpha) (*.f32 2 (*.f32 (PI.f32) (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 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simplify53.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

726×	`associate-/l*_binary32`
529×	`fma-def_binary32`
459×	`*-commutative_binary32`
395×	`associate-*r/_binary32`
387×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2036
1	525	1875
2	2196	1834

Stop Event

1×	node limit

Counts

100 → 116

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

localize62.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.3b	(/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
	0.0b	(.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
	0.0b	(fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)
	0.0b	(log.f32 alpha)
✓	0.0b	(.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
✓	0.3b	(/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
✓	0.4b	(.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))))
✓	0.5b	(/.f32 (+.f32 alpha 1) (PI.f32))

series69.0ms (0.6%)

Counts

4 → 84

Calls

21 calls:

Time	Variable		Point	Expression
22.0ms	cosTheta	@	inf	(/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
20.0ms	alpha	@	0	(/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))
10.0ms	alpha	@	inf	(.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (*.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 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
1.0ms	alpha	@	0	(/.f32 (+.f32 alpha 1) (PI.f32))

rewrite103.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

321×	`expm1-udef_binary32`
321×	`log1p-udef_binary32`
319×	`log-div_binary32`
269×	`log-pow_binary32`
242×	`prod-diff_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	90
1	385	85
2	5524	85

Stop Event

1×	node limit

Counts

4 → 160

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

Outputs
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simplify106.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

785×	`associate-*l/_binary32`
462×	`associate-/l/_binary32`
393×	`associate-/r/_binary32`
345×	`associate-/r*_binary32`
248×	`associate-r_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	286	5322
1	1008	4674
2	4311	4480

Stop Event

1×	node limit

Counts

244 → 261

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

localize77.0ms (0.7%)

Local error

Found 8 expressions with local error:

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

series6.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

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

rewrite90.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

849×	`log-prod_binary32`
280×	`expm1-udef_binary32`
280×	`log1p-udef_binary32`
266×	`pow3_binary32`
259×	`log-div_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	58
1	329	58
2	4425	58

Stop Event

1×	node limit

Counts

3 → 153

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify91.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

797×	`associate-/l*_binary32`
592×	`fma-def_binary32`
428×	`associate-*r/_binary32`
421×	`associate-*l/_binary32`
338×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	178	2650
1	594	2422
2	2403	2381

Stop Event

1×	node limit

Counts

201 → 214

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

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

eval746.0ms (6.3%)

Compiler: Compiled 35700 to 21588 computations (39.5% saved)

prune263.0ms (2.2%)

Pruning

38 alts after pruning (34 fresh and 4 done)

	Pruned	Kept	Total
New	1061	31	1092
Fresh	15	3	18
Picked	1	0	1
Done	1	4	5
Total	1078	38	1116

Error

Counts

1116 → 38

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (exp.f32 (log.f32 (/.f32 (/.f32 (+.f32 alpha -1) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 2 (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
▶	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1))
	0.6b	(/.f32 (-.f32 1 alpha) (.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) (.f32 -2 (.f32 (log.f32 alpha) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.6b	(.f32 (+.f32 (/.f32 1 (PI.f32)) (/.f32 alpha (PI.f32))) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	10.3b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
	1.9b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	31.6b	(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))
▶	1.9b	(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) 2)) (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))) 1)
✓	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))))
	1.9b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (PI.f32) (/.f32 (/.f32 (+.f32 alpha -1) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
	31.6b	(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (+.f32 alpha -1)))
	31.6b	(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta (neg.f32 cosTheta)))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (PI.f32)) (log.f32 alpha))))
	0.6b	(/.f32 (/.f32 1 (.f32 (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)) (/.f32 (PI.f32) 1/2))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))
	0.9b	(.f32 (pow.f32 (cbrt.f32 (/.f32 (+.f32 alpha 1) (PI.f32))) 3) (/.f32 (+.f32 alpha -1) (.f32 (.f32 2 (log.f32 alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	0.5b	(.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)))
✓	31.6b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
▶	0.7b	(/.f32 1 (.f32 (/.f32 (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1) (/.f32 (+.f32 alpha -1) (*.f32 2 (log.f32 alpha)))) (/.f32 (PI.f32) (+.f32 alpha 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (log.f32 alpha) 2) (+.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (-.f32 1 (*.f32 cosTheta cosTheta))))))
	10.3b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	1.8b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (-.f32 (exp.f32 (log1p.f32 (/.f32 (/.f32 (+.f32 alpha -1) (.f32 2 (log.f32 alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)))) 1))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (pow.f32 (cbrt.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2))) 3) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.0b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) cosTheta) (.f32 2 (log.f32 alpha))) (.f32 2 (log.f32 alpha)))))
	0.5b	(.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)))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	31.6b	(/.f32 1/2 (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
▶	1.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
✓	0.4b	(/.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))))
▶	31.6b	(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32))))

Compiler

Compiled 1564 to 1145 computations (26.8% saved)

localize96.0ms (0.8%)

Local error

Found 8 expressions with local error:

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

series5.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite165.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

828×	`log-prod_binary32`
277×	`log-div_binary32`
272×	`expm1-udef_binary32`
272×	`log1p-udef_binary32`
257×	`pow3_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	315	48
2	4339	48

Stop Event

1×	node limit

Counts

2 → 106

Calls

Call 1

Inputs

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

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

Outputs

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simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

791×	`associate-/l*_binary32`
584×	`fma-def_binary32`
425×	`associate-*r/_binary32`
421×	`associate-*l/_binary32`
334×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	2381
1	580	2194
2	2371	2153

Stop Event

1×	node limit

Counts

142 → 157

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

localize29.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

series4.0ms (0%)

Counts

3 → 36

Calls

12 calls:

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

rewrite125.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

607×	`log-prod_binary32`
462×	`exp-prod_binary32`
369×	`pow-prod-down_binary32`
279×	`pow2_binary32`
213×	`pow-unpow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	29
1	213	29
2	2934	29

Stop Event

1×	node limit

Counts

3 → 115

Calls

Call 1

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

Outputs

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

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

simplify44.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-/r*_binary32`
532×	`distribute-lft-out--_binary32`
376×	`distribute-rgt-neg-in_binary32`
353×	`fma-def_binary32`
346×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	480
1	54	480
2	129	480
3	416	480
4	1536	480
5	4653	480

Stop Event

1×	node limit

Counts

151 → 121

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

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

localize93.0ms (0.8%)

Local error

Found 8 expressions with local error:

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

series6.0ms (0.1%)

Counts

3 → 32

Calls

9 calls:

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

rewrite97.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

629×	`log-prod_binary32`
280×	`pow2_binary32`
226×	`fma-def_binary32`
226×	`prod-diff_binary32`
211×	`log-div_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	36
1	221	26
2	3359	26

Stop Event

1×	node limit

Counts

3 → 168

Calls

Call 1

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

Outputs

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

simplify47.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

789×	`fma-neg_binary32`
396×	`sub-neg_binary32`
343×	`div-sub_binary32`
338×	`distribute-neg-frac_binary32`
314×	`fma-def_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	429
1	76	411
2	182	359
3	502	353
4	1980	299
5	5454	299

Stop Event

1×	node limit

Counts

200 → 183

Calls

Call 1

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

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

localize67.0ms (0.6%)

Local error

Found 6 expressions with local error:

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

rewrite0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0

Stop Event

1×

saturated

Counts

0 → 0

Calls

Call 1

Inputs

Outputs

localize71.0ms (0.6%)

Local error

Found 8 expressions with local error:

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

series18.0ms (0.2%)

Counts

4 → 72

Calls

18 calls:

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

rewrite151.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

329×	`expm1-udef_binary32`
329×	`log1p-udef_binary32`
275×	`log-pow_binary32`
261×	`fma-def_binary32`
260×	`prod-diff_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	82
1	391	82
2	5656	82

Stop Event

1×	node limit

Counts

4 → 176

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (/.f32 (PI.f32) (+.f32 alpha 1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (PI.f32) (/.f32 1 (+.f32 alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (/.f32 (PI.f32) (+.f32 alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))) (cbrt.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 2)) (cbrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (/.f32 1 (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))) (sqrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (PI.f32)) (.f32 (sqrt.f32 (PI.f32)) (/.f32 1 (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (neg.f32 (PI.f32)) (/.f32 1 (+.f32 -1 (neg.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (+.f32 alpha 1)) (PI.f32))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) 1) (/.f32 (cbrt.f32 (PI.f32)) (+.f32 alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (PI.f32)) 1) (/.f32 (sqrt.f32 (PI.f32)) (+.f32 alpha 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 (+.f32 alpha 1)) 2)) (/.f32 (PI.f32) (cbrt.f32 (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (pow.f32 (cbrt.f32 (+.f32 alpha 1)) 2)) (cbrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (PI.f32)) (pow.f32 (cbrt.f32 (+.f32 alpha 1)) 2)) (/.f32 (sqrt.f32 (PI.f32)) (cbrt.f32 (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (hypot.f32 1 (sqrt.f32 alpha))) (/.f32 (PI.f32) (hypot.f32 1 (sqrt.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (hypot.f32 1 (sqrt.f32 alpha))) (/.f32 (cbrt.f32 (PI.f32)) (hypot.f32 1 (sqrt.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (PI.f32) (+.f32 1 (pow.f32 alpha 3))) (-.f32 (fma.f32 alpha alpha 1) alpha))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (PI.f32) (fma.f32 alpha alpha -1)) (+.f32 alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (/.f32 (PI.f32) (+.f32 alpha 1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (PI.f32) (+.f32 -1 (neg.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (/.f32 (PI.f32) (+.f32 alpha 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (PI.f32) 3) (pow.f32 (+.f32 alpha 1) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (/.f32 (PI.f32) (+.f32 alpha 1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (-.f32 (log.f32 (PI.f32)) (log1p.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (-.f32 (log.f32 (PI.f32)) (log1p.f32 alpha)) 1))))))
((#(struct:change #<rule egg-rr> (2) ((x -.f32 (exp.f32 (log1p.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))) (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 2)) (cbrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) (.f32 (cbrt.f32 (+.f32 alpha -1)) (/.f32 1/2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))) (sqrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (sqrt.f32 (+.f32 alpha -1)) (.f32 (sqrt.f32 (+.f32 alpha -1)) (/.f32 1/2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (-.f32 1 alpha) (/.f32 1 (.f32 (log.f32 alpha) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (+.f32 alpha -1) (/.f32 1/2 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (+.f32 alpha -1) 1/2) (/.f32 1 (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (/.f32 (+.f32 alpha -1) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) 1) (/.f32 (cbrt.f32 (+.f32 alpha -1)) (.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (+.f32 alpha -1)) 1) (/.f32 (sqrt.f32 (+.f32 alpha -1)) (.f32 2 (log.f32 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) 2) (/.f32 (cbrt.f32 (+.f32 alpha -1)) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (+.f32 alpha -1)) 2) (/.f32 (sqrt.f32 (+.f32 alpha -1)) (log.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (+.f32 alpha -1)) (log.f32 alpha)) (/.f32 (sqrt.f32 (+.f32 alpha -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (log.f32 alpha)) (.f32 (+.f32 alpha -1) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) (log.f32 alpha)) (/.f32 (cbrt.f32 (+.f32 alpha -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (pow.f32 (cbrt.f32 (.f32 2 (log.f32 alpha))) 2)) (/.f32 (+.f32 alpha -1) (cbrt.f32 (.f32 2 (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) (pow.f32 (cbrt.f32 (.f32 2 (log.f32 alpha))) 2)) (cbrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (sqrt.f32 (+.f32 alpha -1)) (pow.f32 (cbrt.f32 (.f32 2 (log.f32 alpha))) 2)) (/.f32 (sqrt.f32 (+.f32 alpha -1)) (cbrt.f32 (.f32 2 (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 1 (sqrt.f32 (.f32 2 (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (sqrt.f32 (.f32 2 (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (/.f32 (pow.f32 (cbrt.f32 (+.f32 alpha -1)) 2) (sqrt.f32 (.f32 2 (log.f32 alpha)))) (/.f32 (cbrt.f32 (+.f32 alpha -1)) (sqrt.f32 (.f32 2 (log.f32 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (cbrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (sqrt.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (.f32 2 (/.f32 (log.f32 alpha) (+.f32 alpha -1))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f32 (pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (exp.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (+.f32 1 (expm1.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (pow.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) 3))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f32 (/.f32 (pow.f32 (+.f32 alpha -1) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f32 (expm1.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f32 (log1p.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (log.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f32 (.f32 (log.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))) 1))))))
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simplify82.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

514×	`associate-/r*_binary32`
413×	`distribute-rgt-in_binary32`
387×	`*-commutative_binary32`
376×	`distribute-lft-in_binary32`
283×	`associate-+l+_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	191	3480
1	650	2898
2	2418	2281

Stop Event

1×	node limit

Counts

248 → 260

Calls

Call 1

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

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

eval809.0ms (6.9%)

Compiler: Compiled 26157 to 16205 computations (38% saved)

prune276.0ms (2.3%)

Pruning

37 alts after pruning (33 fresh and 4 done)

	Pruned	Kept	Total
New	1021	22	1043
Fresh	18	11	29
Picked	1	0	1
Done	4	4	8
Total	1044	37	1081

Error

Counts

1081 → 37

Alt Table

Click to see full alt table

Status	Error	Program
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (.f32 2 (.f32 (PI.f32) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	10.9b	(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) 2)) (/.f32 -1 (log.f32 alpha))) 1)
	1.8b	(/.f32 (/.f32 1 (*.f32 (/.f32 (PI.f32) 1/2) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)))) 1)
	1.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
	1.9b	(.f32 1/2 (.f32 (/.f32 (+.f32 1 alpha) (log.f32 alpha)) (/.f32 (+.f32 alpha -1) (PI.f32))))
▶	1.9b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	1.8b	(.f32 1/2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (PI.f32))))
✓	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))))
	1.8b	(.f32 1/2 (.f32 (neg.f32 (fma.f32 alpha alpha -1)) (/.f32 1 (*.f32 (log.f32 alpha) (neg.f32 (PI.f32))))))
	1.9b	(.f32 1/2 (/.f32 (/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) (fma.f32 alpha alpha -1)) (.f32 (-.f32 1 alpha) (+.f32 1 alpha))) (*.f32 (log.f32 alpha) (PI.f32))))
▶	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	1.8b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) 1)
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (neg.f32 cosTheta) cosTheta))))
	1.9b	(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) 2)) (-.f32 (/.f32 1 (neg.f32 (log.f32 alpha))) (/.f32 (*.f32 alpha alpha) (neg.f32 (log.f32 alpha))))) 1)
✓	0.4b	(/.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))))
	10.3b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 cosTheta cosTheta)))
	1.8b	(.f32 1/2 (/.f32 (/.f32 (.f32 (+.f32 alpha -1) (-.f32 1 (.f32 alpha alpha))) (-.f32 1 alpha)) (.f32 (log.f32 alpha) (PI.f32))))
	1.8b	(.f32 1/2 (.f32 (/.f32 (+.f32 1 alpha) (*.f32 (log.f32 alpha) (PI.f32))) (+.f32 alpha -1)))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (log.f32 alpha) 2) (+.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (-.f32 1 (*.f32 cosTheta cosTheta))))))
▶	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1))
	10.3b	(/.f32 (/.f32 -1/2 (log.f32 alpha)) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (PI.f32)))
	1.9b	(.f32 1/2 (.f32 (+.f32 1 alpha) (*.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))))
	1.0b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))
	10.9b	(*.f32 1/2 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 alpha)))
	1.9b	(/.f32 1 (.f32 (.f32 2 (/.f32 (log.f32 alpha) (+.f32 -1 alpha))) (/.f32 (PI.f32) (+.f32 alpha 1))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) cosTheta) (.f32 2 (log.f32 alpha))) (.f32 2 (log.f32 alpha)))))
▶	10.9b	(.f32 1/2 (/.f32 -1 (.f32 (log.f32 alpha) (PI.f32))))
	3.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log1p.f32 (-.f32 alpha 1)) (PI.f32))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.9b	(.f32 1/2 (.f32 (/.f32 (+.f32 1 alpha) 1) (/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) (PI.f32)))))
	10.3b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
	1.9b	(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 (fma.f32 alpha alpha -1) (PI.f32)))
✓	1.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log.f32 alpha) (PI.f32))))
	1.8b	(.f32 1/2 (.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32))))
▶	1.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (log.f32 (pow.f32 alpha (PI.f32)))))
	1.9b	(.f32 1/2 (.f32 (+.f32 1 alpha) (/.f32 1 (/.f32 (log.f32 alpha) (/.f32 (+.f32 alpha -1) (PI.f32))))))

Compiler

Compiled 1324 to 1021 computations (22.9% saved)

localize57.0ms (0.5%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.2b	(.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))
	0.0b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1))
	0.0b	(+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1)
	0.0b	(log.f32 alpha)
✓	0.0b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) (+.f32 (.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta)) 1))
✓	0.2b	(.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta))
	0.3b	(/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha))
	0.4b	(/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2))

series9.0ms (0.1%)

Counts

2 → 48

Calls

12 calls:

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

rewrite84.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

442×	`prod-diff_binary32`
319×	`log-div_binary32`
298×	`log1p-udef_binary32`
297×	`expm1-udef_binary32`
248×	`log-pow_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	42
1	348	42
2	4943	42

Stop Event

1×	node limit

Counts

2 → 72

Calls

Call 1

Inputs

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

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

Outputs

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

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

725×	`associate-/l*_binary32`
537×	`fma-def_binary32`
464×	`*-commutative_binary32`
393×	`associate-*r/_binary32`
386×	`associate-*l/_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2398
1	533	2132
2	2213	2091

Stop Event

1×	node limit

Counts

120 → 120

Calls

Call 1

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

localize22.0ms (0.2%)

Local error

Found 6 expressions with local error:

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

series2.0ms (0%)

Counts

1 → 8

Calls

3 calls:

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

rewrite53.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

652×	`pow1_binary32`
597×	`add-log-exp_binary32`
597×	`log1p-expm1-u_binary32`
597×	`expm1-log1p-u_binary32`
585×	`add-exp-log_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	138	10
2	1645	10

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

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

Outputs

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

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Rules

3549×	`fma-neg_binary32`
791×	`fma-def_binary32`
388×	`associate--r-_binary32`
336×	`unsub-neg_binary32`
316×	`distribute-rgt-in_binary32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	96
1	32	96
2	55	80
3	115	80
4	230	80
5	594	80
6	2035	80
7	3412	80
8	3940	80
9	3991	80
10	4009	80
11	4011	80
12	5959	80
13	6580	80
14	6846	80
15	6933	80
16	6947	80
17	6951	80
18	7105	80
19	7113	80

Stop Event

1×	node limit

Counts

30 → 25

Calls

Call 1

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

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

localize38.0ms (0.3%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.5b	(/.f32 (+.f32 alpha 1) (PI.f32))
	0.4b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	0.3b	(/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) 2))
	0.0b	(log.f32 alpha)
	0.0b	(log.f32 alpha)
✓	0.3b	(/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) 2))
✓	0.4b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	0.5b	(/.f32 (+.f32 alpha 1) (PI.f32))

series3.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite72.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`log-prod_binary32`
307×	`log-div_binary32`
235×	`expm1-udef_binary32`
235×	`log1p-udef_binary32`
224×	`prod-diff_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	34
1	284	29
2	4214	29

Stop Event

1×	node limit

Counts

2 → 116

Calls

Call 1

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

Outputs

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

simplify45.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

698×	`associate-l_binary32`
686×	`associate-/l/_binary32`
676×	`associate-/r/_binary32`
412×	`fma-def_binary32`
313×	`div-sub_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	479
1	140	443
2	311	435
3	757	345
4	2748	327

Stop Event

1×	node limit

Counts

140 → 132

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

localize50.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	0.1b	(-.f32 (*.f32 alpha alpha) 1)
	0.0b	(.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.0b	(+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))
	0.0b	(log.f32 alpha)
✓	0.0b	(.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
✓	0.1b	(-.f32 (*.f32 alpha alpha) 1)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	0.4b	(.f32 (log.f32 alpha) (.f32 (PI.f32) 2))

series16.0ms (0.1%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
5.0ms	cosTheta	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
1.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
1.0ms	alpha	@	-inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
1.0ms	cosTheta	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
1.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))

rewrite301.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

918×	`prod-diff_binary32`
387×	`egg-rr`
273×	`expm1-udef_binary32`
273×	`log1p-udef_binary32`
242×	`fma-neg_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	54
1	353	46
2	5170	46

Stop Event

1×	node limit

Counts

3 → 545

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify109.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

456×	`associate-/r*_binary32`
455×	`times-frac_binary32`
340×	`fma-def_binary32`
333×	`cancel-sign-sub-inv_binary32`
326×	`associate-/l*_binary32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	92	1935
1	296	1750
2	1149	1629
3	5349	1428

Stop Event

1×	node limit

Counts

605 → 585

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

localize47.0ms (0.4%)

Local error

Found 8 expressions with local error:

New	Error	Program
	2.3b	(pow.f32 alpha (PI.f32))
	0.4b	(*.f32 (+.f32 1 alpha) (-.f32 alpha 1))
	0.3b	(/.f32 (*.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (log.f32 (pow.f32 alpha (PI.f32))))
	0.1b	(log.f32 (pow.f32 alpha (PI.f32)))
✓	0.1b	(log.f32 (pow.f32 alpha (PI.f32)))
✓	0.3b	(/.f32 (*.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (log.f32 (pow.f32 alpha (PI.f32))))
	0.4b	(*.f32 (+.f32 1 alpha) (-.f32 alpha 1))
✓	2.3b	(pow.f32 alpha (PI.f32))

series73.0ms (0.6%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
21.0ms	alpha	@	0	(pow.f32 alpha (PI.f32))
13.0ms	alpha	@	0	(log.f32 (pow.f32 alpha (PI.f32)))
11.0ms	alpha	@	-inf	(log.f32 (pow.f32 alpha (PI.f32)))
10.0ms	alpha	@	inf	(log.f32 (pow.f32 alpha (PI.f32)))
6.0ms	alpha	@	-inf	(/.f32 (*.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (log.f32 (pow.f32 alpha (PI.f32))))

rewrite91.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

570×	`log-prod_binary32`
379×	`pow-prod-down_binary32`
279×	`pow2_binary32`
242×	`pow-unpow_binary32`
239×	`fma-def_binary32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	31
1	222	26
2	3183	26

Stop Event

1×	node limit

Counts

3 → 119

Calls

Call 1

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

Outputs

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

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

simplify56.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

881×	`fma-neg_binary32`
413×	`div-sub_binary32`
315×	`fma-def_binary32`
281×	`neg-mul-1_binary32`
274×	`exp-sum_binary32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	33	413
1	83	413
2	204	393
3	587	387
4	2336	351
5	6565	351

Stop Event

1×	node limit

Counts

155 → 133

Calls

Call 1

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

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

eval1.0s (8.6%)

Compiler: Compiled 49581 to 28438 computations (42.6% saved)

prune244.0ms (2.1%)

Pruning

43 alts after pruning (39 fresh and 4 done)

	Pruned	Kept	Total
New	1332	25	1357
Fresh	14	14	28
Picked	1	0	1
Done	4	4	8
Total	1351	43	1394

Error

Counts

1394 → 43

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	1.8b	(.f32 (+.f32 (/.f32 alpha (PI.f32)) (/.f32 1 (PI.f32))) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) 2)))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) (*.f32 2 (PI.f32)))))
	10.3b	(/.f32 -1/2 (.f32 (.f32 (log.f32 alpha) (PI.f32)) (-.f32 1 (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)) (fma.f32 alpha alpha -1)) (+.f32 (.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta)) 1))
	1.8b	(/.f32 (/.f32 1 (*.f32 (/.f32 (PI.f32) 1/2) (/.f32 (log.f32 alpha) (fma.f32 alpha alpha -1)))) 1)
	1.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
	10.3b	(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))
✓	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))))
	1.9b	(/.f32 (/.f32 (+.f32 alpha -1) (log.f32 alpha)) (*.f32 (/.f32 (PI.f32) (+.f32 alpha 1)) 2))
	1.9b	(/.f32 (+.f32 alpha 1) (/.f32 (PI.f32) (*.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1))))
	11.9b	(.f32 1/2 (/.f32 -1 (.f32 (log1p.f32 (-.f32 alpha 1)) (PI.f32))))
✓	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	1.9b	(/.f32 (.f32 (/.f32 (+.f32 alpha -1) (log.f32 alpha)) (+.f32 alpha 1)) (.f32 2 (PI.f32)))
	1.8b	(/.f32 (+.f32 alpha -1) (.f32 (.f32 (log.f32 alpha) 2) (/.f32 (PI.f32) (+.f32 alpha 1))))
	1.9b	(.f32 1/2 (.f32 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 (.f32 alpha alpha) -1)))
	10.9b	(.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
✓	0.4b	(/.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))))
	1.9b	(/.f32 (.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (-.f32 1 alpha)) (.f32 (log.f32 alpha) -2))
	1.8b	(.f32 1/2 (/.f32 (/.f32 (.f32 (+.f32 alpha -1) (-.f32 1 (.f32 alpha alpha))) (-.f32 1 alpha)) (.f32 (log.f32 alpha) (PI.f32))))
	1.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 alpha) (*.f32 2 (PI.f32))))
	1.8b	(.f32 1/2 (.f32 (/.f32 (+.f32 1 alpha) (*.f32 (log.f32 alpha) (PI.f32))) (+.f32 alpha -1)))
	1.9b	(/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (/.f32 (.f32 (log.f32 alpha) 2) (+.f32 alpha -1))))
	17.0b	(*.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 -1/2 (log.f32 alpha)))
	10.9b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	1.8b	(.f32 1/2 (.f32 (fma.f32 alpha alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (.f32 (log.f32 alpha) 2) (+.f32 (.f32 alpha (.f32 alpha (.f32 cosTheta cosTheta))) (-.f32 1 (*.f32 cosTheta cosTheta))))))
	10.9b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	1.9b	(.f32 1/2 (.f32 (+.f32 1 alpha) (*.f32 (+.f32 alpha -1) (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta)))))
	1.0b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 alpha) (.f32 (-.f32 1 (.f32 cosTheta cosTheta)) 2))))
	0.6b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (+.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha -1) cosTheta) cosTheta) (.f32 2 (log.f32 alpha))) (.f32 2 (log.f32 alpha)))))
	1.9b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (pow.f32 (/.f32 (.f32 (log.f32 alpha) 2) (+.f32 alpha -1)) -1))
	11.0b	(.f32 1/2 (/.f32 -1 (.f32 (.f32 1/3 (.f32 3 (log.f32 alpha))) (PI.f32))))
	3.8b	(.f32 1/2 (/.f32 (.f32 (+.f32 1 alpha) (-.f32 alpha 1)) (*.f32 (log1p.f32 (-.f32 alpha 1)) (PI.f32))))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	10.9b	(.f32 1/2 (.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1 (PI.f32))))
	1.9b	(.f32 1/2 (.f32 (/.f32 (+.f32 1 alpha) 1) (/.f32 (+.f32 alpha -1) (*.f32 (log.f32 alpha) (PI.f32)))))
	1.9b	(/.f32 (*.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) (/.f32 (PI.f32) (+.f32 alpha 1)))
	1.9b	(/.f32 (.f32 (.f32 (/.f32 1/2 (log.f32 alpha)) (+.f32 alpha -1)) (+.f32 -1 (neg.f32 alpha))) (neg.f32 (PI.f32)))
	0.5b	(/.f32 (/.f32 (/.f32 (fma.f32 alpha alpha -1) (log.f32 alpha)) (/.f32 (PI.f32) 1/2)) (+.f32 (+.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 (*.f32 cosTheta cosTheta) -1)) 1))
	1.8b	(/.f32 1/2 (/.f32 (log.f32 alpha) (/.f32 (fma.f32 alpha alpha -1) (PI.f32))))
	1.9b	(.f32 1/2 (.f32 (+.f32 1 alpha) (/.f32 1 (/.f32 (log.f32 alpha) (/.f32 (+.f32 alpha -1) (PI.f32))))))

Compiler

Compiled 782 to 607 computations (22.4% saved)

regimes352.0ms (3%)

Counts

103 → 1

Calls

Call 1

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

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

Calls

4 calls:

89.0ms	(*.f32 alpha alpha)
72.0ms	(/.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))))
70.0ms	cosTheta
50.0ms	alpha

Results

Error	Segments	Branch
0.4b	1	`cosTheta`
0.4b	1	`alpha`
0.4b	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))))`
0.4b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 1855 to 1060 computations (42.9% saved)

regimes225.0ms (1.9%)

Counts

68 → 1

Calls

Call 1

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

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:

55.0ms	alpha
52.0ms	(*.f32 alpha alpha)
52.0ms	cosTheta
38.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

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 1002 to 583 computations (41.8% saved)

regimes126.0ms (1.1%)

Counts

51 → 1

Calls

Call 1

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

3 calls:

57.0ms	alpha
27.0ms	(*.f32 alpha alpha)
25.0ms	cosTheta

Results

Error	Segments	Branch
0.5b	1	`cosTheta`
0.5b	1	`alpha`
0.5b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 694 to 402 computations (42.1% saved)

regimes128.0ms (1.1%)

Counts

50 → 1

Calls

Call 1

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

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

Calls

3 calls:

29.0ms	(*.f32 alpha alpha)
29.0ms	cosTheta
28.0ms	alpha

Results

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

Compiler

Compiled 670 to 389 computations (41.9% saved)

regimes63.0ms (0.5%)

Counts

46 → 1

Calls

Call 1

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

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

Calls

2 calls:

26.0ms	alpha
21.0ms	cosTheta

Results

Error	Segments	Branch
0.9b	1	`cosTheta`
0.9b	1	`alpha`

Compiler

Compiled 585 to 343 computations (41.4% saved)

regimes59.0ms (0.5%)

Counts

45 → 1

Calls

Call 1

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

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

Calls

2 calls:

23.0ms	alpha
21.0ms	cosTheta

Results

Error	Segments	Branch
0.9b	1	`cosTheta`
0.9b	1	`alpha`

Compiler

Compiled 566 to 334 computations (41% saved)

regimes59.0ms (0.5%)

Counts

43 → 1

Calls

Call 1

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

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

Calls

2 calls:

25.0ms	alpha
20.0ms	cosTheta

Results

Error	Segments	Branch
1.8b	1	`cosTheta`
1.8b	1	`alpha`

Compiler

Compiled 530 to 311 computations (41.3% saved)

regimes24.0ms (0.2%)

Counts

17 → 1

Calls

Call 1

Inputs
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(*.f32 1/2 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 alpha)))
(.f32 1/2 (/.f32 -1 (.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 -1 (.f32 (log1p.f32 (-.f32 alpha 1)) (PI.f32))))
(.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(*.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 -1/2 (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1 (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta (neg.f32 cosTheta)))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 -1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32)))

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

Calls

2 calls:

10.0ms	cosTheta
9.0ms	alpha

Results

Error	Segments	Branch
10.3b	1	`cosTheta`
10.3b	1	`alpha`

Compiler

Compiled 170 to 90 computations (47.1% saved)

regimes21.0ms (0.2%)

Accuracy

Total -20.7b remaining (-189.3%)

Threshold costs -20.7b (-189.3%)

Counts

16 → 1

Calls

Call 1

Inputs
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(*.f32 1/2 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 alpha)))
(.f32 1/2 (/.f32 -1 (.f32 (log.f32 alpha) (PI.f32))))
(.f32 1/2 (/.f32 -1 (.f32 (log1p.f32 (-.f32 alpha 1)) (PI.f32))))
(.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(*.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 -1/2 (log.f32 alpha)))
(.f32 1/2 (.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1 (PI.f32))))
(/.f32 1/2 (.f32 (.f32 cosTheta cosTheta) (*.f32 (PI.f32) (log.f32 alpha))))
(/.f32 (/.f32 1/2 (.f32 (PI.f32) (.f32 cosTheta cosTheta))) (log.f32 alpha))
(/.f32 1/2 (.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)) (log.f32 alpha)))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 cosTheta (.f32 cosTheta (PI.f32))))
(/.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (.f32 cosTheta cosTheta))
(/.f32 (/.f32 1/2 (log.f32 alpha)) (.f32 (PI.f32) (.f32 cosTheta cosTheta)))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (log.f32 alpha) (*.f32 cosTheta (neg.f32 cosTheta)))))
(/.f32 -1/2 (.f32 (log.f32 alpha) (neg.f32 (.f32 (PI.f32) (*.f32 cosTheta cosTheta)))))

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

Calls

2 calls:

9.0ms	alpha
8.0ms	cosTheta

Results

Error	Segments	Branch
10.9b	1	`cosTheta`
10.9b	1	`alpha`

Compiler

Compiled 158 to 85 computations (46.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

17×	`*-commutative_binary32`
5×	`+-commutative_binary32`
4×	`sub-neg_binary32`
2×	`neg-sub0_binary32`
2×	`neg-mul-1_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	243
1	74	243
2	79	243
3	82	243
4	83	243

Stop Event

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

end71.0ms (0.6%)

Stop Event

1×

fuel

Compiler

Compiled 332 to 204 computations (38.6% saved)