Details

analyze190.0ms (0.2%)

Algorithm

1×

Search

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

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample6.9s (9%)

Results

6.9s

8256×

body

256

valid

Bogosity

preprocess192.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

1750×	`rational_best-simplify-108`
1570×	`rational_best-simplify-51`
1216×	`rational_best-simplify-47`
886×	`rational_best-simplify-1`
840×	`rational_best-simplify-67`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	146
1	60	146
2	164	146
3	573	146
4	2051	146
5	6232	146
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 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta)))))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 cosTheta (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta))))))
(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 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))))
(/.f32 (+.f32 (.f32 cosTheta cosTheta) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 cosTheta cosTheta))) (+.f32 1 (.f32 alpha (.f32 alpha (+.f32 (*.f32 cosTheta cosTheta) -1))))))
(/.f32 (+.f32 (.f32 cosTheta cosTheta) -1) (.f32 (log.f32 (.f32 cosTheta cosTheta)) (.f32 (PI.f32) (+.f32 1 (.f32 (.f32 alpha alpha) (+.f32 (*.f32 cosTheta cosTheta) -1))))))
(/.f32 (/.f32 (+.f32 (.f32 cosTheta cosTheta) -1) (.f32 (PI.f32) (log.f32 (.f32 cosTheta cosTheta)))) (+.f32 1 (.f32 (.f32 alpha alpha) (+.f32 (.f32 cosTheta cosTheta) -1))))

Compiler

Compiled 28 to 18 computations (35.7% saved)

simplify205.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

1204×	`rational_best-simplify-52`
1178×	`rational_best-simplify-48`
880×	`rational_best-simplify-54`
852×	`rational_best-simplify-57`
782×	`rational_best-simplify-65`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	73
1	35	73
2	89	73
3	297	73
4	1045	73
5	4460	73

Stop Event

1×	node limit

Counts

1 → 4

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

eval2.0ms (0%)

Compiler: Compiled 98 to 46 computations (53.1% saved)

prune4.0ms (0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	4	5

Error

0.3b

Counts

5 → 3

Alt Table

Click to see full alt table

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

Status

Error

Program

▶

0.5b

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

▶

0.5b

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

▶

0.5b

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

Compiler

Compiled 78 to 48 computations (38.5% saved)

localize229.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 93 to 39 computations (58.1% saved)

series142.0ms (0.2%)

Counts

4 → 72

Calls

18 calls:

Time	Variable		Point	Expression
90.0ms	alpha	@	0	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
26.0ms	alpha	@	inf	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
15.0ms	alpha	@	inf	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
2.0ms	alpha	@	0	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
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))))

rewrite675.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

990×	`rational_best-simplify-65`
638×	`rational_best-simplify-67`
600×	`rational_best-simplify-108`
572×	`rational_best-simplify-55`
540×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	122
1	121	122
2	295	122
3	1246	122
4	7509	122

Stop Event

1×	node limit

Counts

4 → 222

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)
(log.f32 (*.f32 alpha alpha))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 0)))) (#(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 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2) (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2) (/.f32 (neg.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2)) (.f32 2 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 2 (.f32 (PI.f32) 2)) (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 2 (.f32 (PI.f32) 2))) 16)))) (#(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 log.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (neg.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (+.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (+.f32 1 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (+.f32 1 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 alpha (/.f32 (/.f32 alpha (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 -1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 alpha (/.f32 (/.f32 alpha (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (neg.f32 (/.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 alpha (/.f32 (/.f32 alpha (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (+.f32 (/.f32 (/.f32 -1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (.f32 alpha (/.f32 (/.f32 alpha (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (+.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 -1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (.f32 alpha alpha)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log.f32 (.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (log.f32 (.f32 alpha alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (.f32 alpha alpha)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (neg.f32 (log.f32 (.f32 alpha alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (log.f32 (.f32 alpha alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1 (log.f32 (.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x .f32 1/2 (.f32 (log.f32 (.f32 alpha alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (log.f32 (.f32 alpha alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log.f32 (.f32 alpha alpha)) 1)))))

simplify930.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1478×	`rational_best-simplify-108`
852×	`rational_best-simplify-49`
810×	`rational_best-simplify-54`
718×	`rational_best-simplify-53`
680×	`rational_best-simplify-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	662	26990
1	1994	24660
2	7740	24168

Stop Event

1×	node limit

Counts

294 → 420

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))))
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(.f32 (+.f32 (+.f32 1 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))) 1) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (.f32 cosTheta cosTheta)) -2))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 alpha alpha) -1)) (/.f32 (/.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (+.f32 (.f32 (.f32 alpha alpha) 2) -2)) (/.f32 (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (.f32 cosTheta cosTheta)) -2))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))
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(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 1 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 2)) (/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (/.f32 (/.f32 1 (-.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (.f32 cosTheta cosTheta)) -2)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) 4)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
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(neg.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
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(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
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(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 2))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta)) 2)
(/.f32 (.f32 4 (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta)) 4)
(/.f32 (+.f32 (.f32 4 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) (.f32 4 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))) 8)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(+.f32 (log.f32 (*.f32 alpha alpha)) 0)
(+.f32 0 (log.f32 (*.f32 alpha alpha)))
(+.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (log.f32 (.f32 alpha alpha)) 2))
(-.f32 (log.f32 (*.f32 alpha alpha)) 0)
(-.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (neg.f32 (log.f32 (.f32 alpha alpha))) 2))
(.f32 (log.f32 (.f32 alpha alpha)) 1)
(.f32 1 (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (log.f32 (*.f32 alpha alpha)) 2) 1/2)
(.f32 1/2 (.f32 (log.f32 (*.f32 alpha alpha)) 2))
(.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) 1/4)
(/.f32 (log.f32 (*.f32 alpha alpha)) 1)
(/.f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) 2)
(/.f32 (.f32 2 (.f32 (log.f32 (*.f32 alpha alpha)) 2)) 4)
(/.f32 (+.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2))) 8)
(pow.f32 (log.f32 (*.f32 alpha alpha)) 1)

Outputs
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 2 (.f32 (log.f32 alpha) (PI.f32)))
(.f32 (PI.f32) (.f32 2 (log.f32 alpha)))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))
(.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha))))
(.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(.f32 (PI.f32) (.f32 -2 (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 (*.f32 -1 (pow.f32 cosTheta 2))))))
(/.f32 -1/2 (.f32 (+.f32 1 (neg.f32 (pow.f32 cosTheta 2))) (.f32 (log.f32 alpha) (PI.f32))))
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(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 2)) (/.f32 1/2 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))))
(.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (/.f32 (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))))
(.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (+.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))) (/.f32 (/.f32 1 (-.f32 (.f32 (+.f32 (.f32 (.f32 alpha alpha) 2) -2) (.f32 cosTheta cosTheta)) -2)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (+.f32 -2 (.f32 2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (/.f32 1 (.f32 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))
(/.f32 (.f32 1 (/.f32 (/.f32 (+.f32 -2 (.f32 2 (.f32 alpha alpha))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2))) (+.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (/.f32 (+.f32 -2 (.f32 2 (.f32 alpha alpha))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)) (+.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) 4)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(.f32 (.f32 (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))) (.f32 4 (+.f32 -1 (.f32 alpha alpha)))) (/.f32 (/.f32 1 (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32)))) (.f32 4 (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))
(/.f32 (.f32 1 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 0)) (+.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (PI.f32) (PI.f32)) (/.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (log.f32 (*.f32 alpha alpha)))))
(pow.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) 1)
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))
(neg.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))
(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(neg.f32 (+.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))))))
(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(neg.f32 (+.f32 (/.f32 0 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))))))
(neg.f32 (+.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (.f32 alpha alpha)) (PI.f32))))))
(-.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))))
(+.f32 (/.f32 0 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(neg.f32 (+.f32 (neg.f32 (/.f32 0 (/.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))))))
(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 2))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta)) 2)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 4 (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta)) 4)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -1 (*.f32 alpha alpha)))) 4)
(/.f32 (+.f32 (.f32 4 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) (.f32 4 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))) 8)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -1 (*.f32 alpha alpha)))) 4)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(/.f32 (.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 4 (.f32 cosTheta (.f32 4 (+.f32 -1 (.f32 alpha alpha))))) 16)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 4 (.f32 cosTheta (.f32 4 (+.f32 -1 (.f32 alpha alpha))))) 16)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(+.f32 (log.f32 (*.f32 alpha alpha)) 0)
(log.f32 (*.f32 alpha alpha))
(+.f32 0 (log.f32 (*.f32 alpha alpha)))
(log.f32 (*.f32 alpha alpha))
(+.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (log.f32 (.f32 alpha alpha)) 2))
(log.f32 (*.f32 alpha alpha))
(-.f32 (log.f32 (*.f32 alpha alpha)) 0)
(log.f32 (*.f32 alpha alpha))
(-.f32 (/.f32 (log.f32 (.f32 alpha alpha)) 2) (/.f32 (neg.f32 (log.f32 (.f32 alpha alpha))) 2))
(log.f32 (*.f32 alpha alpha))
(.f32 (log.f32 (.f32 alpha alpha)) 1)
(log.f32 (*.f32 alpha alpha))
(.f32 1 (log.f32 (.f32 alpha alpha)))
(log.f32 (*.f32 alpha alpha))
(.f32 (.f32 (log.f32 (*.f32 alpha alpha)) 2) 1/2)
(log.f32 (*.f32 alpha alpha))
(.f32 1/2 (.f32 (log.f32 (*.f32 alpha alpha)) 2))
(log.f32 (*.f32 alpha alpha))
(.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) 1/4)
(log.f32 (*.f32 alpha alpha))
(/.f32 (log.f32 (*.f32 alpha alpha)) 1)
(log.f32 (*.f32 alpha alpha))
(/.f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) 2)
(log.f32 (*.f32 alpha alpha))
(/.f32 (.f32 2 (.f32 (log.f32 (*.f32 alpha alpha)) 2)) 4)
(log.f32 (*.f32 alpha alpha))
(/.f32 (+.f32 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2))) 8)
(log.f32 (*.f32 alpha alpha))
(pow.f32 (log.f32 (*.f32 alpha alpha)) 1)
(log.f32 (*.f32 alpha alpha))

localize219.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.2b	(.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)
✓	0.3b	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

Compiler

Compiled 88 to 36 computations (59.1% saved)

series3.0ms (0%)

Counts

2 → 36

Calls

9 calls:

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

rewrite410.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

704×	`rational_best-simplify-65`
560×	`rational_best-simplify-49`
550×	`rational_best-simplify-53`
484×	`rational_best-simplify-67`
478×	`rational_best-simplify-54`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	99	56
2	259	56
3	1027	56
4	6555	56

Stop Event

1×	node limit

Counts

2 → 124

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) 2) (/.f32 (.f32 3/2 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)))))) 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Outputs

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simplify442.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1340×	`rational_best-simplify-47`
1264×	`rational_best-simplify-1`
1098×	`rational_best-simplify-67`
742×	`rational_best-simplify-66`
688×	`rational_best-simplify-108`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	340	6850
1	1007	6416
2	3904	6254

Stop Event

1×	node limit

Counts

160 → 190

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(*.f32 -1 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 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 0)
(+.f32 0 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(+.f32 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(+.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(+.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(+.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 0))
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(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) 2) (/.f32 (.f32 3/2 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha)))) 2))
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(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) 4)))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 0)
(-.f32 0 (neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(-.f32 0 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (-.f32 1 (.f32 alpha alpha))))
(-.f32 0 (+.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (-.f32 1 (.f32 alpha alpha))) 0))
(-.f32 0 (+.f32 (neg.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (neg.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (neg.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha)))) 0))
(-.f32 (/.f32 (/.f32 -1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (+.f32 (neg.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha)))) 0) 0))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))) 2))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (neg.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (.f32 (log.f32 (*.f32 alpha alpha)) 2)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))) 2) 0))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (neg.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (.f32 (log.f32 (*.f32 alpha alpha)) 2)) 0))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (log.f32 (.f32 alpha alpha))) (PI.f32)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(-.f32 (.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) 2) (+.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha)))))
(-.f32 (.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) 2) (+.f32 (+.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (*.f32 alpha alpha)))) 0))
(-.f32 (.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) 2) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (-.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 1 (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 0))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (-.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))) 0))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (+.f32 1 (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) 0))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (neg.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (.f32 (neg.f32 alpha) alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (neg.f32 (/.f32 (.f32 alpha alpha) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
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(.f32 (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(.f32 (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)))
(.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) 2))
(.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) 2)))
(.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4))
(.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (-.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (.f32 (+.f32 (*.f32 alpha alpha) -1) 4)))
(.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (log.f32 (.f32 alpha alpha))) (/.f32 1 (.f32 (PI.f32) 2)))
(.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (log.f32 (.f32 alpha alpha))) (-.f32 (/.f32 1 (PI.f32)) (/.f32 1 (.f32 (PI.f32) 2))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (/.f32 1 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (-.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (/.f32 1 (.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 1 (.f32 2 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4))))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (/.f32 1 (.f32 2 (.f32 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) 4)))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 1 (/.f32 1 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (/.f32 1 (log.f32 (*.f32 alpha alpha)))))
(.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 1 (/.f32 2 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (/.f32 (PI.f32) 2)) (/.f32 1 (/.f32 (/.f32 1 (PI.f32)) 1/2)))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1/4)
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) -1)) (/.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) (/.f32 (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (/.f32 (/.f32 1 (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 1 (PI.f32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (log.f32 (.f32 alpha alpha))) (PI.f32))) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 2)) (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(.f32 (+.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (.f32 1 (+.f32 (/.f32 (*.f32 alpha alpha) 2) -1/2)))
(.f32 (+.f32 (/.f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) (log.f32 (.f32 alpha alpha))) -1) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(pow.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 1)
(neg.f32 (neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(neg.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (-.f32 1 (.f32 alpha alpha))))
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 2))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta)) 2)
(/.f32 (.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta) 4)
(/.f32 (+.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta) (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta)) 8)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32))
(-.f32 (.f32 1/2 (/.f32 (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 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1 (PI.f32)) (log.f32 alpha))))
(*.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)) (+.f32 (pow.f32 alpha 2) -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 1/2 (-.f32 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1 (PI.f32)) (log.f32 alpha))))
(*.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)) (+.f32 (pow.f32 alpha 2) -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 1/2 (-.f32 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32)) (/.f32 (/.f32 1 (PI.f32)) (log.f32 alpha))))
(*.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha)) (+.f32 (pow.f32 alpha 2) -1))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 1 alpha))) (PI.f32)))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
(*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 1 alpha))) (PI.f32))) (.f32 1/2 (/.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))))
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(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 1 alpha))) (PI.f32))) (.f32 1/2 (/.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(.f32 (pow.f32 alpha 2) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (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 (pow.f32 alpha 2) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (log.f32 (/.f32 -1 alpha))) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 -1 alpha))) (PI.f32))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 -1 alpha))))
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(+.f32 (.f32 (pow.f32 alpha 2) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (log.f32 (/.f32 -1 alpha))) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 -1 alpha))) (PI.f32))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 -1 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)))))
(+.f32 (.f32 (pow.f32 alpha 2) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (log.f32 (/.f32 -1 alpha))) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (*.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 alpha)))))
(+.f32 (*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 (/.f32 -1 alpha))) (PI.f32))) (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 -1 alpha))))
(*.f32 -1 cosTheta)
(neg.f32 cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 cosTheta (pow.f32 alpha 2))
(*.f32 (pow.f32 alpha 2) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 cosTheta (pow.f32 alpha 2))
(*.f32 (pow.f32 alpha 2) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
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(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 -1 cosTheta) (.f32 cosTheta (pow.f32 alpha 2)))
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
(+.f32 (.f32 -1 cosTheta) (.f32 (pow.f32 alpha 2) cosTheta))
(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(*.f32 (-.f32 (pow.f32 alpha 2) 1) cosTheta)
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(*.f32 cosTheta (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 0)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(+.f32 0 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
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(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
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(/.f32 (+.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (/.f32 -1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
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(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
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(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (-.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (/.f32 1 (.f32 2 (.f32 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) 4)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 1 (/.f32 1 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (/.f32 1 (PI.f32))))
(.f32 1 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (/.f32 1 (log.f32 (*.f32 alpha alpha)))))
(.f32 1 (/.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (log.f32 (.f32 alpha alpha)))))
(.f32 1 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (log.f32 (*.f32 alpha alpha)))))
(/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) 0) (log.f32 (.f32 alpha alpha)))
(.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 1 (/.f32 2 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha))) (/.f32 (PI.f32) 2)) (/.f32 1 (/.f32 (/.f32 1 (PI.f32)) 1/2)))
(.f32 1 (/.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (PI.f32) 2)) (/.f32 2 (PI.f32))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 1 (/.f32 2 (PI.f32))) (.f32 (PI.f32) (/.f32 (log.f32 (.f32 alpha alpha)) 2))))
(/.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (*.f32 (/.f32 (PI.f32) 2) (/.f32 2 (PI.f32))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1/4)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 alpha alpha) -1)) (/.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) (/.f32 (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (/.f32 (/.f32 1 (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 1 (PI.f32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (log.f32 (.f32 alpha alpha))) (PI.f32))) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 2)) (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) 2)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (+.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (.f32 1 (+.f32 (/.f32 (*.f32 alpha alpha) 2) -1/2)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(.f32 (+.f32 (/.f32 (.f32 (log.f32 (.f32 alpha alpha)) 2) (log.f32 (.f32 alpha alpha))) -1) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (+.f32 -1 (/.f32 (.f32 2 (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (log.f32 (.f32 alpha alpha))))
(.f32 (+.f32 -1 (.f32 alpha alpha)) (/.f32 (+.f32 -1 (/.f32 (.f32 2 (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(pow.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) 1)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(neg.f32 (neg.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha)))
(neg.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (-.f32 1 (.f32 alpha alpha))))
(neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (*.f32 alpha alpha))))
(neg.f32 (.f32 1 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) -1)
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 0)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 2))
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta)) 2)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta) 4)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (+.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta) (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta)) 8)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta) 1)
(.f32 cosTheta (+.f32 -1 (.f32 alpha alpha)))

localize350.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 85 to 35 computations (58.8% saved)

series4.0ms (0%)

Counts

3 → 48

Calls

12 calls:

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

rewrite388.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

924×	`rational_best-simplify-67`
696×	`rational_best-simplify-52`
686×	`rational_best-simplify-89`
682×	`rational_best-simplify-47`
616×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	83
1	112	83
2	326	83
3	1413	83

Stop Event

1×	node limit

Counts

3 → 332

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) (+.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) (/.f32 (neg.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) (*.f32 cosTheta cosTheta)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) (*.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (+.f32 cosTheta cosTheta)) (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta) (*.f32 2 (+.f32 cosTheta cosTheta))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (+.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)))))

simplify689.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1132×	`rational_best-simplify-53`
1114×	`rational_best-simplify-49`
848×	`rational_best-simplify-65`
726×	`rational_best-simplify-55`
662×	`rational_best-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	790	19318
1	2315	17384

Stop Event

1×	node limit

Counts

380 → 496

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(/.f32 -1 (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (pow.f32 alpha 2) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (pow.f32 alpha 2) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(*.f32 -1 (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 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 0)
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (log.f32 (.f32 alpha alpha))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 0 (PI.f32)))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (neg.f32 (/.f32 0 (PI.f32))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (/.f32 0 (PI.f32))))
(+.f32 0 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(+.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(+.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(+.f32 (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 (.f32 alpha alpha)))))
(+.f32 (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2))) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 0 (PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 2) (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 2) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 2) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (/.f32 0 (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 2) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(+.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))))
(+.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(+.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)))
(+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
(+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 2))
(+.f32 (/.f32 (.f32 alpha (/.f32 alpha (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (+.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 2)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 0)
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (log.f32 (.f32 alpha alpha))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 0 (PI.f32)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (neg.f32 (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))))
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(-.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (+.f32 (neg.f32 (/.f32 -1 (PI.f32))) (neg.f32 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (/.f32 (/.f32 1 (PI.f32)) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (/.f32 (neg.f32 (/.f32 -1 (PI.f32))) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (/.f32 (/.f32 2 (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 -1 (PI.f32)) (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32))))
(-.f32 (/.f32 -1 (PI.f32)) (+.f32 (/.f32 0 (PI.f32)) (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)))))
(-.f32 (/.f32 -1 (PI.f32)) (+.f32 (neg.f32 (/.f32 0 (PI.f32))) (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)))))
(-.f32 (/.f32 -1 (PI.f32)) (+.f32 (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32))) 0))
(-.f32 (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32))) (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)))
(-.f32 (/.f32 0 (PI.f32)) (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) 2)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) 2)) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (+.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)) (/.f32 0 (PI.f32))) 2))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (+.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)) (/.f32 0 (PI.f32))) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (.f32 -2 (+.f32 (.f32 alpha alpha) -1)) (*.f32 (PI.f32) 4)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (.f32 -2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (/.f32 (*.f32 (PI.f32) 4) (PI.f32))))
(-.f32 (/.f32 (.f32 alpha (+.f32 alpha alpha)) (PI.f32)) (+.f32 (/.f32 1 (PI.f32)) (/.f32 (.f32 alpha alpha) (PI.f32))))
(-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 2)) (/.f32 1/2 (PI.f32))))
(-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (-.f32 (/.f32 1 (PI.f32)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))))
(-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 (+.f32 1 (-.f32 1 (.f32 alpha alpha))) (*.f32 (PI.f32) 2)))
(-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 1 (PI.f32))) 2))
(-.f32 (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (PI.f32)) 2) (/.f32 1/2 (PI.f32)))
(-.f32 (+.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 -1 (PI.f32))) (-.f32 0 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))))
(-.f32 (-.f32 (/.f32 -1 (PI.f32)) (/.f32 0 (PI.f32))) (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32))))
(-.f32 (-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 2))) (/.f32 1/2 (PI.f32)))
(-.f32 (-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 1 (PI.f32))) (-.f32 0 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))))
(-.f32 (-.f32 (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2)) (/.f32 1 (PI.f32))) (-.f32 (/.f32 0 (PI.f32)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))))
(-.f32 (/.f32 (/.f32 -1 (PI.f32)) (/.f32 (PI.f32) (PI.f32))) (/.f32 (neg.f32 (/.f32 (*.f32 alpha alpha) (PI.f32))) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) 2)) (/.f32 (PI.f32) (PI.f32))) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) 2)))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) (.f32 (PI.f32) 2)) 2) (/.f32 (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 2)) 2))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) 2)) 2) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 2)) 2))
(-.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (+.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 1 (PI.f32))) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 1 (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) 4)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 4)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) (.f32 (PI.f32) 4)) (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 4)))
(-.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32))) 4) (/.f32 (.f32 -2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) 4))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (PI.f32)) 4) (/.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)) 4))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (PI.f32)) (/.f32 (.f32 (PI.f32) 4) (PI.f32))) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (*.f32 (PI.f32) 4) (PI.f32))))
(.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (PI.f32)))
(.f32 (PI.f32) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (PI.f32)))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 1)
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (/.f32 1 (/.f32 (PI.f32) (PI.f32))))
(.f32 1 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (/.f32 1/2 (PI.f32)))
(.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) 1/2)
(.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) (/.f32 1 (+.f32 2 (/.f32 0 (PI.f32)))))
(.f32 2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (PI.f32) 2)))
(.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (/.f32 1 (.f32 (PI.f32) 4)))
(.f32 (/.f32 1 (PI.f32)) (+.f32 (.f32 alpha alpha) -1))
(.f32 (/.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) (PI.f32)) 1/4)
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (/.f32 1 (/.f32 (.f32 (PI.f32) 4) (PI.f32))))
(.f32 1/2 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))))
(.f32 (/.f32 1/2 (PI.f32)) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(.f32 (/.f32 1 (.f32 (PI.f32) 4)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 1 (.f32 2 (.f32 (PI.f32) 4))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) (PI.f32)) (/.f32 1 (/.f32 2 (PI.f32))))
(.f32 (.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) -1)) (/.f32 (/.f32 1 (PI.f32)) (PI.f32)))
(.f32 (.f32 (PI.f32) (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) (/.f32 (/.f32 1/2 (PI.f32)) (PI.f32)))
(.f32 (.f32 (PI.f32) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (*.f32 (PI.f32) 4)) (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32))) (/.f32 1 (PI.f32)))
(.f32 (.f32 (PI.f32) (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)))) (/.f32 1/2 (PI.f32)))
(.f32 (+.f32 (/.f32 1 (PI.f32)) (/.f32 1 (PI.f32))) (.f32 1 (-.f32 (/.f32 (*.f32 alpha alpha) 2) 1/2)))
(pow.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) 1)
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) 0))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) 2))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)
(/.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta))) 2)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 cosTheta cosTheta)) 4)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta)) 16)
(/.f32 (.f32 (.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(/.f32 (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta) (*.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 4)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)

Outputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32))) (.f32 1/2 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32))))
(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.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 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32))) (.f32 1/2 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32))))
(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.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 (/.f32 (pow.f32 alpha 2) (log.f32 alpha)) (PI.f32))) (.f32 1/2 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32))))
(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.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 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
(*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (/.f32 1/2 (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 (PI.f32) (log.f32 (/.f32 1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (/.f32 1/2 (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 (PI.f32) (log.f32 (/.f32 1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (/.f32 1/2 (PI.f32))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(*.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 -1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 -1 alpha)))) (.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 -1 alpha)))) (.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 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)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))) (.f32 1/2 (/.f32 1 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))))
(+.f32 (.f32 -1/2 (/.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (log.f32 (/.f32 -1 alpha)))) (.f32 1/2 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (/.f32 -1 alpha)))))
(/.f32 -1 (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(/.f32 (pow.f32 alpha 2) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(/.f32 (pow.f32 alpha 2) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(-.f32 (/.f32 (pow.f32 alpha 2) (PI.f32)) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 (pow.f32 alpha 2) -1) (PI.f32))
(*.f32 -1 (pow.f32 cosTheta 2))
(neg.f32 (pow.f32 cosTheta 2))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (pow.f32 (.f32 cosTheta alpha) 2))
(*.f32 (pow.f32 cosTheta 2) (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (pow.f32 (.f32 cosTheta alpha) 2))
(*.f32 (pow.f32 cosTheta 2) (+.f32 (pow.f32 alpha 2) -1))
(+.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 2)) (.f32 -1 (pow.f32 cosTheta 2)))
(+.f32 (.f32 -1 (pow.f32 cosTheta 2)) (pow.f32 (.f32 cosTheta alpha) 2))
(*.f32 (pow.f32 cosTheta 2) (+.f32 (pow.f32 alpha 2) -1))
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(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) 2))
(-.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) (.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))))
(/.f32 (-.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) 2)) (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 2))) 2)
(/.f32 (+.f32 (-.f32 (+.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 alpha (+.f32 alpha alpha))) (neg.f32 (.f32 alpha alpha))) -3) (.f32 (PI.f32) 4))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 2)) (+.f32 2 (/.f32 0 (PI.f32)))))
(/.f32 (-.f32 (/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (.f32 (PI.f32) 2)) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) 2)) 2)
(/.f32 (-.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) 4))
(-.f32 (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))) (/.f32 (/.f32 1 (PI.f32)) (+.f32 2 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) 2) (PI.f32)) (/.f32 1/2 (PI.f32)))
(/.f32 (-.f32 (+.f32 -1/2 (/.f32 (*.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (PI.f32) 4)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (*.f32 (PI.f32) 4)))
(/.f32 (-.f32 (/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (.f32 (PI.f32) 2)) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) 2)) 2)
(/.f32 (-.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) 4))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) (.f32 (PI.f32) 4)) (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 4)))
(/.f32 (-.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) 2)) (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 2))) 2)
(/.f32 (+.f32 (-.f32 (+.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 alpha (+.f32 alpha alpha))) (neg.f32 (.f32 alpha alpha))) -3) (.f32 (PI.f32) 4))
(-.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32))) 4) (/.f32 (.f32 -2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) 4))
(/.f32 (-.f32 (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32))) (.f32 (+.f32 -1 (.f32 alpha alpha)) (/.f32 -2 (PI.f32)))) 4)
(/.f32 (.f32 -2 (-.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32)))) 4)
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (PI.f32)) 4) (/.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32)) 4))
(/.f32 (-.f32 (/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (.f32 (PI.f32) 2)) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) 2)) 2)
(/.f32 (-.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) 4))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (PI.f32)) (/.f32 (.f32 (PI.f32) 4) (PI.f32))) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (*.f32 (PI.f32) 4) (PI.f32))))
(/.f32 (-.f32 (/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (PI.f32)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32))) (/.f32 (.f32 (PI.f32) 4) (PI.f32)))
(/.f32 (-.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3) (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) (/.f32 (*.f32 (PI.f32) 4) (PI.f32))))
(.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (PI.f32) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 1)
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (/.f32 1 (/.f32 (PI.f32) (PI.f32))))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 1 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (/.f32 1/2 (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) 1/2)
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) (/.f32 1 (+.f32 2 (/.f32 0 (PI.f32)))))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (PI.f32) 2)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (/.f32 1 (.f32 (PI.f32) 4)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 1 (PI.f32)) (+.f32 (.f32 alpha alpha) -1))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) (PI.f32)) 1/4)
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (/.f32 1 (/.f32 (.f32 (PI.f32) 4) (PI.f32))))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 1/2 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 1/2 (PI.f32)) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 1 (.f32 (PI.f32) 4)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 1 (.f32 2 (.f32 (PI.f32) 4))))
(.f32 (.f32 2 (.f32 (+.f32 -1 (.f32 alpha alpha)) 4)) (/.f32 1/2 (*.f32 (PI.f32) 4)))
(.f32 (/.f32 1/8 (PI.f32)) (.f32 (+.f32 -1 (*.f32 alpha alpha)) 8))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) (PI.f32)) (/.f32 1 (/.f32 2 (PI.f32))))
(.f32 1 (/.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) (PI.f32)) (/.f32 2 (PI.f32))))
(.f32 1 (-.f32 (/.f32 (.f32 -2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (PI.f32))) 2) 0))
(.f32 (.f32 (PI.f32) (+.f32 (*.f32 alpha alpha) -1)) (/.f32 (/.f32 1 (PI.f32)) (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 (PI.f32) (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) (/.f32 (/.f32 1/2 (PI.f32)) (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 (PI.f32) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (*.f32 (PI.f32) 4)) (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 (PI.f32) (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32))) (/.f32 1 (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (.f32 (PI.f32) (.f32 -2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)))) (/.f32 1/2 (PI.f32)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(.f32 (+.f32 (/.f32 1 (PI.f32)) (/.f32 1 (PI.f32))) (.f32 1 (-.f32 (/.f32 (*.f32 alpha alpha) 2) 1/2)))
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(pow.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) 1)
(/.f32 (+.f32 -1 (*.f32 alpha alpha)) (PI.f32))
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) 0))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) 2))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 cosTheta cosTheta))) 2)
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 cosTheta cosTheta)) 4)
(/.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (+.f32 -1 (.f32 alpha alpha)) 4))) 4)
(/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 4 (.f32 cosTheta cosTheta))) 4)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 -1 (.f32 alpha alpha)) 4))) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 8 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) cosTheta)) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 2 (.f32 cosTheta (.f32 (+.f32 -1 (*.f32 alpha alpha)) 4)))) 16)
(/.f32 (.f32 cosTheta (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 -1 (.f32 alpha alpha)) 8))) 16)
(/.f32 (.f32 (.f32 (+.f32 cosTheta cosTheta) (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 -1 (.f32 alpha alpha)) 4))) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 8 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) 16)
(/.f32 (.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) cosTheta) (*.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 (+.f32 cosTheta cosTheta) (.f32 2 (.f32 cosTheta (.f32 (+.f32 -1 (*.f32 alpha alpha)) 4)))) 16)
(/.f32 (.f32 cosTheta (.f32 (+.f32 cosTheta cosTheta) (.f32 (+.f32 -1 (.f32 alpha alpha)) 8))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)) 4)
(/.f32 (.f32 cosTheta (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 2 (+.f32 cosTheta cosTheta)))) 4)
(/.f32 (.f32 2 (.f32 cosTheta (.f32 (+.f32 -1 (.f32 alpha alpha)) (+.f32 cosTheta cosTheta)))) 4)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))

eval3.4s (4.5%)

Compiler: Compiled 47104 to 23382 computations (50.4% saved)

prune1.7s (2.2%)

Pruning

31 alts after pruning (29 fresh and 2 done)

	Pruned	Kept	Total
New	1136	29	1165
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	1137	31	1168

Error

Counts

1168 → 31

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
✓	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (-.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) 2) (/.f32 1/2 (PI.f32))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.5b	(/.f32 (/.f32 (-.f32 (+.f32 -1 (+.f32 (.f32 2 (.f32 alpha alpha)) (.f32 alpha alpha))) (+.f32 3 (neg.f32 (.f32 alpha alpha)))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.5b	(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) 2)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (log.f32 (.f32 alpha alpha)))) (/.f32 -1/2 (log.f32 (.f32 alpha alpha)))) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.7b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
▶	0.4b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 (.f32 2 (.f32 alpha alpha)) (+.f32 -2 (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
▶	10.6b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (-.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (-.f32 (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (neg.f32 (/.f32 (.f32 alpha alpha) (PI.f32))) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
✓	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))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	0.5b	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
	0.6b	(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	0.5b	(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) -2) (.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
▶	0.6b	(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	2.2b	(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
	0.6b	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (PI.f32)))
▶	0.6b	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1 (log.f32 (.f32 alpha alpha))))

Compiler

Compiled 1784 to 1160 computations (35% saved)

localize532.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))
	0.2b	(.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)
✓	0.3b	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
✓	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

Compiler

Compiled 89 to 36 computations (59.6% saved)

series44.0ms (0.1%)

Counts

3 → 48

Calls

12 calls:

Time	Variable		Point	Expression
17.0ms	alpha	@	0	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
7.0ms	alpha	@	inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))))
1.0ms	alpha	@	-inf	(pow.f32 (*.f32 alpha alpha) (PI.f32))
1.0ms	alpha	@	0	(pow.f32 (*.f32 alpha alpha) (PI.f32))
1.0ms	alpha	@	inf	(pow.f32 (*.f32 alpha alpha) (PI.f32))

rewrite421.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1734×	`rational_best-4`
1734×	`rational_best-2`
1734×	`rational_best-3`
1734×	`rational_best-1`
1734×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	77
1	105	77
2	249	77
3	815	77
4	4148	77

Stop Event

1×	node limit

Counts

3 → 173

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 2) (/.f32 (neg.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta (*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 cosTheta (*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4))) (*.f32 cosTheta (*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4)))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (+.f32 cosTheta cosTheta)) (*.f32 cosTheta (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) (*.f32 cosTheta (*.f32 2 (+.f32 cosTheta cosTheta)))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)))))

simplify396.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1080×	`rational_best-simplify-1`
992×	`rational_best-simplify-63`
818×	`rational_best-simplify-108`
630×	`rational_best-simplify-3`
538×	`rational_best-simplify-57`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	402	8367
1	1144	7841
2	4415	7739

Stop Event

1×	node limit

Counts

221 → 243

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) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(*.f32 (-.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 (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 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 0)
(+.f32 0 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(+.f32 (/.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2) (/.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2))
(+.f32 (fabs.f32 (/.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2)) (fabs.f32 (/.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2)))
(-.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 0)
(-.f32 (/.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2) (/.f32 (neg.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) 2))
(.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 1)
(.f32 1 (pow.f32 (.f32 alpha alpha) (PI.f32)))
(*.f32 (pow.f32 alpha (PI.f32)) (pow.f32 alpha (PI.f32)))
(.f32 (.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 2) 1/2)
(.f32 1/2 (.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 2))
(.f32 (.f32 (pow.f32 alpha (PI.f32)) 2) (/.f32 (pow.f32 alpha (PI.f32)) 2))
(.f32 (.f32 2 (.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2)) 1/4)
(*.f32 (neg.f32 (pow.f32 alpha (PI.f32))) (neg.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (fabs.f32 (pow.f32 alpha (PI.f32))) (fabs.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (pow.f32 (neg.f32 alpha) (PI.f32)) (pow.f32 (neg.f32 alpha) (PI.f32)))
(*.f32 (pow.f32 (fabs.f32 alpha) (PI.f32)) (pow.f32 (fabs.f32 alpha) (PI.f32)))
(.f32 1/4 (.f32 2 (.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2)))
(.f32 (/.f32 (pow.f32 alpha (PI.f32)) 2) (.f32 (pow.f32 alpha (PI.f32)) 2))
(*.f32 (fabs.f32 (pow.f32 (neg.f32 alpha) (PI.f32))) (fabs.f32 (pow.f32 (neg.f32 alpha) (PI.f32))))
(*.f32 (fabs.f32 (pow.f32 (fabs.f32 alpha) (PI.f32))) (fabs.f32 (pow.f32 (fabs.f32 alpha) (PI.f32))))
(.f32 (pow.f32 (.f32 alpha alpha) (/.f32 (PI.f32) 2)) (pow.f32 (*.f32 alpha alpha) (/.f32 (PI.f32) 2)))
(*.f32 (pow.f32 (+.f32 alpha alpha) (PI.f32)) (pow.f32 (/.f32 alpha 2) (PI.f32)))
(.f32 (pow.f32 1/2 (PI.f32)) (pow.f32 (.f32 alpha (+.f32 alpha alpha)) (PI.f32)))
(.f32 (pow.f32 (.f32 alpha (+.f32 alpha alpha)) (PI.f32)) (pow.f32 1/2 (PI.f32)))
(*.f32 (pow.f32 (/.f32 alpha 2) (PI.f32)) (pow.f32 (+.f32 alpha alpha) (PI.f32)))
(/.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 1)
(/.f32 (.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2) 2)
(/.f32 (.f32 2 (.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)) 2)) 4)
(/.f32 (+.f32 (.f32 2 (.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2)) (.f32 2 (.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)) 2))) 8)
(fabs.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32)))
(fabs.f32 (neg.f32 (pow.f32 (*.f32 alpha alpha) (PI.f32))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 0)
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (+.f32 1 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))))
(+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 0 (+.f32 2 (/.f32 0 (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))))
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Outputs
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 -2 (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
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(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1 (*.f32 (log.f32 alpha) (PI.f32)))))
(*.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 -1 (pow.f32 alpha 2)))
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(*.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 -1 (pow.f32 alpha 2)))
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(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(.f32 (+.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (+.f32 (/.f32 (.f32 alpha alpha) 2) -1/2))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(.f32 (/.f32 (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(.f32 (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) 4)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 (*.f32 alpha alpha) -1) 4)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(pow.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
(+.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(+.f32 0 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2))
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 0)
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)) 2) (/.f32 (neg.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) 2))
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2))) 2)
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))
(/.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) 4))) 4)
(/.f32 (.f32 cosTheta (.f32 4 (.f32 (+.f32 -1 (.f32 alpha alpha)) cosTheta))) 4)
(/.f32 (.f32 cosTheta (.f32 4 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))) (.f32 cosTheta 4)) 4)
(/.f32 (+.f32 (.f32 cosTheta (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) 4))) (.f32 cosTheta (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) 4)))) 8)
(/.f32 (.f32 cosTheta (.f32 4 (.f32 (+.f32 -1 (.f32 alpha alpha)) cosTheta))) 4)
(/.f32 (.f32 cosTheta (.f32 4 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))) (.f32 cosTheta 4)) 4)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) 4))) 16)
(/.f32 (.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 cosTheta (*.f32 2 (+.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 4 (.f32 4 (*.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 cosTheta (*.f32 2 (+.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 cosTheta (*.f32 2 (+.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 4 (.f32 4 (*.f32 cosTheta cosTheta)))) 16)
(pow.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)) 1)
(.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))
(.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))

localize254.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 69 to 30 computations (56.5% saved)

series66.0ms (0.1%)

Counts

3 → 28

Calls

9 calls:

Time	Variable		Point	Expression
34.0ms	alpha	@	-inf	(*.f32 (log.f32 alpha) (PI.f32))
20.0ms	alpha	@	inf	(*.f32 (log.f32 alpha) (PI.f32))
9.0ms	alpha	@	0	(*.f32 (log.f32 alpha) (PI.f32))
1.0ms	alpha	@	-inf	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
1.0ms	alpha	@	inf	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

rewrite416.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

736×	`rational_best-simplify-67`
726×	`rational_best-simplify-63`
688×	`rational_best-simplify-54`
684×	`rational_best-simplify-55`
672×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	45
1	89	45
2	183	45
3	500	45
4	1828	45

Stop Event

1×	node limit

Counts

3 → 202

Calls

Call 1

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

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha alpha) -1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (*.f32 alpha 1/2)) (-.f32 1 (*.f32 alpha (*.f32 alpha 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (*.f32 alpha 1/2)) (+.f32 (-.f32 1/2 (*.f32 alpha (*.f32 alpha 1/2))) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (*.f32 alpha 1/2)) (/.f32 (+.f32 1 (-.f32 1 (*.f32 alpha alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (*.f32 alpha 1/2)) (/.f32 (+.f32 (*.f32 alpha (neg.f32 alpha)) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1/2 (*.f32 alpha (*.f32 alpha 1/2))) (-.f32 1/2 (*.f32 alpha (*.f32 alpha 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1/2 (*.f32 alpha (*.f32 alpha 1/2))) (/.f32 (*.f32 -2 (+.f32 (*.f32 alpha alpha) -1)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1 (*.f32 alpha (*.f32 alpha 1/2))) (neg.f32 (*.f32 alpha (*.f32 alpha 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -2) 2) (neg.f32 (*.f32 alpha (*.f32 alpha 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (-.f32 (/.f32 (*.f32 alpha (*.f32 alpha 1/2)) 2) 1/4) (+.f32 -1/2 (*.f32 alpha (*.f32 alpha 1/2)))) (-.f32 0 (-.f32 (/.f32 (*.f32 alpha (*.f32 alpha 1/2)) 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (*.f32 alpha (*.f32 alpha 1/2)) (-.f32 1/2 (*.f32 alpha (*.f32 alpha 1/2)))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 (*.f32 alpha alpha) (+.f32 -1/2 (*.f32 alpha (*.f32 alpha 1/2)))) 2) (/.f32 (+.f32 3/2 (neg.f32 (*.f32 alpha (*.f32 alpha 1/2)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 3) 2) 2) (/.f32 (-.f32 1/2 (*.f32 alpha (*.f32 alpha 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 3) 4) (/.f32 (-.f32 1 (*.f32 alpha alpha)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 (*.f32 alpha alpha) (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha)))) 4) (/.f32 (+.f32 3 (*.f32 alpha (neg.f32 alpha))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (-.f32 (/.f32 (*.f32 alpha (*.f32 alpha 1/2)) 2) 1/4) (*.f32 alpha (*.f32 alpha 1/2))) (-.f32 1/2 (-.f32 (/.f32 (*.f32 alpha (*.f32 alpha 1/2)) 2) 1/4)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 (*.f32 alpha alpha) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/4 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) 1/8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))))

simplify542.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1428×	`rational_best-simplify-65`
1314×	`rational_best-simplify-63`
954×	`rational_best-simplify-108`
686×	`rational_best-simplify-47`
532×	`rational_best-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	496	7328
1	1395	6038
2	4624	5740

Stop Event

1×	node limit

Counts

230 → 284

Calls

Call 1

Inputs
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
-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 (log.f32 (pow.f32 alpha (PI.f32))) 0)
(+.f32 0 (log.f32 (pow.f32 alpha (PI.f32))))
(+.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)))
(+.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) 4) (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 3)) 4))
(+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 3)) 4) (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) 4))
(+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 3)) 4) (+.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) 4) 0))
(+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2))))
(+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (-.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2)))
(-.f32 (log.f32 (pow.f32 alpha (PI.f32))) 0)
(-.f32 (log.f32 (pow.f32 alpha (PI.f32))) (/.f32 (*.f32 (log.f32 (pow.f32 alpha (PI.f32))) 0) 2))
(-.f32 0 (neg.f32 (log.f32 (pow.f32 alpha (PI.f32)))))
(-.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2))
(-.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) (/.f32 (*.f32 (log.f32 (pow.f32 alpha (PI.f32))) -4) 8))
(-.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) 4) (/.f32 (*.f32 (log.f32 (pow.f32 alpha (PI.f32))) -3) 4))
(-.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 3)) 4) (/.f32 (neg.f32 (log.f32 (pow.f32 alpha (PI.f32)))) 4))
(-.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (+.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) (/.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) 2)))
(-.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (/.f32 (.f32 -3 (.f32 (log.f32 alpha) (*.f32 (PI.f32) 1/2))) 2))
(-.f32 (+.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2))) (/.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) 2))
(-.f32 (-.f32 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 1/2)) 2) (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2)) (/.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) 2))
(-.f32 (/.f32 (.f32 3 (.f32 (log.f32 alpha) (*.f32 (PI.f32) 1/2))) 2) (/.f32 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) 2))
(-.f32 (/.f32 (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) 3) 8) (/.f32 (.f32 (log.f32 (pow.f32 alpha (PI.f32))) -2) 8))
(-.f32 (/.f32 (.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) 5/2) 8) (/.f32 (.f32 (log.f32 (pow.f32 alpha (PI.f32))) -3) 8))
(/.f32 (log.f32 (pow.f32 alpha (PI.f32))) 1)
(/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) 2)
(/.f32 (neg.f32 (log.f32 (pow.f32 alpha (PI.f32)))) -1)
(/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 4)) 4)
(/.f32 (.f32 (log.f32 alpha) (.f32 2 (*.f32 (PI.f32) 4))) 8)
(/.f32 (.f32 (.f32 (PI.f32) 4) (*.f32 (log.f32 alpha) 4)) 16)
(/.f32 (.f32 (.f32 2 (.f32 (log.f32 alpha) 4)) (.f32 2 (*.f32 (PI.f32) 4))) 64)
(/.f32 (.f32 (.f32 2 (.f32 (PI.f32) 4)) (.f32 2 (*.f32 (log.f32 alpha) 4))) 64)
(/.f32 (.f32 (.f32 (log.f32 alpha) 2) (.f32 2 (.f32 (PI.f32) 4))) 16)
(/.f32 (.f32 (.f32 (PI.f32) 2) (.f32 2 (.f32 (log.f32 alpha) 4))) 16)
(pow.f32 (log.f32 (pow.f32 alpha (PI.f32))) 1)
(neg.f32 (neg.f32 (log.f32 (pow.f32 alpha (PI.f32)))))
(log.f32 (pow.f32 alpha (PI.f32)))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) 0)
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (PI.f32)))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (neg.f32 (/.f32 0 (PI.f32))))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (log.f32 alpha)))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) 0))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) (/.f32 0 (PI.f32))))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 alpha))))
(+.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) (/.f32 0 (log.f32 alpha))))
(+.f32 0 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(+.f32 (/.f32 0 (PI.f32)) (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(+.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))
(+.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (+.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 0 (log.f32 alpha))))
(+.f32 (/.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2) (+.f32 (/.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2) (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))))
(+.f32 (/.f32 0 (log.f32 alpha)) (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) 0)
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (PI.f32)))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (neg.f32 (/.f32 0 (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (log.f32 alpha)))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) 0))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 alpha))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) (/.f32 0 (log.f32 alpha))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (PI.f32)) (neg.f32 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (neg.f32 (/.f32 0 (PI.f32))) 0))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (neg.f32 (/.f32 0 (PI.f32))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (neg.f32 (/.f32 0 (PI.f32))) (neg.f32 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (neg.f32 (/.f32 0 (PI.f32))) (/.f32 0 (log.f32 alpha))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 (/.f32 0 (log.f32 alpha)) (neg.f32 (/.f32 0 (PI.f32)))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (/.f32 0 (PI.f32)) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (neg.f32 (/.f32 0 (PI.f32))) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (/.f32 0 (log.f32 alpha)) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (/.f32 (*.f32 (PI.f32) 2) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (/.f32 0 (PI.f32)) (/.f32 (*.f32 (PI.f32) 2) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (/.f32 (.f32 (log.f32 alpha) (.f32 (PI.f32) 2)) (PI.f32))))
(-.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (/.f32 (*.f32 (PI.f32) 4) (PI.f32))))
(-.f32 0 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (+.f32 (/.f32 0 (log.f32 alpha)) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (+.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (+.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 0 (PI.f32))) 2))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (neg.f32 (/.f32 -1/2 (PI.f32))) (*.f32 (log.f32 alpha) 2)))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (neg.f32 (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32))))) 4))
(-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (neg.f32 (/.f32 -1 (log.f32 alpha))) (*.f32 (PI.f32) 4)))
(-.f32 (neg.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))))
(-.f32 (+.f32 (/.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2) (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) (-.f32 (/.f32 0 (PI.f32)) (/.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2)))
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(-.f32 (-.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (neg.f32 (/.f32 0 (PI.f32)))) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))))
(-.f32 (/.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) (/.f32 (PI.f32) (PI.f32))) (/.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) (/.f32 (PI.f32) (PI.f32))))
(-.f32 (/.f32 (/.f32 -3/4 (log.f32 (pow.f32 alpha (PI.f32)))) 2) (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 (log.f32 alpha) 4)))
(-.f32 (/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (.f32 (PI.f32) 2) (PI.f32))) (/.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 (.f32 (PI.f32) 2) (PI.f32))))
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(*.f32 (PI.f32) (/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)))
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(*.f32 (/.f32 -1/2 (PI.f32)) (/.f32 1 (log.f32 alpha)))
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(*.f32 (/.f32 -1/2 (PI.f32)) (/.f32 1 (/.f32 (log.f32 (pow.f32 alpha (PI.f32))) (PI.f32))))
(*.f32 2 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))
(*.f32 (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))) 1/2)
(.f32 (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 1 (/.f32 (.f32 (PI.f32) 2) (PI.f32))))
(*.f32 -2 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))))
(*.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 1/2 (PI.f32)))
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(*.f32 (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32)))) -1/2)
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(*.f32 (/.f32 1/2 (PI.f32)) (/.f32 -1 (log.f32 alpha)))
(.f32 (/.f32 1/2 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) 1/2)))
(*.f32 (neg.f32 (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 -1 (PI.f32)))
(.f32 (/.f32 1/2 (log.f32 alpha)) (/.f32 -1/2 (.f32 (PI.f32) 1/2)))
(*.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))) -1)
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(*.f32 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))) 1/4)
(.f32 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))) (/.f32 1 (/.f32 (.f32 (PI.f32) 4) (PI.f32))))
(.f32 -4 (/.f32 (/.f32 1/2 (PI.f32)) (.f32 (log.f32 alpha) 4)))
(.f32 -4 (/.f32 (/.f32 1 (PI.f32)) (.f32 2 (*.f32 (log.f32 alpha) 4))))
(*.f32 (/.f32 -2 (log.f32 alpha)) (/.f32 (/.f32 1/2 (PI.f32)) 2))
(*.f32 (/.f32 -2 (log.f32 alpha)) (/.f32 (/.f32 1 (PI.f32)) 4))
(*.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2)
(.f32 (/.f32 -1/4 (PI.f32)) (/.f32 1 (.f32 (log.f32 alpha) 1/2)))
(*.f32 (/.f32 -1/4 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) 1/2))
(*.f32 (/.f32 -2 (PI.f32)) (-.f32 0 (/.f32 -1/4 (log.f32 alpha))))
(.f32 (/.f32 -2 (PI.f32)) (/.f32 1 (/.f32 (.f32 (log.f32 alpha) (*.f32 (PI.f32) 4)) (PI.f32))))
(*.f32 (/.f32 -1/4 (log.f32 alpha)) (/.f32 2 (PI.f32)))
(.f32 (/.f32 -1/4 (log.f32 alpha)) (/.f32 1 (.f32 (PI.f32) 1/2)))
(*.f32 1/4 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))))
(.f32 (/.f32 (/.f32 1/2 (PI.f32)) (.f32 (log.f32 alpha) 4)) -4)
(*.f32 (/.f32 (/.f32 1/2 (PI.f32)) 2) (/.f32 -2 (log.f32 alpha)))
(*.f32 (/.f32 -4 (log.f32 (pow.f32 alpha (PI.f32)))) 1/8)
(.f32 -8 (/.f32 1 (.f32 (.f32 (PI.f32) 4) (.f32 (log.f32 alpha) 4))))
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(*.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) -2)
(*.f32 (/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(*.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (PI.f32)) (/.f32 1 (/.f32 (log.f32 alpha) (PI.f32))))
(*.f32 (/.f32 (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 2 (PI.f32))))
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(*.f32 (/.f32 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 4 (PI.f32))))
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(.f32 (+.f32 (/.f32 1 (PI.f32)) (/.f32 1 (PI.f32))) (.f32 1 (/.f32 -1/4 (log.f32 alpha))))
(*.f32 (+.f32 (/.f32 1/2 (PI.f32)) (/.f32 1/2 (PI.f32))) (/.f32 -1/2 (log.f32 alpha)))
(.f32 (.f32 (PI.f32) (/.f32 -1/2 (log.f32 alpha))) (/.f32 (/.f32 1 (PI.f32)) (PI.f32)))
(.f32 (.f32 (PI.f32) -1/2) (/.f32 (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 -1 (log.f32 alpha))) (/.f32 (/.f32 1/2 (PI.f32)) (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 -2 (log.f32 alpha))) (/.f32 (/.f32 (/.f32 1/2 (PI.f32)) 2) (PI.f32)))
(.f32 (.f32 (PI.f32) -2) (/.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) (PI.f32)))
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(.f32 (.f32 (PI.f32) (/.f32 -1/2 (PI.f32))) (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32)))))
(.f32 (.f32 (PI.f32) (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 1/2 (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 -1 (PI.f32))) (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(.f32 (.f32 (PI.f32) (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 1/4 (PI.f32)))
(.f32 (.f32 (PI.f32) -4) (/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 (log.f32 alpha) 4)) (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 -1/2 (PI.f32)))
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(.f32 (.f32 (PI.f32) (/.f32 1 (PI.f32))) (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
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(.f32 (.f32 (PI.f32) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))) (/.f32 -2 (PI.f32)))
(.f32 (.f32 (PI.f32) (/.f32 1/2 (PI.f32))) (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))))
(pow.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) 1)
(neg.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(-.f32 (*.f32 alpha alpha) 1)
(-.f32 (+.f32 (*.f32 alpha alpha) -1) 0)
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (-.f32 1 (.f32 alpha (.f32 alpha 1/2))))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))) 1/2))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (/.f32 (+.f32 1 (-.f32 1 (*.f32 alpha alpha))) 2))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (/.f32 (+.f32 (*.f32 alpha (neg.f32 alpha)) 2) 2))
(-.f32 (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2))) (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))))
(-.f32 (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2))) (/.f32 (.f32 -2 (+.f32 (.f32 alpha alpha) -1)) 4))
(-.f32 (+.f32 -1 (.f32 alpha (.f32 alpha 1/2))) (neg.f32 (.f32 alpha (.f32 alpha 1/2))))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) 2) (neg.f32 (.f32 alpha (*.f32 alpha 1/2))))
(-.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) 2) 1/2)
(-.f32 (+.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4) (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2)))) (-.f32 0 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(-.f32 (-.f32 (.f32 alpha (.f32 alpha 1/2)) (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2)))) 1/2)
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2)))) 2) (/.f32 (+.f32 3/2 (neg.f32 (.f32 alpha (*.f32 alpha 1/2)))) 2))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) 2) 2) (/.f32 (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))) 2))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) 4) (/.f32 (-.f32 1 (*.f32 alpha alpha)) 4))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) 4) (/.f32 (+.f32 3 (*.f32 alpha (neg.f32 alpha))) 4))
(-.f32 (+.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4) (.f32 alpha (.f32 alpha 1/2))) (-.f32 1/2 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(.f32 (+.f32 (.f32 alpha alpha) -1) 1)
(.f32 1 (+.f32 (.f32 alpha alpha) -1))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 1/2)
(.f32 1/2 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 1/4)
(.f32 1/4 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 1/8)
(/.f32 (+.f32 (*.f32 alpha alpha) -1) 1)
(/.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 2)
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) 4)
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) 8)
(pow.f32 (+.f32 (*.f32 alpha alpha) -1) 1)

Outputs
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -1))
(*.f32 (PI.f32) (neg.f32 (log.f32 (/.f32 1 alpha))))
(*.f32 (log.f32 (/.f32 1 alpha)) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -1))
(*.f32 (PI.f32) (neg.f32 (log.f32 (/.f32 1 alpha))))
(*.f32 (log.f32 (/.f32 1 alpha)) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -1))
(*.f32 (PI.f32) (neg.f32 (log.f32 (/.f32 1 alpha))))
(*.f32 (log.f32 (/.f32 1 alpha)) (neg.f32 (PI.f32)))
(.f32 -1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -1))
(*.f32 (PI.f32) (neg.f32 (log.f32 (/.f32 1 alpha))))
(*.f32 (log.f32 (/.f32 1 alpha)) (neg.f32 (PI.f32)))
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(*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (PI.f32) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
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(*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
(.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32))
(.f32 (PI.f32) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))))
(*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
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(/.f32 -1/2 (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(/.f32 (/.f32 -1/2 (PI.f32)) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
(/.f32 -1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (PI.f32)))
(/.f32 -1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha))))))
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(/.f32 -1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha))))))
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(/.f32 -1/2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha))))))
(/.f32 -1/2 (*.f32 (PI.f32) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha))))))
(/.f32 (/.f32 -1/2 (PI.f32)) (+.f32 (log.f32 -1) (neg.f32 (log.f32 (/.f32 -1 alpha)))))
-1
(-.f32 (pow.f32 alpha 2) 1)
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(pow.f32 alpha 2)
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(-.f32 (pow.f32 alpha 2) 1)
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(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)) 2)
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (/.f32 -1/4 (PI.f32)) (/.f32 1 (.f32 (log.f32 alpha) 1/2)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1/4 (PI.f32)) (/.f32 (/.f32 1 (log.f32 alpha)) 1/2))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -2 (PI.f32)) (-.f32 0 (/.f32 -1/4 (log.f32 alpha))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (/.f32 -2 (PI.f32)) (/.f32 1 (/.f32 (.f32 (log.f32 alpha) (*.f32 (PI.f32) 4)) (PI.f32))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -1/4 (log.f32 alpha)) (/.f32 2 (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (/.f32 -1/4 (log.f32 alpha)) (/.f32 1 (.f32 (PI.f32) 1/2)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 1/4 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (/.f32 (/.f32 1/2 (PI.f32)) (.f32 (log.f32 alpha) 4)) -4)
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 (/.f32 1/2 (PI.f32)) 2) (/.f32 -2 (log.f32 alpha)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 -4 (log.f32 (pow.f32 alpha (PI.f32)))) 1/8)
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 -8 (/.f32 1 (.f32 (.f32 (PI.f32) 4) (.f32 (log.f32 alpha) 4))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 -8 (/.f32 1/2 (.f32 (log.f32 alpha) (.f32 2 (.f32 (PI.f32) 4)))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (/.f32 -4 (log.f32 alpha)) (/.f32 1/2 (.f32 (PI.f32) 4)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (/.f32 -4 (log.f32 alpha)) (/.f32 1 (.f32 2 (*.f32 (PI.f32) 4))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) -2)
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 1 (PI.f32))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(*.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (PI.f32)) (/.f32 1 (/.f32 (log.f32 alpha) (PI.f32))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 2 (PI.f32))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (/.f32 (/.f32 -1 (PI.f32)) (PI.f32)) (/.f32 1 (/.f32 (.f32 (log.f32 alpha) 2) (PI.f32))))
(.f32 1 (/.f32 (/.f32 -1 (.f32 (PI.f32) (PI.f32))) (/.f32 (*.f32 2 (log.f32 alpha)) (PI.f32))))
(.f32 1 (-.f32 (/.f32 (/.f32 -1 (PI.f32)) (.f32 2 (log.f32 alpha))) 0))
(/.f32 (/.f32 -1 (PI.f32)) (*.f32 2 (log.f32 alpha)))
(*.f32 (/.f32 (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)) (/.f32 1 (/.f32 4 (PI.f32))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (/.f32 -4 (PI.f32)) (/.f32 1 (/.f32 (.f32 (log.f32 alpha) (.f32 2 (.f32 (PI.f32) 4))) (PI.f32))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (+.f32 (/.f32 1 (PI.f32)) (/.f32 1 (PI.f32))) (.f32 1 (/.f32 -1/4 (log.f32 alpha))))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (+.f32 (/.f32 1/2 (PI.f32)) (/.f32 1/2 (PI.f32))) (/.f32 -1/2 (log.f32 alpha)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (/.f32 -1/2 (log.f32 alpha))) (/.f32 (/.f32 1 (PI.f32)) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) -1/2) (/.f32 (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32)))) (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 -1 (log.f32 alpha))) (/.f32 (/.f32 1/2 (PI.f32)) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (/.f32 -2 (log.f32 alpha))) (/.f32 (/.f32 (/.f32 1/2 (PI.f32)) 2) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) -2) (/.f32 (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha))) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 1 (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 -1/2 (PI.f32))) (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 1/2 (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 -1 (PI.f32))) (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 -2 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 1/4 (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) -4) (/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (*.f32 (log.f32 alpha) 4)) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (/.f32 1 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 -1/2 (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32))))) (/.f32 -1 (PI.f32)))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 1 (PI.f32))) (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(.f32 (.f32 (PI.f32) (/.f32 1 (log.f32 alpha))) (/.f32 (/.f32 -1/2 (PI.f32)) (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (neg.f32 (/.f32 (/.f32 -1/4 (PI.f32)) (log.f32 alpha)))) (/.f32 -2 (PI.f32)))
(/.f32 (+.f32 (/.f32 -1/4 (PI.f32)) (/.f32 -1/4 (PI.f32))) (log.f32 alpha))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(.f32 (.f32 (PI.f32) (/.f32 1/2 (PI.f32))) (/.f32 -1 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(pow.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) 1)
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(neg.f32 (/.f32 1/2 (log.f32 (pow.f32 alpha (PI.f32)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(-.f32 (*.f32 alpha alpha) 1)
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (+.f32 (*.f32 alpha alpha) -1) 0)
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (-.f32 1 (.f32 alpha (.f32 alpha 1/2))))
(-.f32 (.f32 1/2 (.f32 alpha alpha)) (-.f32 1 (.f32 1/2 (.f32 alpha alpha))))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))) 1/2))
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (/.f32 (+.f32 1 (-.f32 1 (*.f32 alpha alpha))) 2))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 1/2 (/.f32 (-.f32 1 (*.f32 alpha alpha)) 2)))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 1/2 (-.f32 1/2 (/.f32 (*.f32 alpha alpha) 2))))
(-.f32 (.f32 1/2 (.f32 alpha alpha)) (/.f32 (-.f32 2 (*.f32 alpha alpha)) 2))
(-.f32 (.f32 alpha (.f32 alpha 1/2)) (/.f32 (+.f32 (*.f32 alpha (neg.f32 alpha)) 2) 2))
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2))) (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))))
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2))) (/.f32 (.f32 -2 (+.f32 (.f32 alpha alpha) -1)) 4))
(-.f32 (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2))) (/.f32 (.f32 -2 (+.f32 -1 (.f32 alpha alpha))) 4))
(+.f32 (-.f32 (.f32 1/2 (.f32 alpha alpha)) (/.f32 (.f32 -2 (+.f32 -1 (.f32 alpha alpha))) 4)) -1/2)
(-.f32 (+.f32 -1 (.f32 alpha (.f32 alpha 1/2))) (neg.f32 (.f32 alpha (.f32 alpha 1/2))))
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) 2) (neg.f32 (.f32 alpha (*.f32 alpha 1/2))))
(-.f32 (/.f32 (+.f32 -2 (.f32 alpha alpha)) 2) (neg.f32 (.f32 alpha (*.f32 alpha 1/2))))
(-.f32 (+.f32 -1 (/.f32 (.f32 alpha alpha) 2)) (/.f32 (.f32 alpha alpha) -2))
(-.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) 2) 1/2)
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (+.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4) (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2)))) (-.f32 0 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4))) (neg.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) (-.f32 1/4 (+.f32 -1/2 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/4 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2))))))
(-.f32 (/.f32 (.f32 alpha alpha) 4) (-.f32 1/4 (+.f32 (.f32 1/2 (.f32 alpha alpha)) (+.f32 (/.f32 (.f32 alpha alpha) 4) -3/4))))
(-.f32 (-.f32 (.f32 alpha (.f32 alpha 1/2)) (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2)))) 1/2)
(+.f32 -1 (*.f32 alpha alpha))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1/2 (.f32 alpha (.f32 alpha 1/2)))) 2) (/.f32 (+.f32 3/2 (neg.f32 (.f32 alpha (*.f32 alpha 1/2)))) 2))
(/.f32 (-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (.f32 alpha alpha))) (+.f32 (neg.f32 (.f32 alpha (*.f32 alpha 1/2))) 3/2)) 2)
(/.f32 (+.f32 (-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (.f32 alpha alpha))) (neg.f32 (.f32 alpha (*.f32 alpha 1/2)))) -3/2) 2)
(+.f32 (/.f32 (-.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha)))) (.f32 alpha (neg.f32 alpha))) 4) -3/4)
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) 2) 2) (/.f32 (-.f32 1/2 (.f32 alpha (.f32 alpha 1/2))) 2))
(-.f32 (/.f32 (.f32 3 (+.f32 -1 (.f32 alpha alpha))) 4) (-.f32 1/4 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2)))
(-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) (-.f32 1/4 (/.f32 (.f32 3 (+.f32 -1 (.f32 alpha alpha))) 4)))
(/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 3 (+.f32 -1 (*.f32 alpha alpha))))) 4)
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) 4) (/.f32 (-.f32 1 (*.f32 alpha alpha)) 4))
(-.f32 (/.f32 (.f32 3 (+.f32 -1 (.f32 alpha alpha))) 4) (-.f32 1/4 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2)))
(-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) (-.f32 1/4 (/.f32 (.f32 3 (+.f32 -1 (.f32 alpha alpha))) 4)))
(/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 3 (+.f32 -1 (*.f32 alpha alpha))))) 4)
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) (+.f32 -1 (.f32 alpha (+.f32 alpha alpha)))) 4) (/.f32 (+.f32 3 (*.f32 alpha (neg.f32 alpha))) 4))
(/.f32 (-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (.f32 alpha alpha))) (+.f32 (neg.f32 (.f32 alpha (*.f32 alpha 1/2))) 3/2)) 2)
(/.f32 (+.f32 (-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (.f32 alpha alpha))) (neg.f32 (.f32 alpha (*.f32 alpha 1/2)))) -3/2) 2)
(+.f32 (/.f32 (-.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha)))) (.f32 alpha (neg.f32 alpha))) 4) -3/4)
(-.f32 (+.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4) (.f32 alpha (.f32 alpha 1/2))) (-.f32 1/2 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(-.f32 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/2 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4))) (neg.f32 (-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) 1/4)))
(-.f32 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2) (-.f32 1/4 (+.f32 -1/2 (+.f32 (.f32 alpha (.f32 alpha 1/2)) (+.f32 -1/4 (/.f32 (.f32 alpha (.f32 alpha 1/2)) 2))))))
(-.f32 (/.f32 (.f32 alpha alpha) 4) (-.f32 1/4 (+.f32 (.f32 1/2 (.f32 alpha alpha)) (+.f32 (/.f32 (.f32 alpha alpha) 4) -3/4))))
(.f32 (+.f32 (.f32 alpha alpha) -1) 1)
(+.f32 -1 (*.f32 alpha alpha))
(.f32 1 (+.f32 (.f32 alpha alpha) -1))
(+.f32 -1 (*.f32 alpha alpha))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 1/2)
(+.f32 -1 (*.f32 alpha alpha))
(.f32 1/2 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(+.f32 -1 (*.f32 alpha alpha))
(.f32 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 1/4)
(+.f32 -1 (*.f32 alpha alpha))
(.f32 1/4 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4))
(+.f32 -1 (*.f32 alpha alpha))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) 1/8)
(+.f32 -1 (*.f32 alpha alpha))
(/.f32 (+.f32 (*.f32 alpha alpha) -1) 1)
(+.f32 -1 (*.f32 alpha alpha))
(/.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 2)
(+.f32 -1 (*.f32 alpha alpha))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) 4)
(+.f32 -1 (*.f32 alpha alpha))
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 alpha alpha) -1) 4)) 8)
(+.f32 -1 (*.f32 alpha alpha))
(pow.f32 (+.f32 (*.f32 alpha alpha) -1) 1)
(+.f32 -1 (*.f32 alpha alpha))

localize446.0ms (0.6%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 110 to 49 computations (55.5% saved)

series24.0ms (0%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
14.0ms	alpha	@	-inf	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1 (log.f32 (.f32 alpha alpha))))
2.0ms	alpha	@	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32))
1.0ms	alpha	@	inf	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32))
1.0ms	cosTheta	@	0	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32))
1.0ms	cosTheta	@	inf	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32))

rewrite729.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

952×	`rational_best-4`
952×	`rational_best-2`
952×	`rational_best-3`
952×	`rational_best-1`
952×	`exponential-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	153
1	145	147
2	416	147
3	2092	147

Stop Event

1×	node limit

Counts

3 → 265

Calls

Call 1

Inputs

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

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

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

Outputs

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simplify1.8s (2.4%)

Algorithm

1×	egg-herbie

Rules

1400×	`rational_best-simplify-49`
1214×	`rational_best-simplify-54`
1194×	`rational_best-simplify-53`
1060×	`rational_best-simplify-55`
932×	`rational_best-simplify-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	819	35633
1	2677	33863

Stop Event

1×	node limit

Counts

325 → 571

Calls

Call 1

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

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

localize416.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(log.f32 (*.f32 alpha alpha))
	0.2b	(.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)
✓	0.3b	(.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (*.f32 alpha alpha)))
✓	0.5b	(/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha)))

Compiler

Compiled 118 to 56 computations (52.5% saved)

series4.0ms (0%)

Counts

2 → 24

Calls

6 calls:

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

rewrite668.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1910×	`rational_best-2`
1910×	`rational_best-3`
1910×	`rational_best-1`
1908×	`rational_best-4`
1908×	`exponential-1`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	68
1	92	62
2	230	62
3	846	62
4	4615	62

Stop Event

1×	node limit

Counts

2 → 196

Calls

Call 1

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

Outputs

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alpha alpha))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (/.f32 2 (PI.f32)) (log.f32 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (/.f32 (*.f32 (/.f32 4 (PI.f32)) (/.f32 (-.f32 1 (*.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) (/.f32 (/.f32 4 (PI.f32)) (log.f32 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (/.f32 (-.f32 1 (*.f32 alpha alpha)) (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1)))))

simplify511.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1174×	`rational_best-simplify-108`
954×	`rational_best-simplify-47`
770×	`rational_best-simplify-49`
730×	`rational_best-simplify-53`
612×	`rational_best-simplify-55`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	459	8908
1	1456	7626
2	6294	7582

Stop Event

1×	node limit

Counts

220 → 263

Calls

Call 1

Inputs
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.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)))))
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(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
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(+.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 (.f32 alpha alpha)))))
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(+.f32 (/.f32 0 (+.f32 (.f32 (PI.f32) 2) (/.f32 0 (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))) 0)
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(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))) (/.f32 0 (PI.f32)))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 (/.f32 0 (PI.f32)) 0))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 (.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (neg.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))) 0))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))) (/.f32 0 (log.f32 (*.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))) (/.f32 0 (PI.f32))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 (/.f32 0 (PI.f32)) (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha))) (neg.f32 (/.f32 0 (PI.f32))))
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(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 0 (log.f32 (.f32 alpha alpha))) (+.f32 1 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
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(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (+.f32 (PI.f32) (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (+.f32 2 (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 0 (+.f32 (.f32 (PI.f32) 2) (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (neg.f32 (/.f32 0 (log.f32 (.f32 alpha alpha)))) (+.f32 1 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 0 (neg.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha)))))
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(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (+.f32 (/.f32 0 (PI.f32)) (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (+.f32 (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32))) (/.f32 0 (log.f32 (*.f32 alpha alpha)))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (/.f32 (neg.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha)))) 2))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (/.f32 (neg.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (/.f32 (neg.f32 (/.f32 1 (log.f32 (.f32 alpha alpha)))) (*.f32 (PI.f32) 2)))
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(-.f32 (/.f32 (/.f32 3 (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2)))) (+.f32 2 (/.f32 0 (log.f32 (.f32 alpha alpha))))) (/.f32 (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32))) (+.f32 2 (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(-.f32 (/.f32 (/.f32 3 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 4)) (/.f32 (/.f32 -1 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 4)))
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(.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) 1)
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(.f32 2 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)))
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(.f32 (/.f32 (/.f32 4 (PI.f32)) (log.f32 (.f32 alpha alpha))) 1/4)
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(-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (+.f32 (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha))) (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)))))
(-.f32 (/.f32 (/.f32 0 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(-.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2)))) (/.f32 (neg.f32 (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2)))))
(-.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2)))) (/.f32 (neg.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 2))
(-.f32 (-.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32)) (/.f32 (.f32 alpha (/.f32 alpha (PI.f32))) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (PI.f32))))
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(-.f32 (-.f32 (/.f32 (/.f32 0 (PI.f32)) (log.f32 (.f32 alpha alpha))) (/.f32 (/.f32 0 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))))
(/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))
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(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
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(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (log.f32 (*.f32 alpha alpha)) 2)) (/.f32 (PI.f32) 2))
(/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 2) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2))))
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (log.f32 (.f32 alpha alpha))) 2)
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (log.f32 (.f32 alpha alpha))) (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (.f32 (log.f32 (*.f32 alpha alpha)) 2))
(/.f32 (/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 2) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) 2))
(/.f32 (/.f32 (-.f32 1/2 (/.f32 (.f32 alpha alpha) 2)) (PI.f32)) (/.f32 (log.f32 (.f32 alpha alpha)) 2))
(/.f32 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (pow.f32 (*.f32 alpha alpha) 2)))) 1/2)
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(/.f32 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 2 (PI.f32)) (log.f32 (*.f32 alpha alpha))))
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(pow.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1)

Outputs
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))
(/.f32 1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (*.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 -1 alpha)))
(/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 -1 alpha))))
(/.f32 (/.f32 -1/2 (PI.f32)) (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)))))
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(/.f32 (.f32 4 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))) (+.f32 0 (/.f32 (.f32 (log.f32 (.f32 alpha alpha)) 4) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2)) (PI.f32)) (.f32 (log.f32 (*.f32 alpha alpha)) 4))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (/.f32 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2)) (log.f32 (.f32 alpha alpha))) (*.f32 (PI.f32) 4))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) 2))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (PI.f32))) (neg.f32 (log.f32 (*.f32 alpha alpha))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 1 (PI.f32)) (log.f32 (*.f32 alpha alpha)))) -1)
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (neg.f32 (+.f32 1 (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (*.f32 alpha alpha)))) (neg.f32 (PI.f32)))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (.f32 alpha alpha)))) (neg.f32 (+.f32 (PI.f32) (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 2) (neg.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2)))))
(/.f32 (-.f32 (-.f32 1 (.f32 alpha alpha)) (neg.f32 (-.f32 1 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2))))
(/.f32 (.f32 -2 (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (pow.f32 (.f32 alpha alpha) 2))))
(+.f32 0 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (PI.f32))) (.f32 -2 (log.f32 (.f32 alpha alpha))))
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32))) (.f32 (log.f32 (.f32 alpha alpha)) -2))
(/.f32 (.f32 (/.f32 2 (PI.f32)) (+.f32 -1 (.f32 alpha alpha))) (.f32 (log.f32 (.f32 alpha alpha)) -2))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (neg.f32 (.f32 (PI.f32) (.f32 (log.f32 (*.f32 alpha alpha)) 4))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (log.f32 (.f32 alpha alpha)))) (.f32 -2 (PI.f32)))
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) -2))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (log.f32 (.f32 alpha alpha)))) (neg.f32 (+.f32 (.f32 (PI.f32) 2) (/.f32 0 (log.f32 (*.f32 alpha alpha))))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 2 (PI.f32)) (log.f32 (*.f32 alpha alpha)))) -2)
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 2 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (neg.f32 (+.f32 2 (/.f32 0 (log.f32 (.f32 alpha alpha))))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 4 (PI.f32))) (neg.f32 (.f32 (log.f32 (.f32 alpha alpha)) 4)))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 4 (log.f32 (.f32 alpha alpha)))) (neg.f32 (.f32 (PI.f32) 4)))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 4 (PI.f32)) (log.f32 (*.f32 alpha alpha)))) -4)
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 4 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (neg.f32 (/.f32 (+.f32 2 (/.f32 0 (log.f32 (.f32 alpha alpha)))) 1/2)))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 8 (PI.f32))) (neg.f32 (.f32 2 (.f32 (log.f32 (*.f32 alpha alpha)) 4))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 1 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))))) (neg.f32 (/.f32 1 (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))))) (neg.f32 (/.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))))) (neg.f32 (/.f32 (.f32 (PI.f32) 2) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (/.f32 2 (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))))) (neg.f32 (/.f32 2 (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (+.f32 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2)) (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2))) (+.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4)) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (+.f32 (.f32 (/.f32 4 (PI.f32)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))) (.f32 (/.f32 4 (PI.f32)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))))) 8)
(/.f32 (.f32 4 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 4 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (PI.f32))) 4)
(/.f32 (.f32 2 (/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 2) (log.f32 (.f32 alpha alpha)))) (*.f32 (PI.f32) 4))
(/.f32 (.f32 2 (/.f32 (.f32 2 (-.f32 1 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (*.f32 (PI.f32) 4))
(/.f32 (.f32 (/.f32 2 (log.f32 (.f32 alpha alpha))) (.f32 2 (-.f32 1 (.f32 alpha alpha)))) (*.f32 (PI.f32) 4))
(/.f32 (.f32 4 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2))) (.f32 (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4)) 4))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (.f32 2 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2))) (.f32 (log.f32 (.f32 alpha alpha)) 4))
(/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 2 (/.f32 (PI.f32) 2))) (.f32 (log.f32 (.f32 alpha alpha)) 4))
(/.f32 (.f32 (.f32 2 (.f32 (-.f32 1 (.f32 alpha alpha)) 2)) (/.f32 (/.f32 4 (PI.f32)) (log.f32 (*.f32 alpha alpha)))) 16)
(/.f32 (.f32 (/.f32 4 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 2 (.f32 2 (-.f32 1 (.f32 alpha alpha))))) 16)
(/.f32 (.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 4) (/.f32 (/.f32 8 (PI.f32)) (log.f32 (.f32 alpha alpha)))) 32)
(/.f32 (.f32 (/.f32 (/.f32 4 (PI.f32)) (log.f32 (.f32 alpha alpha))) (.f32 2 (.f32 (-.f32 1 (*.f32 alpha alpha)) 2))) 16)
(/.f32 (.f32 (/.f32 4 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 2 (.f32 2 (-.f32 1 (.f32 alpha alpha))))) 16)
(/.f32 (.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 4) (/.f32 (/.f32 8 (PI.f32)) (log.f32 (.f32 alpha alpha)))) 32)
(/.f32 (.f32 (/.f32 (.f32 (-.f32 1 (.f32 alpha alpha)) 2) (log.f32 (.f32 alpha alpha))) (/.f32 2 (PI.f32))) 4)
(/.f32 (.f32 2 (/.f32 (/.f32 (.f32 2 (-.f32 1 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))) (PI.f32))) 4)
(/.f32 (.f32 2 (/.f32 (.f32 2 (-.f32 1 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))) 4)
(/.f32 (.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (/.f32 2 (log.f32 (*.f32 alpha alpha)))) 4)
(/.f32 (.f32 4 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 4 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (PI.f32))) 4)
(/.f32 (.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (/.f32 4 (PI.f32))) 4)
(/.f32 (.f32 4 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 4 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (PI.f32))) 4)
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (PI.f32) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (log.f32 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (/.f32 (PI.f32) 2)) (log.f32 (.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 2 (PI.f32)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))
(/.f32 (/.f32 (.f32 (/.f32 4 (PI.f32)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 4 (PI.f32)) (log.f32 (.f32 alpha alpha))))
(/.f32 (.f32 4 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) 4)
(/.f32 (.f32 4 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))) (PI.f32))) 4)
(pow.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))) 1)
(/.f32 (+.f32 (.f32 (neg.f32 alpha) (/.f32 alpha (PI.f32))) (/.f32 1 (PI.f32))) (log.f32 (.f32 alpha alpha)))
(/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (PI.f32))

localize471.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 cosTheta (+.f32 -2 (.f32 2 (*.f32 alpha alpha))))
✓	0.2b	(+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1)
✓	0.3b	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
	3.1b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

Compiler

Compiled 133 to 69 computations (48.1% saved)

series295.0ms (0.4%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
265.0ms	cosTheta	@	inf	(.f32 cosTheta (+.f32 -2 (.f32 2 (*.f32 alpha alpha))))
8.0ms	cosTheta	@	0	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
5.0ms	alpha	@	0	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
5.0ms	alpha	@	inf	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
3.0ms	cosTheta	@	inf	(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))

rewrite331.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

904×	`rational_best-simplify-65`
654×	`rational_best-simplify-47`
638×	`rational_best-simplify-54`
572×	`rational_best-simplify-67`
562×	`rational_best-simplify-49`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	22	141
1	161	129
2	388	129
3	1331	129

Stop Event

1×	node limit

Counts

3 → 213

Calls

Call 1

Inputs

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

(+.f32 (+.f32 -1 (*.f32 2 (*.f32 alpha alpha))) -1)

(*.f32 cosTheta (+.f32 -2 (*.f32 2 (*.f32 alpha alpha))))

Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 2 (neg.f32 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (/.f32 (+.f32 4 (neg.f32 (*.f32 alpha (+.f32 alpha alpha)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (+.f32 alpha alpha)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1 (*.f32 alpha alpha)) (-.f32 0 (+.f32 -1 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha alpha) -1/2) (/.f32 (+.f32 1 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha alpha) (+.f32 (*.f32 alpha alpha) -3/2)) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (*.f32 alpha alpha) 2) (neg.f32 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 3) 4) (/.f32 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (+.f32 -3 (*.f32 alpha (*.f32 alpha 4)))) 4) (/.f32 (+.f32 4 (neg.f32 (*.f32 alpha (+.f32 alpha alpha)))) 4))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 2 (+.f32 -1 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (*.f32 alpha (*.f32 alpha 4)) 4) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (-.f32 (*.f32 alpha (*.f32 alpha 4)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 alpha (*.f32 alpha 4)) 4) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 2) (/.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 2) (/.f32 (*.f32 cosTheta (-.f32 2 (*.f32 alpha (+.f32 alpha alpha)))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 cosTheta (-.f32 (*.f32 alpha (*.f32 alpha 4)) 4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) (*.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (+.f32 cosTheta cosTheta)) (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4)) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) (*.f32 2 (+.f32 cosTheta cosTheta))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 cosTheta (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2)) 1)))))

simplify1.3s (1.7%)

Algorithm

1×	egg-herbie

Rules

1484×	`rational_best-simplify-108`
988×	`rational_best-simplify-49`
934×	`rational_best-simplify-54`
854×	`rational_best-simplify-53`
628×	`rational_best-simplify-65`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	658	33559
1	2065	30915

Stop Event

1×	node limit

Counts

273 → 431

Calls

Call 1

Inputs
(/.f32 -1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
(-.f32 (+.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))) (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2)))))) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
(-.f32 (+.f32 (.f32 4 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))) (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2))) (+.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))) (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))))))) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32)))))) (.f32 -1/2 (/.f32 (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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)))))))
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(/.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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/2 (/.f32 (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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))))))))
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(.f32 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
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(+.f32 (.f32 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1/16 (/.f32 (.f32 (pow.f32 cosTheta 6) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1/4 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (.f32 1/8 (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 3)) (*.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))))
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(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
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(-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2)
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(-.f32 (+.f32 -1 (.f32 alpha alpha)) (-.f32 0 (+.f32 -1 (.f32 alpha alpha))))
(-.f32 (+.f32 (.f32 alpha alpha) -1/2) (/.f32 (+.f32 1 (-.f32 2 (.f32 alpha (+.f32 alpha alpha)))) 2))
(-.f32 (+.f32 (.f32 alpha alpha) (+.f32 (.f32 alpha alpha) -3/2)) 1/2)
(-.f32 (-.f32 (.f32 alpha alpha) 2) (neg.f32 (.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 3) 4) (/.f32 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))) 4))
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(.f32 2 (+.f32 -1 (.f32 alpha alpha)))
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(.f32 1 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(.f32 (-.f32 (.f32 alpha (*.f32 alpha 4)) 4) 1/2)
(.f32 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) 1/4)
(.f32 1/2 (-.f32 (.f32 alpha (*.f32 alpha 4)) 4))
(/.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)
(/.f32 (-.f32 (.f32 alpha (.f32 alpha 4)) 4) 2)
(/.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) 4)
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4)) 8)
(pow.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)
(+.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 0)
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(-.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 0)
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(/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 1)
(/.f32 (.f32 cosTheta (-.f32 (.f32 alpha (*.f32 alpha 4)) 4)) 2)
(/.f32 (.f32 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) 4)
(/.f32 (+.f32 (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta)) 8)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4)) 16)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(pow.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 1)

Outputs
(/.f32 -1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 (/.f32 (/.f32 -1 (log.f32 alpha)) (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2)))) (PI.f32))
(-.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
(-.f32 (.f32 (-.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (PI.f32) (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2)))))) (pow.f32 alpha 2)) (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))))
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(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (pow.f32 cosTheta 2) (log.f32 (/.f32 1 alpha)))))
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(-.f32 (.f32 alpha alpha) (+.f32 (+.f32 1 (neg.f32 (.f32 alpha alpha))) 1))
(-.f32 (+.f32 (.f32 alpha alpha) -1/2) (/.f32 (+.f32 1 (-.f32 2 (.f32 alpha (+.f32 alpha alpha)))) 2))
(-.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 1/2 (/.f32 (-.f32 2 (.f32 alpha (+.f32 alpha alpha))) 2)))
(-.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 1/2 (-.f32 1 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2))))
(-.f32 (+.f32 (.f32 alpha alpha) (+.f32 (.f32 alpha alpha) -3/2)) 1/2)
(-.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -3/2) 1/2)
(-.f32 (-.f32 (.f32 alpha alpha) 2) (neg.f32 (.f32 alpha alpha)))
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 3) 4) (/.f32 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))) 4))
(/.f32 (-.f32 (.f32 3 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))) (-.f32 2 (*.f32 alpha (+.f32 alpha alpha)))) 4)
(/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (-.f32 2 (.f32 3 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))))) 4)
(-.f32 (/.f32 (+.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (+.f32 -3 (.f32 alpha (.f32 alpha 4)))) 4) (/.f32 (+.f32 4 (neg.f32 (.f32 alpha (+.f32 alpha alpha)))) 4))
(/.f32 (-.f32 (+.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (+.f32 -3 (.f32 alpha (.f32 alpha 4)))) (+.f32 4 (neg.f32 (.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (+.f32 (-.f32 (+.f32 (.f32 alpha (.f32 alpha 4)) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -4)) (neg.f32 (.f32 alpha (+.f32 alpha alpha)))) -4) 4)
(.f32 2 (+.f32 -1 (.f32 alpha alpha)))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 1)
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(.f32 1 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(.f32 (-.f32 (.f32 alpha (*.f32 alpha 4)) 4) 1/2)
(.f32 1/2 (-.f32 (.f32 alpha (*.f32 alpha 4)) 4))
(.f32 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) 1/4)
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(.f32 1/2 (-.f32 (.f32 alpha (*.f32 alpha 4)) 4))
(/.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(/.f32 (-.f32 (.f32 alpha (.f32 alpha 4)) 4) 2)
(-.f32 (/.f32 (.f32 alpha (.f32 alpha 4)) 2) 2)
(/.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) 4)
(/.f32 (.f32 4 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))) 4)
(/.f32 (.f32 2 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4)) 8)
(/.f32 (.f32 4 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))) 4)
(pow.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 1)
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(+.f32 -2 (*.f32 alpha (+.f32 alpha alpha)))
(+.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 0)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(+.f32 0 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)))
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 2) (/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 2))
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(-.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 0)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(-.f32 (/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 2) (/.f32 (.f32 cosTheta (-.f32 2 (.f32 alpha (+.f32 alpha alpha)))) 2))
(/.f32 (-.f32 (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))) (.f32 cosTheta (-.f32 2 (.f32 alpha (+.f32 alpha alpha))))) 2)
(/.f32 (.f32 cosTheta (-.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))))) 2)
(/.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 1)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(/.f32 (.f32 cosTheta (-.f32 (.f32 alpha (*.f32 alpha 4)) 4)) 2)
(/.f32 (.f32 (.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) 4)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 4 cosTheta)) 4)
(/.f32 (+.f32 (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta) (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) cosTheta)) 8)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 4 cosTheta)) 4)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4)) 16)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 4 cosTheta)) 4)
(/.f32 (.f32 (.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 4 cosTheta)) 4)
(pow.f32 (.f32 cosTheta (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) 1)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))

eval7.6s (10%)

Compiler: Compiled 81781 to 42424 computations (48.1% saved)

prune3.8s (5%)

Pruning

28 alts after pruning (27 fresh and 1 done)

	Pruned	Kept	Total
New	1955	14	1969
Fresh	11	13	24
Picked	1	0	1
Done	5	1	6
Total	1972	28	2000

Error

Counts

2000 → 28

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
✓	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) 2)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (log.f32 (.f32 alpha alpha)))) (/.f32 -1/2 (log.f32 (.f32 alpha alpha)))) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha))) (+.f32 -2 (+.f32 -2 (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 4 (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
	0.5b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
▶	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.7b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
▶	0.4b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
▶	10.6b	(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 -1 (*.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
▶	0.6b	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.6b	(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
	0.6b	(/.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))))
	0.5b	(/.f32 (neg.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (.f32 alpha alpha)))) (neg.f32 (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.8b	(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (neg.f32 (.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	2.2b	(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
▶	0.6b	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))

Compiler

Compiled 1528 to 1004 computations (34.3% saved)

localize485.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta)
✓	0.3b	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2))))
✓	0.4b	(.f32 (.f32 alpha alpha) (*.f32 alpha alpha))
✓	3.1b	(pow.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 (PI.f32) 2))

Compiler

Compiled 124 to 53 computations (57.3% saved)

series72.0ms (0.1%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
39.0ms	alpha	@	0	(pow.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 (PI.f32) 2))
26.0ms	alpha	@	inf	(pow.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 (PI.f32) 2))
3.0ms	alpha	@	inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2))))
3.0ms	alpha	@	0	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2))))
0.0ms	alpha	@	-inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2))))

rewrite427.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1978×	`rational_best-4`
1978×	`rational_best-2`
1978×	`rational_best-3`
1978×	`rational_best-1`
374×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	107
1	110	107
2	284	107
3	931	107
4	4810	107

Stop Event

1×	node limit

Counts

3 → 167

Calls

Call 1

Inputs

(pow.f32 (*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha)) (/.f32 (PI.f32) 2))

(*.f32 (*.f32 alpha alpha) (*.f32 alpha alpha))

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 2) (/.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (fabs.f32 (/.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 2)) (fabs.f32 (/.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 2) (/.f32 (neg.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2)) (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 alpha (*.f32 (PI.f32) 1/2)) (pow.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 alpha (*.f32 (PI.f32) 1/2)) (pow.f32 (*.f32 alpha (*.f32 alpha (neg.f32 alpha))) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 (PI.f32) 1/2)) (pow.f32 alpha (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2)) 2) (/.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (neg.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2))) (neg.f32 (pow.f32 (*.f32 alpha alpha) (*.f32 (PI.f32) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha (*.f32 alpha alpha)) (/.f32 (PI.f32) 4)) (*.f32 (pow.f32 (*.f32 alpha (*.f32 alpha alpha)) (/.f32 (PI.f32) 4)) (pow.f32 alpha (*.f32 (PI.f32) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 alpha (/.f32 (PI.f32) 4)) (*.f32 (pow.f32 alpha (/.f32 (PI.f32) 4)) (pow.f32 (*.f32 alpha (*.f32 alpha alpha)) (*.f32 (PI.f32) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha (+.f32 alpha alpha)) (*.f32 (PI.f32) 1/2)) (pow.f32 (/.f32 (*.f32 alpha alpha) 2) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (+.f32 alpha alpha) (*.f32 (PI.f32) 1/2)) (pow.f32 (/.f32 (*.f32 alpha (*.f32 alpha alpha)) 2) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (pow.f32 (*.f32 alpha (*.f32 (*.f32 alpha alpha) (+.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) (pow.f32 1/2 (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 2 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))) (*.f32 2 (*.f32 2 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f32 (neg.f32 (pow.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))))))))

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egg-rr> (2) ((x pow.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 (PI.f32) 1/2) (log.f32 (*.f32 alpha (*.f32 alpha (*.f32 alpha alpha)))))) 1)))))

simplify643.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

1252×	`rational_best-simplify-1`
1036×	`rational_best-simplify-67`
854×	`rational_best-simplify-66`
838×	`rational_best-simplify-108`
822×	`rational_best-simplify-63`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	419	9295
1	1231	9203
2	4647	9085

Stop Event

1×	node limit

Counts

203 → 238

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))))
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32)))))
(.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32)))))
(+.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 0)
(+.f32 0 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)))
(+.f32 (/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 2) (/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 2))
(+.f32 (fabs.f32 (/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 2)) (fabs.f32 (/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 2)))
(-.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 0)
(-.f32 (/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 2) (/.f32 (neg.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2))) 2))
(.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)) 1)
(.f32 1 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))
(.f32 (pow.f32 (.f32 alpha alpha) (.f32 (PI.f32) 1/2)) (pow.f32 (.f32 alpha alpha) (*.f32 (PI.f32) 1/2)))
(.f32 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2))) 1/2)
(.f32 (pow.f32 alpha (.f32 (PI.f32) 1/2)) (pow.f32 (.f32 alpha (.f32 alpha alpha)) (*.f32 (PI.f32) 1/2)))
(.f32 (pow.f32 alpha (.f32 (PI.f32) 1/2)) (pow.f32 (.f32 alpha (.f32 alpha (neg.f32 alpha))) (*.f32 (PI.f32) 1/2)))
(.f32 (pow.f32 (.f32 alpha (.f32 alpha alpha)) (.f32 (PI.f32) 1/2)) (pow.f32 alpha (*.f32 (PI.f32) 1/2)))
(.f32 1/2 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2))))
(.f32 (.f32 (pow.f32 (.f32 alpha alpha) (.f32 (PI.f32) 1/2)) 2) (/.f32 (pow.f32 (.f32 alpha alpha) (.f32 (PI.f32) 1/2)) 2))
(.f32 (.f32 2 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (*.f32 (PI.f32) 1/2)))) 1/4)
(.f32 (neg.f32 (pow.f32 (.f32 alpha alpha) (.f32 (PI.f32) 1/2))) (neg.f32 (pow.f32 (.f32 alpha alpha) (*.f32 (PI.f32) 1/2))))
(.f32 (pow.f32 (.f32 alpha (.f32 alpha alpha)) (/.f32 (PI.f32) 4)) (.f32 (pow.f32 (.f32 alpha (.f32 alpha alpha)) (/.f32 (PI.f32) 4)) (pow.f32 alpha (*.f32 (PI.f32) 1/2))))
(.f32 (pow.f32 alpha (/.f32 (PI.f32) 4)) (.f32 (pow.f32 alpha (/.f32 (PI.f32) 4)) (pow.f32 (.f32 alpha (.f32 alpha alpha)) (*.f32 (PI.f32) 1/2))))
(.f32 (pow.f32 (.f32 alpha (+.f32 alpha alpha)) (.f32 (PI.f32) 1/2)) (pow.f32 (/.f32 (.f32 alpha alpha) 2) (*.f32 (PI.f32) 1/2)))
(.f32 (pow.f32 (+.f32 alpha alpha) (.f32 (PI.f32) 1/2)) (pow.f32 (/.f32 (.f32 alpha (.f32 alpha alpha)) 2) (*.f32 (PI.f32) 1/2)))
(.f32 (pow.f32 (.f32 alpha (.f32 (.f32 alpha alpha) (+.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) (pow.f32 1/2 (.f32 (PI.f32) 1/2)))
(/.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)) 1)
(/.f32 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (*.f32 (PI.f32) 1/2))) 2)
(/.f32 (.f32 2 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)))) 4)
(/.f32 (+.f32 (.f32 2 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)))) (.f32 2 (.f32 2 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2))))) 8)
(fabs.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2)))
(fabs.f32 (neg.f32 (pow.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) (.f32 (PI.f32) 1/2))))
(+.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) 0)
(+.f32 0 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) 2) (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) 2))
(+.f32 (fabs.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) 2)) (fabs.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) 2)))
(-.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) 0)
(-.f32 (/.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))) 2) (/.f32 (.f32 (.f32 alpha alpha) (.f32 alpha (neg.f32 alpha))) 2))
(/.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha))) 1)
(/.f32 (.f32 alpha (.f32 (*.f32 alpha alpha) (+.f32 alpha alpha))) 2)
(/.f32 (.f32 2 (.f32 alpha (.f32 (.f32 alpha alpha) (+.f32 alpha alpha)))) 4)
(/.f32 (.f32 (.f32 alpha alpha) (*.f32 alpha (neg.f32 alpha))) -1)
(/.f32 (+.f32 (.f32 2 (.f32 alpha (.f32 (.f32 alpha alpha) (+.f32 alpha alpha)))) (.f32 2 (.f32 alpha (.f32 (.f32 alpha alpha) (+.f32 alpha alpha))))) 8)
(/.f32 (.f32 (.f32 2 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (*.f32 alpha (+.f32 alpha alpha)))) 16)
(/.f32 (.f32 (.f32 2 (+.f32 alpha alpha)) (.f32 2 (.f32 (*.f32 alpha alpha) (+.f32 alpha alpha)))) 16)
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(pow.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) 1)

Outputs
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 2 (.f32 (log.f32 alpha) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 2 (log.f32 alpha))))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(exp.f32 (.f32 -2 (.f32 (log.f32 (/.f32 -1 alpha)) (PI.f32))))
(exp.f32 (.f32 (PI.f32) (.f32 (log.f32 (/.f32 -1 alpha)) -2)))
(exp.f32 (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 -1 alpha)))))
(exp.f32 (.f32 (log.f32 (/.f32 -1 alpha)) (.f32 (PI.f32) -2)))
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(pow.f32 alpha 4)
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
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(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32)))))
(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1 (*.f32 (log.f32 alpha) (PI.f32)))))
(*.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 (pow.f32 alpha 2) 1))
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(-.f32 (.f32 1/2 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32)))) (.f32 1 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32)))))
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(*.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 (pow.f32 alpha 2) 1))
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(.f32 1/2 (-.f32 (/.f32 (pow.f32 alpha 2) (.f32 (log.f32 alpha) (PI.f32))) (/.f32 1 (*.f32 (log.f32 alpha) (PI.f32)))))
(*.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (-.f32 (pow.f32 alpha 2) 1))
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(+.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)))))
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(+.f32 (.f32 (pow.f32 alpha 2) (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
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(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)) (.f32 (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))) (PI.f32))))
(.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (/.f32 (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) 4) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (/.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) 4)) (+.f32 (/.f32 (.f32 (PI.f32) 1/2) (PI.f32)) (/.f32 0 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (/.f32 (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) 4)) (+.f32 (/.f32 0 (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))) (/.f32 (.f32 (PI.f32) 1/2) (PI.f32))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))))) 1)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (/.f32 1 (+.f32 1 (/.f32 0 (.f32 (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))) (PI.f32))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 1 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2) (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (+.f32 (.f32 alpha alpha) -1))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)) 1/2)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)) (/.f32 1 (+.f32 2 (/.f32 0 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))) (PI.f32))) 2))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 1/2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) 2) (.f32 (+.f32 (*.f32 alpha alpha) -1) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) 1/4)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (/.f32 1 (/.f32 (+.f32 2 (/.f32 0 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)))) 1/2)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 1 (.f32 2 (.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)) (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (/.f32 1 (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4)) (/.f32 1 (/.f32 4 (.f32 (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))) (PI.f32)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 (.f32 alpha alpha) -1)) (/.f32 (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (+.f32 (.f32 alpha (+.f32 alpha alpha)) -2)) (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))))) (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (*.f32 alpha alpha)))) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)) 4))) (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (.f32 (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha))))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 (/.f32 1 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) 2) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(.f32 (+.f32 (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32))) (/.f32 2 (.f32 (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))) (PI.f32)))) (.f32 1 (+.f32 (/.f32 (*.f32 alpha alpha) 2) -1/2)))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))
(pow.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))) 1)
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)))))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha (.f32 alpha (.f32 alpha alpha)))))))
(.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))))

localize185.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

Compiler

Compiled 49 to 24 computations (51% saved)

series8.0ms (0%)

Counts

1 → 24

Calls

6 calls:

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

rewrite598.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

876×	`rational_best-simplify-3`
796×	`rational_best-simplify-70`
716×	`rational_best-simplify-49`
634×	`rational_best-simplify-53`
430×	`rational_best-simplify-65`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	43
1	123	41
2	291	41
3	1045	37
4	5923	37

Stop Event

1×	node limit

Counts

1 → 128

Calls

Call 1

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

Outputs

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simplify396.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1538×	`rational_best-simplify-1`
1180×	`rational_best-simplify-65`
918×	`rational_best-simplify-63`
700×	`rational_best-simplify-108`
652×	`rational_best-simplify-66`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	365	6852
1	1018	6702
2	3861	6548

Stop Event

1×	node limit

Counts

152 → 191

Calls

Call 1

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

localize245.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 105 to 50 computations (52.4% saved)

series29.0ms (0%)

Counts

2 → 32

Calls

9 calls:

Time	Variable		Point	Expression
17.0ms	alpha	@	inf	(/.f32 1/2 (log.f32 alpha))
3.0ms	alpha	@	-inf	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))
2.0ms	alpha	@	inf	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))
2.0ms	alpha	@	0	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))
1.0ms	cosTheta	@	inf	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))

rewrite293.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

1000×	`rational_best-simplify-55`
964×	`rational_best-4`
964×	`rational_best-2`
964×	`rational_best-3`
964×	`rational_best-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	84
1	150	84
2	418	84
3	2082	84

Stop Event

1×	node limit

Counts

2 → 81

Calls

Call 1

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

Outputs

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

simplify400.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

1398×	`rational_best-simplify-55`
1250×	`rational_best-simplify-1`
1034×	`rational_best-simplify-63`
826×	`rational_best-simplify-50`
804×	`rational_best-simplify-108`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	341	12065
1	1119	10411
2	4085	10117

Stop Event

1×	node limit

Counts

113 → 205

Calls

Call 1

Inputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (.f32 (pow.f32 alpha 2) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 (.f32 1/2 (/.f32 (.f32 (pow.f32 cosTheta 4) (.f32 (pow.f32 alpha 6) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))) (.f32 -1/2 (/.f32 (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 4) (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -1 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2) (PI.f32)))))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))))
(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
(-.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(-.f32 (+.f32 (.f32 1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2)) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6)))) (+.f32 (.f32 1/2 (/.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (pow.f32 alpha 2))) (.f32 -1/2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32)))) (.f32 -1 (/.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 4) (PI.f32)))))) (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2)))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4)))))) (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))))
(/.f32 1/2 (.f32 (+.f32 (log.f32 -1) (.f32 -1 (log.f32 (/.f32 -1 alpha)))) (*.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (log.f32 alpha) 2)) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32)))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 (log.f32 alpha) 2)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (.f32 2 (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 4)) (.f32 (.f32 (.f32 (PI.f32) 2) (.f32 (log.f32 alpha) 4)) 2))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32))) (.f32 2 (.f32 (log.f32 alpha) 4)))
(/.f32 (.f32 (/.f32 2 (log.f32 alpha)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 4 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32)))) (.f32 (.f32 2 (.f32 (log.f32 alpha) 4)) 4))
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(/.f32 (.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32))) (/.f32 2 (log.f32 alpha))) 16)
(/.f32 (.f32 (/.f32 2 (log.f32 alpha)) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32)))) 16)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32))) (-.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 4)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)) (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))) 4)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2) (PI.f32))) 4)
(/.f32 (.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 4)) 4)
(pow.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (.f32 (PI.f32) (-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 cosTheta cosTheta) 2)) -2))) 1)
(+.f32 (/.f32 1/2 (log.f32 alpha)) 0)
(+.f32 0 (/.f32 1/2 (log.f32 alpha)))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) 2) (/.f32 (/.f32 1/2 (log.f32 alpha)) 2))
(-.f32 (/.f32 1/2 (log.f32 alpha)) 0)
(*.f32 1 (/.f32 1/2 (log.f32 alpha)))
(*.f32 1/2 (/.f32 1 (log.f32 alpha)))
(*.f32 (/.f32 1/2 (log.f32 alpha)) 1)
(.f32 2 (/.f32 1/2 (.f32 (log.f32 alpha) 2)))
(.f32 2 (/.f32 1 (.f32 (log.f32 alpha) 4)))
(.f32 2 (.f32 (/.f32 1/2 (log.f32 alpha)) 1/2))
(*.f32 (/.f32 1 (log.f32 alpha)) 1/2)
(.f32 (/.f32 1 (.f32 (log.f32 alpha) 4)) 2)
(.f32 4 (/.f32 1/2 (.f32 (log.f32 alpha) 4)))
(.f32 4 (/.f32 1 (.f32 2 (*.f32 (log.f32 alpha) 4))))
(*.f32 (/.f32 2 (log.f32 alpha)) 1/4)
(pow.f32 (/.f32 1/2 (log.f32 alpha)) 1)

Outputs
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 -1/2 (.f32 (PI.f32) (.f32 (+.f32 1 (*.f32 -1 (pow.f32 cosTheta 2))) (log.f32 alpha))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (neg.f32 (pow.f32 cosTheta 2))))
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(-.f32 (.f32 (-.f32 (/.f32 1 (.f32 (PI.f32) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (log.f32 alpha)))) (.f32 -1 (/.f32 (/.f32 (pow.f32 cosTheta 2) (log.f32 alpha)) (.f32 (PI.f32) (pow.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) 2))))) (.f32 (pow.f32 alpha 2) 1/2)) (.f32 1 (/.f32 1/2 (.f32 (PI.f32) (.f32 (+.f32 1 (.f32 -1 (pow.f32 cosTheta 2))) (log.f32 alpha))))))
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(/.f32 -1/2 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))
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(/.f32 (.f32 2 (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 4)) (.f32 (.f32 (.f32 (PI.f32) 2) (.f32 (log.f32 alpha) 4)) 2))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32))) (.f32 2 (.f32 (log.f32 alpha) 4)))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (.f32 (/.f32 2 (log.f32 alpha)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 2 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))) 4)
(/.f32 (.f32 4 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32)))) (.f32 (.f32 2 (.f32 (log.f32 alpha) 4)) 4))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (.f32 2 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) 2) (PI.f32))) (.f32 (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) 4)) 2))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (.f32 2 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (log.f32 alpha))) (.f32 2 (.f32 (PI.f32) 4)))
(/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta)))))) (*.f32 (log.f32 alpha) 4))
(/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (log.f32 alpha) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (*.f32 2 (PI.f32)))))
(/.f32 (.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32))) (/.f32 2 (log.f32 alpha))) 16)
(/.f32 (.f32 2 (/.f32 (/.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) (log.f32 alpha))) 16)
(/.f32 (.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 8) (/.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))))) 16)
(/.f32 (.f32 1 (/.f32 (.f32 8 (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))))))) 16)
(/.f32 (.f32 (/.f32 2 (log.f32 alpha)) (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32)))) 16)
(/.f32 (.f32 2 (/.f32 (/.f32 (.f32 4 (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) (log.f32 alpha))) 16)
(/.f32 (.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) 8) (/.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))))) 16)
(/.f32 (.f32 1 (/.f32 (.f32 8 (+.f32 -1 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))))))) 16)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (PI.f32))) (-.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 4)
(/.f32 (.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 2 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))) 4)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (PI.f32)) (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 2 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))))) 4)
(/.f32 (.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 2 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))) 4)
(/.f32 (.f32 (/.f32 (/.f32 1 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (/.f32 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2) (PI.f32))) 4)
(/.f32 (.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 2 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))) 4)
(/.f32 (.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) 4)) 4)
(/.f32 (.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 2 (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))))) 4)
(/.f32 (.f32 2 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (.f32 (log.f32 alpha) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))) 4)
(pow.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (.f32 (PI.f32) (-.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (.f32 cosTheta cosTheta) 2)) -2))) 1)
(/.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (PI.f32)) (-.f32 (.f32 2 (.f32 (+.f32 -1 (.f32 alpha alpha)) (*.f32 cosTheta cosTheta))) -2)) (log.f32 alpha))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 alpha)) (.f32 (PI.f32) (-.f32 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 2 (.f32 cosTheta cosTheta))) -2)))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (-.f32 (.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) -2)) (.f32 (log.f32 alpha) (PI.f32)))
(+.f32 (/.f32 1/2 (log.f32 alpha)) 0)
(/.f32 1/2 (log.f32 alpha))
(+.f32 0 (/.f32 1/2 (log.f32 alpha)))
(/.f32 1/2 (log.f32 alpha))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) 2) (/.f32 (/.f32 1/2 (log.f32 alpha)) 2))
(/.f32 1/2 (log.f32 alpha))
(-.f32 (/.f32 1/2 (log.f32 alpha)) 0)
(/.f32 1/2 (log.f32 alpha))
(*.f32 1 (/.f32 1/2 (log.f32 alpha)))
(/.f32 1/2 (log.f32 alpha))
(*.f32 1/2 (/.f32 1 (log.f32 alpha)))
(/.f32 1/2 (log.f32 alpha))
(*.f32 (/.f32 1/2 (log.f32 alpha)) 1)
(/.f32 1/2 (log.f32 alpha))
(.f32 2 (/.f32 1/2 (.f32 (log.f32 alpha) 2)))
(/.f32 1/2 (log.f32 alpha))
(.f32 2 (/.f32 1 (.f32 (log.f32 alpha) 4)))
(/.f32 1/2 (log.f32 alpha))
(.f32 2 (.f32 (/.f32 1/2 (log.f32 alpha)) 1/2))
(/.f32 1/2 (log.f32 alpha))
(*.f32 (/.f32 1 (log.f32 alpha)) 1/2)
(/.f32 1/2 (log.f32 alpha))
(.f32 (/.f32 1 (.f32 (log.f32 alpha) 4)) 2)
(/.f32 1/2 (log.f32 alpha))
(.f32 4 (/.f32 1/2 (.f32 (log.f32 alpha) 4)))
(/.f32 1/2 (log.f32 alpha))
(.f32 4 (/.f32 1 (.f32 2 (*.f32 (log.f32 alpha) 4))))
(/.f32 1/2 (log.f32 alpha))
(*.f32 (/.f32 2 (log.f32 alpha)) 1/4)
(/.f32 1/2 (log.f32 alpha))
(pow.f32 (/.f32 1/2 (log.f32 alpha)) 1)
(/.f32 1/2 (log.f32 alpha))

localize410.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 104 to 63 computations (39.4% saved)

series32.0ms (0%)

Counts

3 → 32

Calls

9 calls:

Time	Variable		Point	Expression
25.0ms	alpha	@	-inf	(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))
2.0ms	alpha	@	-inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (*.f32 -2 (log.f32 (/.f32 1 alpha)))))
1.0ms	alpha	@	0	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (*.f32 -2 (log.f32 (/.f32 1 alpha)))))
1.0ms	alpha	@	inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (*.f32 -2 (log.f32 (/.f32 1 alpha)))))
0.0ms	alpha	@	inf	(.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))

rewrite541.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

782×	`rational_best-simplify-67`
700×	`rational_best-simplify-108`
680×	`rational_best-simplify-64`
650×	`rational_best-simplify-89`
572×	`rational_best-4`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	79
1	116	79
2	308	79
3	1337	79
4	7617	79

Stop Event

1×	node limit

Counts

3 → 190

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (+.f32 (/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 3) 4) (/.f32 (*.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (PI.f32) 2)) 4))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (PI.f32) -4)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (*.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) 8)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (*.f32 (PI.f32) 2)) (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) -4))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) -4)) (*.f32 2 (*.f32 (PI.f32) 2))) 16)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2)) (*.f32 (PI.f32) -2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x log.f32 (pow.f32 (/.f32 1 alpha) (*.f32 (PI.f32) -2)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (neg.f32 (/.f32 0 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 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((#(struct:change #<rule egg-rr> (2) ((x +.f32 (log.f32 (/.f32 1 alpha)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (log.f32 (/.f32 1 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (/.f32 (log.f32 (/.f32 1 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (+.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (log.f32 (/.f32 1 alpha)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (/.f32 (neg.f32 (log.f32 (/.f32 1 alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (log.f32 (/.f32 1 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (log.f32 (/.f32 1 alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (log.f32 (/.f32 1 alpha)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (*.f32 (log.f32 (/.f32 1 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2)) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (log.f32 (/.f32 1 alpha)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (log.f32 (/.f32 1 alpha)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2)) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2)) (*.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2))) 8)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (log.f32 (/.f32 1 alpha)) 1)))))

simplify820.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1116×	`rational_best-simplify-108`
784×	`rational_best-simplify-49`
762×	`rational_best-simplify-54`
760×	`rational_best-simplify-53`
654×	`rational_best-simplify-55`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	482	11926
1	1438	10856
2	6732	10646

Stop Event

1×	node limit

Counts

222 → 306

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) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 -2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))))
(.f32 -2 (.f32 (PI.f32) (+.f32 (log.f32 -1) (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 (/.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) (log.f32 (/.f32 -1 alpha))) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 1 (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))) (.f32 -1/2 (/.f32 (pow.f32 alpha 2) (.f32 (+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha))) (PI.f32)))))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(*.f32 -1 (log.f32 alpha))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (log.f32 -1) (log.f32 (/.f32 -1 alpha)))
(+.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)
(+.f32 0 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
(+.f32 (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2))
(+.f32 (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (+.f32 (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) 0))
(-.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)
(-.f32 (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))
(-.f32 (/.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 3) 4) (/.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) 2)) 4))
(/.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 1)
(/.f32 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4)) 2)
(/.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4) 4)
(/.f32 (.f32 2 (.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) 8)
(/.f32 (.f32 (.f32 2 (.f32 (PI.f32) 2)) (.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) -4))) 16)
(/.f32 (.f32 (.f32 2 (.f32 (log.f32 (/.f32 1 alpha)) -4)) (.f32 2 (*.f32 (PI.f32) 2))) 16)
(/.f32 (.f32 (.f32 2 (.f32 (log.f32 (/.f32 1 alpha)) 2)) (.f32 (PI.f32) -2)) 4)
(pow.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 1)
(log.f32 (pow.f32 (/.f32 1 alpha) (*.f32 (PI.f32) -2)))
(+.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0)
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
(+.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (neg.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 0))
(+.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(+.f32 0 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
(+.f32 (.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2) (/.f32 (/.f32 1/2 (log.f32 (/.f32 1 alpha))) (PI.f32)))
(+.f32 (.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2) (+.f32 (/.f32 (/.f32 1/2 (log.f32 (/.f32 1 alpha))) (PI.f32)) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(+.f32 (.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2) (neg.f32 (/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 (/.f32 1 alpha))) (PI.f32)) (.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2))
(+.f32 (/.f32 (/.f32 1/2 (log.f32 (/.f32 1 alpha))) (PI.f32)) (+.f32 (.f32 (/.f32 (/.f32 (.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
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(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) 2) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (PI.f32) -4))) 2))
(-.f32 (/.f32 (/.f32 (+.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 alpha (+.f32 alpha alpha))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) 2) (/.f32 (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (.f32 (log.f32 (/.f32 1 alpha)) (*.f32 (PI.f32) -4))) 2))
(-.f32 (/.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (+.f32 2 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))) (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (+.f32 2 (/.f32 0 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))))
(-.f32 (/.f32 (/.f32 (+.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 alpha (+.f32 alpha alpha))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (+.f32 2 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))) (/.f32 (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (+.f32 2 (/.f32 0 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))))
(-.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 3) (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) (/.f32 (-.f32 1 (.f32 alpha alpha)) (.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)))
(-.f32 (/.f32 (+.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 alpha (+.f32 alpha alpha))) (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) (/.f32 (+.f32 3 (neg.f32 (.f32 alpha alpha))) (.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)))
(.f32 1 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
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(.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
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(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (/.f32 1 (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
(.f32 2 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))))
(.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 1 (PI.f32)))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (/.f32 1 alpha))) (/.f32 1 (*.f32 (PI.f32) -2)))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (PI.f32) -2)) (/.f32 1 (log.f32 (/.f32 1 alpha))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2)
(.f32 (/.f32 1 (PI.f32)) (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))
(.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 (*.f32 alpha alpha) -1))
(.f32 (.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) 1/2)
(.f32 (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2) (/.f32 1 (+.f32 2 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))))
(.f32 (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 2) (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) -4)))
(.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (/.f32 1 (.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)))
(.f32 (-.f32 (.f32 (*.f32 alpha alpha) -1/2) -1/2) (/.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (PI.f32)))
(.f32 1/2 (.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2))
(.f32 -1/2 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (/.f32 1 alpha))))
(.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 (PI.f32) -2)))
(.f32 (/.f32 1 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)))
(.f32 (/.f32 1 (.f32 (PI.f32) -2)) (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (/.f32 1 alpha))))
(.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) -4)) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 2))
(.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) (.f32 (+.f32 (*.f32 alpha alpha) -1) 4))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (log.f32 (pow.f32 (/.f32 1 alpha) -2)) 2)) (/.f32 1 (*.f32 (PI.f32) 2)))
(.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 (log.f32 (/.f32 1 alpha)) 2)) (/.f32 1 (*.f32 (PI.f32) -4)))
(.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 (PI.f32) -2)) (/.f32 1/2 (log.f32 (/.f32 1 alpha))))
(.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) -1/4)
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) 1/4)
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (+.f32 (/.f32 (*.f32 (PI.f32) 2) (/.f32 (PI.f32) 2)) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))
(.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) 4) (PI.f32)) (/.f32 1 (.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) -4))))
(.f32 (.f32 2 (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 1 (.f32 2 (.f32 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (+.f32 (/.f32 1 (PI.f32)) (/.f32 0 (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (/.f32 (PI.f32) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (/.f32 1 alpha))) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (+.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (/.f32 0 (PI.f32)))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) -2)) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (+.f32 (/.f32 1 (*.f32 (PI.f32) -2)) (/.f32 0 (log.f32 (/.f32 1 alpha))))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (/.f32 1 alpha))) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 1 (/.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (PI.f32))))
(.f32 (/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2)) (/.f32 1 (/.f32 2 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (/.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2)) (/.f32 1 (+.f32 (/.f32 -2 (/.f32 (.f32 (PI.f32) -2) 2)) (/.f32 0 (log.f32 (/.f32 1 alpha))))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 (.f32 alpha alpha) -1)) (/.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))) (/.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (PI.f32) -4))) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32))) (/.f32 (/.f32 1 (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))) (/.f32 (/.f32 1 (PI.f32)) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 1 (.f32 (PI.f32) -2)) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) -2))) (/.f32 (/.f32 1 (log.f32 (/.f32 1 alpha))) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (/.f32 1 alpha)))) (/.f32 -1/2 (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 2)) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) 2)) (/.f32 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) -4)) (*.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) (.f32 (+.f32 (.f32 alpha alpha) -1) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 4)) (.f32 (PI.f32) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(.f32 (+.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha))))) (.f32 1 (-.f32 (/.f32 (*.f32 alpha alpha) 2) 1/2)))
(pow.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2))) 1)
(neg.f32 (-.f32 (/.f32 0 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (pow.f32 (/.f32 1 alpha) -2)))))
(neg.f32 (-.f32 (/.f32 -1/2 (.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (PI.f32)) (log.f32 (/.f32 1 alpha))) -1/2)))
(+.f32 (log.f32 (/.f32 1 alpha)) 0)
(+.f32 0 (log.f32 (/.f32 1 alpha)))
(+.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (/.f32 (log.f32 (/.f32 1 alpha)) 2))
(+.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (+.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) 0))
(-.f32 (log.f32 (/.f32 1 alpha)) 0)
(-.f32 (/.f32 (log.f32 (/.f32 1 alpha)) 2) (/.f32 (neg.f32 (log.f32 (/.f32 1 alpha))) 2))
(*.f32 1 (log.f32 (/.f32 1 alpha)))
(*.f32 (log.f32 (/.f32 1 alpha)) 1)
(.f32 (.f32 (log.f32 (/.f32 1 alpha)) 2) 1/2)
(.f32 1/2 (.f32 (log.f32 (/.f32 1 alpha)) 2))
(.f32 (.f32 2 (*.f32 (log.f32 (/.f32 1 alpha)) 2)) 1/4)
(/.f32 (log.f32 (/.f32 1 alpha)) 1)
(/.f32 (*.f32 (log.f32 (/.f32 1 alpha)) 2) 2)
(/.f32 (.f32 2 (.f32 (log.f32 (/.f32 1 alpha)) 2)) 4)
(/.f32 (+.f32 (.f32 2 (.f32 (log.f32 (/.f32 1 alpha)) 2)) (.f32 2 (.f32 (log.f32 (/.f32 1 alpha)) 2))) 8)
(pow.f32 (log.f32 (/.f32 1 alpha)) 1)

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

localize743.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
✓	0.3b	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
✓	0.5b	(+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2))

Compiler

Compiled 143 to 56 computations (60.8% saved)

series5.0ms (0%)

Counts

3 → 60

Calls

15 calls:

Time	Variable		Point	Expression
1.0ms	cosTheta	@	inf	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
1.0ms	alpha	@	inf	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
1.0ms	alpha	@	0	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
1.0ms	alpha	@	-inf	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
0.0ms	cosTheta	@	0	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))

rewrite717.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

880×	`rational_best-4`
880×	`rational_best-2`
880×	`rational_best-3`
880×	`rational_best-1`
880×	`exponential-1`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	153
1	184	153
2	449	129
3	1979	129

Stop Event

1×	node limit

Counts

3 → 242

Calls

Call 1

Inputs

(+.f32 (+.f32 -1/2 (*.f32 alpha alpha)) (+.f32 (*.f32 alpha alpha) -3/2))

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

(*.f32 cosTheta (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 1/2 (-.f32 3/2 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 (-.f32 1/2 (*.f32 alpha alpha)) 3/2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 (+.f32 1/2 (-.f32 3/2 (*.f32 alpha alpha))) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 (+.f32 (-.f32 1/2 (*.f32 alpha alpha)) 3/2) 0))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha alpha) (+.f32 2 (neg.f32 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1/2 (*.f32 alpha alpha)) (-.f32 3/2 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha alpha) -3/2) (-.f32 1/2 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 alpha (+.f32 alpha alpha)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 0 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -1/2 (*.f32 alpha (+.f32 alpha alpha))) 3/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (*.f32 alpha alpha) -2) (neg.f32 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 -3/2 (*.f32 alpha (+.f32 alpha alpha))) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 -2 (-.f32 1/2 (*.f32 alpha alpha))) (+.f32 (-.f32 3/2 (*.f32 alpha alpha)) (+.f32 -1/2 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (*.f32 -2 (-.f32 3/2 (*.f32 alpha alpha))) (+.f32 (-.f32 1/2 (*.f32 alpha alpha)) (+.f32 (*.f32 alpha alpha) -3/2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2) (-.f32 (-.f32 1/2 (*.f32 alpha alpha)) (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2) (-.f32 (-.f32 3/2 (*.f32 alpha alpha)) (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (/.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2) (/.f32 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (/.f32 (*.f32 alpha alpha) 2) 1/2) (-.f32 (-.f32 3/2 (*.f32 alpha alpha)) (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (/.f32 (*.f32 alpha alpha) 2) 3/2) (-.f32 (-.f32 1/2 (*.f32 alpha alpha)) (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2) (-.f32 3/2 (*.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (-.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2) (-.f32 1/2 (*.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2) (*.f32 alpha alpha)) (-.f32 1/2 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2) (+.f32 (*.f32 alpha alpha) -3/2)) (-.f32 0 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2) (+.f32 -1/2 (*.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (*.f32 alpha alpha) 2) (+.f32 -1/2 (*.f32 alpha alpha))) (-.f32 3/2 (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (*.f32 alpha alpha) 2) (+.f32 (*.f32 alpha alpha) -3/2)) (-.f32 1/2 (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2) (*.f32 alpha alpha)) (-.f32 3/2 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f32 (+.f32 (/.f32 (*.f32 alpha alpha) 2) (+.f32 (*.f32 alpha alpha) -2)) (-.f32 0 (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (*.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2) 2)))) 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simplify1.1s (1.5%)

Algorithm

1×	egg-herbie

Rules

1250×	`rational_best-simplify-108`
1156×	`rational_best-simplify-54`
812×	`rational_best-simplify-49`
690×	`rational_best-simplify-55`
654×	`rational_best-simplify-53`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	728	30438
1	2138	28998

Stop Event

1×	node limit

Counts

302 → 365

Calls

Call 1

Inputs
-2
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(*.f32 2 (pow.f32 alpha 2))
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(*.f32 2 (pow.f32 alpha 2))
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(/.f32 -1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))))
(-.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
(-.f32 (+.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))) (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2)))))) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
(-.f32 (+.f32 (.f32 4 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 4) (pow.f32 alpha 6))) (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2))) (+.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (.f32 -2 (/.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (.f32 (pow.f32 cosTheta 2) (pow.f32 alpha 4))) (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))))))) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (.f32 (pow.f32 alpha 2) (PI.f32)))))) (.f32 -1/2 (/.f32 (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/2 (/.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 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (log.f32 (/.f32 1 alpha)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/4 (/.f32 (.f32 (pow.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/2 (/.f32 (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 -1/2 (/.f32 (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (-.f32 (.f32 1/2 (/.f32 1 (.f32 (pow.f32 cosTheta 2) (.f32 (PI.f32) (log.f32 (/.f32 -1 alpha)))))) (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/4 (/.f32 (.f32 (pow.f32 (+.f32 2 (.f32 -2 (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 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 (.f32 -1/4 (/.f32 (+.f32 2 (.f32 -2 (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 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (.f32 -1/4 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1/4 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (.f32 1/8 (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 3)) (*.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32))))))
(+.f32 (.f32 1/2 (/.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1/16 (/.f32 (.f32 (pow.f32 cosTheta 6) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 4)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (+.f32 (.f32 -1/4 (/.f32 (.f32 (pow.f32 cosTheta 2) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)) (.f32 (log.f32 (pow.f32 alpha 2)) (PI.f32)))) (.f32 1/8 (/.f32 (.f32 (pow.f32 cosTheta 4) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 3)) (*.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 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)))))))
(-.f32 (+.f32 (.f32 4 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (.f32 2 (pow.f32 alpha 2)) 2)))))))
(-.f32 (+.f32 (.f32 4 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (.f32 8 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 8) (.f32 (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 3) (PI.f32)))))) (.f32 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (*.f32 2 (pow.f32 alpha 2)) 2))))))))
(/.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 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)))))))
(-.f32 (+.f32 (.f32 4 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (.f32 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (.f32 2 (pow.f32 alpha 2)) 2)))))))
(-.f32 (+.f32 (.f32 4 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 6) (.f32 (PI.f32) (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 2)))))) (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 2) (PI.f32))))) (+.f32 (.f32 8 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 8) (.f32 (pow.f32 (-.f32 (.f32 2 (pow.f32 alpha 2)) 2) 3) (PI.f32)))))) (.f32 2 (/.f32 1 (.f32 (log.f32 (pow.f32 alpha 2)) (.f32 (pow.f32 cosTheta 4) (.f32 (PI.f32) (-.f32 (*.f32 2 (pow.f32 alpha 2)) 2))))))))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(.f32 cosTheta (-.f32 (.f32 2 (pow.f32 alpha 2)) 2))
(*.f32 -2 cosTheta)
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(.f32 2 (.f32 (pow.f32 alpha 2) cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(.f32 2 (.f32 (pow.f32 alpha 2) cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(+.f32 (.f32 2 (.f32 (pow.f32 alpha 2) cosTheta)) (*.f32 -2 cosTheta))
(-.f32 (.f32 alpha alpha) (+.f32 1/2 (-.f32 3/2 (.f32 alpha alpha))))
(-.f32 (.f32 alpha alpha) (+.f32 (-.f32 1/2 (.f32 alpha alpha)) 3/2))
(-.f32 (.f32 alpha alpha) (+.f32 (+.f32 1/2 (-.f32 3/2 (.f32 alpha alpha))) 0))
(-.f32 (.f32 alpha alpha) (+.f32 (+.f32 (-.f32 1/2 (.f32 alpha alpha)) 3/2) 0))
(-.f32 (.f32 alpha alpha) (+.f32 2 (neg.f32 (.f32 alpha alpha))))
(-.f32 (+.f32 -1/2 (.f32 alpha alpha)) (-.f32 3/2 (.f32 alpha alpha)))
(-.f32 (+.f32 (.f32 alpha alpha) -3/2) (-.f32 1/2 (.f32 alpha alpha)))
(-.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 0)
(-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2)
(-.f32 0 (-.f32 2 (*.f32 alpha (+.f32 alpha alpha))))
(-.f32 (+.f32 -1/2 (*.f32 alpha (+.f32 alpha alpha))) 3/2)
(-.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1) 1)
(-.f32 (+.f32 (.f32 alpha alpha) -2) (neg.f32 (.f32 alpha alpha)))
(-.f32 (+.f32 -3/2 (*.f32 alpha (+.f32 alpha alpha))) 1/2)
(-.f32 (.f32 -2 (-.f32 1/2 (.f32 alpha alpha))) (+.f32 (-.f32 3/2 (.f32 alpha alpha)) (+.f32 -1/2 (.f32 alpha alpha))))
(-.f32 (.f32 -2 (-.f32 3/2 (.f32 alpha alpha))) (+.f32 (-.f32 1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)))
(-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -3/2) 2) (-.f32 (-.f32 1/2 (.f32 alpha alpha)) (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))
(-.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) 2) (-.f32 (-.f32 3/2 (.f32 alpha alpha)) (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))
(-.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 2) (/.f32 (-.f32 2 (.f32 alpha (+.f32 alpha alpha))) 2))
(-.f32 (-.f32 (/.f32 (.f32 alpha alpha) 2) 1/2) (-.f32 (-.f32 3/2 (.f32 alpha alpha)) (/.f32 (*.f32 alpha alpha) 2)))
(-.f32 (-.f32 (/.f32 (.f32 alpha alpha) 2) 3/2) (-.f32 (-.f32 1/2 (.f32 alpha alpha)) (/.f32 (*.f32 alpha alpha) 2)))
(-.f32 (-.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) 2) (-.f32 3/2 (.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))
(-.f32 (-.f32 (/.f32 (+.f32 (.f32 alpha alpha) -3/2) 2) (-.f32 1/2 (.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))
(-.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -3/2) 2) (.f32 alpha alpha)) (-.f32 1/2 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))
(-.f32 (+.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) 2) (+.f32 (.f32 alpha alpha) -3/2)) (-.f32 0 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))
(-.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -3/2) 2) (+.f32 -1/2 (.f32 alpha alpha))) (-.f32 0 (/.f32 (+.f32 (*.f32 alpha alpha) -3/2) 2)))
(-.f32 (+.f32 (/.f32 (.f32 alpha alpha) 2) (+.f32 -1/2 (.f32 alpha alpha))) (-.f32 3/2 (/.f32 (*.f32 alpha alpha) 2)))
(-.f32 (+.f32 (/.f32 (.f32 alpha alpha) 2) (+.f32 (.f32 alpha alpha) -3/2)) (-.f32 1/2 (/.f32 (*.f32 alpha alpha) 2)))
(-.f32 (+.f32 (/.f32 (+.f32 -1/2 (.f32 alpha alpha)) 2) (.f32 alpha alpha)) (-.f32 3/2 (/.f32 (+.f32 -1/2 (*.f32 alpha alpha)) 2)))
(-.f32 (+.f32 (/.f32 (.f32 alpha alpha) 2) (+.f32 (.f32 alpha alpha) -2)) (-.f32 0 (/.f32 (*.f32 alpha alpha) 2)))
(.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 1)
(.f32 1 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(.f32 1/2 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2))
(.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 2) 1/2)
(.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 4) 1/4)
(/.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 1)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 2) 2)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 4) 4)
(pow.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 1)
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(/.f32 (.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 4) cosTheta) 4)
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(pow.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 1)

Outputs
-2
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(*.f32 2 (pow.f32 alpha 2))
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(*.f32 2 (pow.f32 alpha 2))
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(-.f32 (*.f32 2 (pow.f32 alpha 2)) 2)
(/.f32 -1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32))))
(/.f32 (/.f32 (/.f32 -1 (log.f32 alpha)) (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2)))) (PI.f32))
(-.f32 (.f32 (-.f32 (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))) (.f32 -2 (/.f32 (pow.f32 cosTheta 2) (.f32 (log.f32 alpha) (.f32 (pow.f32 (+.f32 2 (.f32 -2 (pow.f32 cosTheta 2))) 2) (PI.f32)))))) (pow.f32 alpha 2)) (/.f32 1 (.f32 (log.f32 alpha) (.f32 (+.f32 2 (*.f32 -2 (pow.f32 cosTheta 2))) (PI.f32)))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (/.f32 (/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 2) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 1 (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
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(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (/.f32 (/.f32 1 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 1 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (PI.f32))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 1 (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 1 (PI.f32)) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 2 (/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))) (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (PI.f32))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 2) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))) (/.f32 (/.f32 1 (.f32 2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 4)) (/.f32 (/.f32 1 (.f32 (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 4)) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(.f32 (+.f32 (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (PI.f32))) (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (PI.f32)))) (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(pow.f32 (/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) 1)
(/.f32 (/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (+.f32 2 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))))
(+.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 0)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(+.f32 0 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta))
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(+.f32 (/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 2) (/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 2))
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(-.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 0)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 1)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (+.f32 cosTheta cosTheta)) 2)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))
(/.f32 (.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 4) cosTheta) 4)
(/.f32 (.f32 cosTheta (.f32 4 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))))) 4)
(/.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (*.f32 4 cosTheta)) 4)
(/.f32 (.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 4) (.f32 2 (+.f32 cosTheta cosTheta))) 16)
(/.f32 (.f32 4 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (+.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 8) (+.f32 cosTheta cosTheta)) 16)
(/.f32 (.f32 (.f32 2 (+.f32 cosTheta cosTheta)) (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) 4)) 16)
(/.f32 (.f32 4 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (+.f32 cosTheta cosTheta)))) 16)
(/.f32 (.f32 (.f32 (+.f32 -2 (*.f32 alpha (+.f32 alpha alpha))) 8) (+.f32 cosTheta cosTheta)) 16)
(pow.f32 (.f32 (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))) cosTheta) 1)
(.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha))))

eval5.6s (7.3%)

Compiler: Compiled 75996 to 41829 computations (45% saved)

prune3.2s (4.2%)

Pruning

36 alts after pruning (33 fresh and 3 done)

	Pruned	Kept	Total
New	1862	19	1881
Fresh	8	14	22
Picked	1	0	1
Done	2	3	5
Total	1873	36	1909

Error

Counts

1909 → 36

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
▶	0.6b	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
▶	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
✓	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
▶	10.6b	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 2 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) 2)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha))) (+.f32 -2 (+.f32 -2 (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 4 (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
▶	0.5b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
✓	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.8b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.7b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	10.6b	(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.8b	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 -2 cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	0.6b	(/.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))))
	0.5b	(/.f32 (neg.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (.f32 alpha alpha)))) (neg.f32 (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.8b	(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (neg.f32 (.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	10.6b	(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
▶	11.1b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	10.6b	(/.f32 -2 (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	2.2b	(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
✓	0.6b	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))
	0.6b	(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 1/2 (log.f32 alpha)))
	10.6b	(.f32 (/.f32 1 (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))) (/.f32 -1/2 (log.f32 alpha)))
	10.6b	(.f32 (/.f32 1 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	10.6b	(.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 (/.f32 1 (PI.f32)) (+.f32 2 (.f32 cosTheta (*.f32 cosTheta -2)))))
	10.6b	(neg.f32 (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32))))

Compiler

Compiled 1658 to 1138 computations (31.4% saved)

localize226.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 104 to 43 computations (58.7% saved)

series37.0ms (0%)

Counts

2 → 48

Calls

12 calls:

Time	Variable		Point	Expression
14.0ms	alpha	@	inf	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
11.0ms	cosTheta	@	0	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha))))
4.0ms	alpha	@	inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha))))
2.0ms	alpha	@	0	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha))))
1.0ms	alpha	@	-inf	(/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha))))

rewrite438.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1318×	`rational_best-simplify-89`
932×	`rational_best-simplify-64`
872×	`rational_best-4`
872×	`rational_best-2`
872×	`rational_best-3`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	138
1	135	138
2	392	138
3	1922	138

Stop Event

1×	node limit

Counts

2 → 218

Calls

Call 1

Inputs

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 0 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (neg.f32 (/.f32 0 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (neg.f32 (/.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (neg.f32 (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 0 (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 0 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 0 (PI.f32)) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 (/.f32 -1 (log.f32 (*.f32 alpha alpha))) (PI.f32)) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (*.f32 alpha alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (neg.f32 (/.f32 (/.f32 (/.f32 1 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (/.f32 -1 (log.f32 (*.f32 alpha alpha))) (PI.f32)) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (*.f32 alpha alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32)))) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))) (-.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))) (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))) (-.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (PI.f32)) (*.f32 (log.f32 (*.f32 alpha alpha)) (-.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (*.f32 cosTheta cosTheta) 2)) -2))) (/.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (/.f32 -1 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2)) (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))) (*.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 0 (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 0 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))) (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 -1 (*.f32 alpha (+.f32 alpha alpha))) (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (log.f32 (*.f32 alpha alpha)))) (*.f32 (PI.f32) 2)) (/.f32 (/.f32 (/.f32 -1 (log.f32 (*.f32 alpha alpha))) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 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simplify864.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

1408×	`rational_best-simplify-49`
1352×	`rational_best-simplify-55`
1228×	`rational_best-simplify-53`
1218×	`rational_best-simplify-54`
1138×	`rational_best-simplify-50`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	793	36262
1	2559	35440

Stop Event

1×	node limit

Counts

266 → 505

Calls

Call 1

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

localize80.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

Compiler

Compiled 17 to 8 computations (52.9% saved)

localize190.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
	0.2b	(log.f32 (/.f32 1 alpha))
✓	0.5b	(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))

Compiler

Compiled 57 to 37 computations (35.1% saved)

series102.0ms (0.1%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
75.0ms	alpha	@	0	(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
17.0ms	cosTheta	@	0	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
4.0ms	cosTheta	@	inf	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
1.0ms	alpha	@	-inf	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
1.0ms	alpha	@	0	(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))

rewrite468.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1118×	`rational_best-simplify-89`
958×	`rational_best-simplify-65`
842×	`rational_best-simplify-67`
608×	`rational_best-4`
608×	`rational_best-2`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	18	74
1	137	72
2	375	72
3	1523	68

Stop Event

1×	node limit

Counts

2 → 425

Calls

Call 1

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (log.f32 (/.f32 1 alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (neg.f32 (/.f32 0 (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 (/.f32 0 (PI.f32)) 0))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 (/.f32 0 (log.f32 (/.f32 1 alpha))) (/.f32 0 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (/.f32 (log.f32 (/.f32 1 alpha)) (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 (/.f32 0 (log.f32 (/.f32 1 alpha))) (/.f32 (log.f32 (/.f32 1 alpha)) (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (/.f32 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha))) (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 (/.f32 1 alpha)))) (/.f32 0 (/.f32 (*.f32 (log.f32 (/.f32 1 alpha)) 2) (log.f32 (/.f32 1 alpha)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (/.f32 1/2 (*.f32 (PI.f32) (log.f32 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simplify776.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1026×	`rational_best-simplify-1`
932×	`rational_best-simplify-54`
812×	`rational_best-simplify-50`
704×	`rational_best-simplify-89`
626×	`rational_best-simplify-64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	911	25007
1	2707	21541

Stop Event

1×	node limit

Counts

461 → 552

Calls

Call 1

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

localize243.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

Compiler

Compiled 96 to 45 computations (53.1% saved)

series21.0ms (0%)

Counts

2 → 36

Calls

9 calls:

Time	Variable		Point	Expression
15.0ms	cosTheta	@	0	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
1.0ms	alpha	@	-inf	(/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 alpha))
1.0ms	alpha	@	-inf	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
1.0ms	alpha	@	0	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
1.0ms	alpha	@	inf	(/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 alpha))

rewrite430.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1286×	`rational_best-4`
1286×	`rational_best-2`
1286×	`rational_best-3`
1286×	`rational_best-1`
1286×	`exponential-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	96
1	154	96
2	496	96
3	2914	96

Stop Event

1×	node limit

Counts

2 → 201

Calls

Call 1

Inputs

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

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

Outputs

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(*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (+.f32 (/.f32 0 (PI.f32)) (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (+.f32 (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) 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(PI.f32)))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 2 (*.f32 (log.f32 alpha) (PI.f32))))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (/.f32 (/.f32 0 (log.f32 alpha)) (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) 2))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2) (/.f32 (/.f32 0 (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 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(/.f32 0 (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 2 (*.f32 (log.f32 alpha) (PI.f32))))) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 0 (log.f32 alpha)) (*.f32 (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))) (*.f32 (PI.f32) 2))) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (PI.f32)) 1/2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 0 (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) (*.f32 (PI.f32) 2)) (*.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 (log.f32 alpha) (+.f32 1 (*.f32 (+.f32 (*.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))) 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alpha) -1) (log.f32 alpha)) 1)))))

simplify549.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

1646×	`rational_best-simplify-108`
1118×	`rational_best-simplify-54`
1040×	`rational_best-simplify-49`
922×	`rational_best-simplify-55`
844×	`rational_best-simplify-53`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	618	21255
1	1934	20271

Stop Event

1×	node limit

Counts

237 → 359

Calls

Call 1

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

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

localize336.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32))
✓	0.3b	(/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (*.f32 alpha alpha)))
✓	0.6b	(-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha)))

Compiler

Compiled 127 to 45 computations (64.6% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

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

rewrite313.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`rational_best-simplify-52`
880×	`rational_best-simplify-89`
676×	`rational_best-4`
676×	`rational_best-2`
676×	`rational_best-3`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	125
1	113	125
2	335	107
3	1563	71

Stop Event

1×	node limit

Counts

3 → 285

Calls

Call 1

Inputs

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

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

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

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 alpha (+.f32 alpha alpha)) (-.f32 -1 (*.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 alpha alpha) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 alpha alpha) (-.f32 (*.f32 alpha alpha) (+.f32 1 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (*.f32 alpha alpha) -1) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (*.f32 alpha alpha) -1) (-.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1) (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 0 (+.f32 (*.f32 alpha alpha) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1) (*.f32 alpha (neg.f32 alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (*.f32 alpha (neg.f32 alpha)) (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 -1 (*.f32 alpha alpha))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (*.f32 alpha (*.f32 alpha 3)) 2) (neg.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 -1 (*.f32 alpha alpha)) (*.f32 alpha (+.f32 alpha alpha)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 -1 (*.f32 alpha alpha)) (neg.f32 (*.f32 (*.f32 alpha alpha) -2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) 2) (/.f32 (+.f32 (*.f32 alpha alpha) -1) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (*.f32 alpha (neg.f32 alpha)) 2) (/.f32 (-.f32 (*.f32 alpha (*.f32 alpha 3)) 2) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (-.f32 (*.f32 alpha (*.f32 alpha 3)) 2) 2) (/.f32 (*.f32 alpha (neg.f32 alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (*.f32 alpha alpha) (+.f32 1 (*.f32 alpha alpha))) (*.f32 alpha alpha))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (*.f32 (*.f32 alpha alpha) 4) (+.f32 1 (*.f32 alpha alpha))) (*.f32 (*.f32 alpha alpha) -2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) (/.f32 (+.f32 1 (*.f32 alpha alpha)) 2)) (neg.f32 (/.f32 (+.f32 1 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (+.f32 (*.f32 alpha (+.f32 alpha alpha)) -1) (/.f32 (*.f32 alpha alpha) 2)) (neg.f32 (/.f32 (*.f32 alpha alpha) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (-.f32 (*.f32 alpha alpha) (/.f32 (+.f32 1 (*.f32 alpha alpha)) 2)) (-.f32 (*.f32 alpha alpha) (/.f32 (+.f32 1 (*.f32 alpha alpha)) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1 (+.f32 (*.f32 alpha alpha) -1))))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2) 1/2)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (-.f32 1 (*.f32 alpha alpha)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 1/4)))) (#(struct:change #<rule egg-rr> (2) ((x *.f32 1/2 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 1 (*.f32 alpha alpha)) -1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (*.f32 (+.f32 (*.f32 alpha alpha) -1) 4) 4)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (-.f32 (*.f32 (*.f32 alpha alpha) 4) 2) (*.f32 (*.f32 alpha alpha) -2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (+.f32 (*.f32 (*.f32 alpha alpha) -2) (-.f32 (*.f32 (*.f32 alpha alpha) 4) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f32 (-.f32 (*.f32 2 (*.f32 (*.f32 alpha alpha) 4)) (*.f32 2 (-.f32 (*.f32 alpha (+.f32 alpha alpha)) -2))) 4)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f32 (+.f32 (*.f32 alpha alpha) -1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f32 (-.f32 1 (*.f32 alpha alpha)))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (/.f32 (/.f32 0 (log.f32 (*.f32 alpha alpha))) (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (/.f32 0 (log.f32 (*.f32 alpha alpha))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (/.f32 0 (PI.f32)))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (neg.f32 (/.f32 0 (PI.f32))))))) (#(struct:change #<rule egg-rr> (2) ((x +.f32 (/.f32 (/.f32 (+.f32 (*.f32 alpha alpha) -1) (log.f32 (*.f32 alpha alpha))) (PI.f32)) (neg.f32 (/.f32 (/.f32 0 (log.f32 (*.f32 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simplify656.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

1108×	`rational_best-simplify-48`
1086×	`rational_best-simplify-108`
752×	`rational_best-simplify-3`
750×	`rational_best-simplify-55`
694×	`rational_best-simplify-53`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	637	11429
1	1857	11047
2	7092	10945

Stop Event

1×	node limit

Counts

321 → 378

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

eval5.9s (7.7%)

Compiler: Compiled 81775 to 47268 computations (42.2% saved)

prune4.6s (6.1%)

Pruning

39 alts after pruning (32 fresh and 7 done)

	Pruned	Kept	Total
New	2263	10	2273
Fresh	6	22	28
Picked	0	1	1
Done	1	6	7
Total	2270	39	2309

Error

Counts

2309 → 39

Alt Table

Click to see full alt table

Status	Error	Program
	0.5b	(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.7b	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) 3) (+.f32 (.f32 alpha (+.f32 alpha alpha)) 1)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
✓	0.6b	(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
✓	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
	0.7b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
✓	0.5b	(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
	10.6b	(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.8b	(/.f32 (/.f32 (-.f32 (/.f32 (.f32 (.f32 alpha alpha) 4) (PI.f32)) (/.f32 (+.f32 (+.f32 1 (.f32 alpha alpha)) (.f32 alpha (+.f32 alpha alpha))) (PI.f32))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 2 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) 2)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha))) (+.f32 -2 (+.f32 -2 (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 4 (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
✓	0.5b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
✓	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	0.8b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.7b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
	0.5b	(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
	0.5b	(/.f32 (/.f32 (.f32 (/.f32 1 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
	11.1b	(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
	11.1b	(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
	0.8b	(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 -2 cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
	0.8b	(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
	0.6b	(/.f32 (neg.f32 (.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
	10.6b	(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
✓	11.1b	(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
	11.1b	(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
	10.6b	(/.f32 -2 (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
	2.2b	(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
✓	0.6b	(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 alpha)))
	10.6b	(.f32 (/.f32 (/.f32 2 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 1/4 (log.f32 (/.f32 1 alpha))))
	0.6b	(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 1/2 (log.f32 alpha)))
	10.6b	(.f32 (/.f32 4 (PI.f32)) (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 1 alpha)) 4)))
	10.6b	(.f32 (/.f32 1 (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))) (/.f32 -1/2 (log.f32 alpha)))
	11.1b	(*.f32 (/.f32 1 (log.f32 alpha)) (/.f32 -1/2 (PI.f32)))
	10.6b	(.f32 (/.f32 1 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
	10.6b	(neg.f32 (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32))))

Compiler

Compiled 906 to 630 computations (30.5% saved)

regimes847.0ms (1.1%)

Counts

75 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 1 (log.f32 alpha)) (/.f32 -1/2 (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
(neg.f32 (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(.f32 (/.f32 1 (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))) (/.f32 -1/2 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 -1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 (/.f32 1 (PI.f32)) (+.f32 2 (.f32 cosTheta (*.f32 cosTheta -2)))))
(.f32 (/.f32 (/.f32 2 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 1/4 (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 4 (PI.f32)) (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 1 alpha)) 4)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 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 (neg.f32 cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 -2 (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 1/2 (log.f32 alpha)))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 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 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
(/.f32 (neg.f32 (.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1 (log.f32 (.f32 alpha alpha))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (PI.f32)))
(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 -2 cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (.f32 (/.f32 1 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
(/.f32 (neg.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (.f32 alpha alpha)))) (neg.f32 (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 2 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) 3) (+.f32 (.f32 alpha (+.f32 alpha alpha)) 1)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 2 (.f32 alpha alpha)) (+.f32 -2 (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha))) (+.f32 -2 (+.f32 -2 (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 4 (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (+.f32 -1 (+.f32 (.f32 2 (.f32 alpha alpha)) (.f32 alpha alpha))) (+.f32 3 (neg.f32 (.f32 alpha alpha)))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 (+.f32 (+.f32 -1 (.f32 2 (.f32 alpha alpha))) -1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (-.f32 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) -2)))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (/.f32 (PI.f32) 2)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) 2) (/.f32 1/2 (PI.f32))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 (.f32 alpha alpha) -2) (.f32 (PI.f32) 2)) (.f32 (/.f32 alpha (PI.f32)) (/.f32 alpha 2))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (.f32 2 (log.f32 (.f32 alpha alpha)))) (/.f32 -1/2 (log.f32 (.f32 alpha alpha)))) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (-.f32 (/.f32 (.f32 (.f32 alpha alpha) 4) (PI.f32)) (/.f32 (+.f32 (+.f32 1 (.f32 alpha alpha)) (.f32 alpha (+.f32 alpha alpha))) (PI.f32))) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (-.f32 (/.f32 -1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (neg.f32 (/.f32 (.f32 alpha alpha) (PI.f32))) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (.f32 (log.f32 (.f32 alpha alpha)) (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))) (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha))))
(/.f32 (-.f32 (/.f32 (/.f32 (+.f32 -1 (.f32 alpha (+.f32 alpha alpha))) (PI.f32)) (.f32 (log.f32 (.f32 alpha alpha)) 2)) (/.f32 1/2 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) -2) (.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (/.f32 (/.f32 1/2 (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))

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

Calls

4 calls:

157.0ms	(/.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))))
147.0ms	alpha
130.0ms	(*.f32 alpha alpha)
114.0ms	cosTheta

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 1802 to 887 computations (50.8% saved)

regimes775.0ms (1%)

Counts

63 → 1

Calls

Call 1

Inputs
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(*.f32 (/.f32 1 (log.f32 alpha)) (/.f32 -1/2 (PI.f32)))
(/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha)))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
(neg.f32 (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (.f32 (log.f32 alpha) (PI.f32))))
(.f32 (/.f32 1 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(.f32 (/.f32 1 (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))) (/.f32 -1/2 (log.f32 alpha)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 -1 (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 -1 (log.f32 alpha)) (/.f32 (/.f32 1 (PI.f32)) (+.f32 2 (.f32 cosTheta (*.f32 cosTheta -2)))))
(.f32 (/.f32 (/.f32 2 (PI.f32)) (-.f32 1 (.f32 cosTheta cosTheta))) (/.f32 1/4 (log.f32 (/.f32 1 alpha))))
(/.f32 (/.f32 (/.f32 1/2 (PI.f32)) (log.f32 (/.f32 1 alpha))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 4 (PI.f32)) (/.f32 (/.f32 1/2 (-.f32 1 (.f32 cosTheta cosTheta))) (*.f32 (log.f32 (/.f32 1 alpha)) 4)))
(/.f32 (/.f32 -1/2 (.f32 (log.f32 alpha) (PI.f32))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 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 (neg.f32 cosTheta) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(/.f32 -2 (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (neg.f32 cosTheta))))
(.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 1/2 (log.f32 alpha)))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1/2 (log.f32 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 (.f32 alpha alpha) -1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 2 (log.f32 alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 2 (log.f32 alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (PI.f32) 2))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (*.f32 (log.f32 alpha) 2)) (PI.f32))
(/.f32 (neg.f32 (.f32 (/.f32 1/2 (.f32 (log.f32 alpha) (PI.f32))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (PI.f32)) (/.f32 1 (log.f32 (.f32 alpha alpha))))
(.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (log.f32 (.f32 alpha alpha))) (/.f32 1 (PI.f32)))
(/.f32 (.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 -1/2 (+.f32 -1/2 (.f32 alpha alpha))) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (log.f32 (*.f32 alpha alpha)) (PI.f32))))
(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 -2 cosTheta))) (.f32 (PI.f32) (log.f32 (*.f32 alpha alpha)))))
(/.f32 (/.f32 (.f32 (/.f32 1 (log.f32 alpha)) (+.f32 (.f32 alpha alpha) -1)) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (PI.f32) (.f32 -2 (log.f32 (/.f32 1 alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (PI.f32)) (.f32 -2 (log.f32 (/.f32 1 alpha)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (neg.f32 (.f32 (/.f32 (/.f32 1 (PI.f32)) (log.f32 (.f32 alpha alpha))) (-.f32 1 (.f32 alpha alpha)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(+.f32 1 (-.f32 -1 (/.f32 (/.f32 (/.f32 (-.f32 1 (.f32 alpha alpha)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (*.f32 alpha alpha))))))))
(/.f32 (neg.f32 (/.f32 (.f32 (+.f32 (.f32 alpha alpha) -1) (/.f32 1 (log.f32 (.f32 alpha alpha)))) (neg.f32 (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 (.f32 (PI.f32) 1/2) (log.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 2 (.f32 alpha alpha))) (.f32 (PI.f32) (.f32 (log.f32 (/.f32 1 alpha)) -4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 (-.f32 (.f32 alpha (+.f32 alpha alpha)) (+.f32 1 (.f32 alpha alpha))) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (/.f32 (-.f32 (+.f32 -1/2 (/.f32 (.f32 alpha (+.f32 alpha alpha)) 2)) 1/2) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (+.f32 (+.f32 -1/2 (.f32 alpha alpha)) (+.f32 (.f32 alpha alpha) -3/2)) (.f32 (+.f32 2 (.f32 cosTheta (.f32 cosTheta (+.f32 -2 (.f32 alpha (+.f32 alpha alpha)))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (/.f32 (-.f32 (.f32 (.f32 alpha alpha) 3) (+.f32 (.f32 alpha (+.f32 alpha alpha)) 1)) (PI.f32)) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (-.f32 (.f32 alpha alpha) (-.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) 3))) (.f32 (PI.f32) (.f32 (log.f32 (.f32 alpha alpha)) 4))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 2 (.f32 alpha alpha)) (+.f32 -2 (+.f32 -2 (.f32 2 (.f32 alpha alpha))))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 (/.f32 (+.f32 (.f32 alpha (+.f32 alpha (+.f32 alpha alpha))) (+.f32 -2 (+.f32 -2 (.f32 alpha alpha)))) (.f32 (PI.f32) (.f32 4 (log.f32 (.f32 alpha alpha))))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (+.f32 -1 (+.f32 (.f32 2 (.f32 alpha alpha)) (.f32 alpha alpha))) (+.f32 3 (neg.f32 (.f32 alpha alpha)))) 4) (.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (+.f32 -1 (.f32 alpha alpha))))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))))
(/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32))))
(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(/.f32 (/.f32 -1/2 (log.f32 (pow.f32 alpha (PI.f32)))) (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (*.f32 cosTheta cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (*.f32 cosTheta (neg.f32 cosTheta))))

Outputs
(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))

Calls

4 calls:

279.0ms	(*.f32 alpha alpha)
217.0ms	alpha
106.0ms	(/.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))))
93.0ms	cosTheta

Results

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

Compiler

Compiled 1413 to 720 computations (49% saved)

regimes544.0ms (0.7%)

Counts

44 → 1

Calls

Call 1

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

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

Calls

4 calls:

196.0ms	alpha
123.0ms	(*.f32 alpha alpha)
91.0ms	cosTheta
69.0ms	(/.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 892 to 464 computations (48% saved)

regimes447.0ms (0.6%)

Counts

30 → 1

Calls

Call 1

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

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

Calls

4 calls:

234.0ms	(*.f32 alpha alpha)
81.0ms	(/.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))))
60.0ms	cosTheta
42.0ms	alpha

Results

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

Compiler

Compiled 541 to 296 computations (45.3% saved)

regimes180.0ms (0.2%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

3 calls:

56.0ms	(*.f32 alpha alpha)
55.0ms	cosTheta
40.0ms	alpha

Results

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

Compiler

Compiled 443 to 247 computations (44.2% saved)

regimes330.0ms (0.4%)

Counts

25 → 1

Calls

Call 1

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

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

Calls

3 calls:

202.0ms	cosTheta
79.0ms	(*.f32 alpha alpha)
36.0ms	alpha

Results

Error	Segments	Branch
0.7b	1	`cosTheta`
0.7b	1	`alpha`
0.7b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 395 to 223 computations (43.5% saved)

regimes176.0ms (0.2%)

Counts

21 → 1

Calls

Call 1

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

Calls

3 calls:

47.0ms	cosTheta
46.0ms	alpha
40.0ms	(*.f32 alpha alpha)

Results

Error	Segments	Branch
0.7b	1	`cosTheta`
0.7b	1	`alpha`
0.7b	1	`(*.f32 alpha alpha)`

Compiler

Compiled 310 to 179 computations (42.3% saved)

regimes169.0ms (0.2%)

Counts

19 → 1

Calls

Call 1

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

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

Calls

2 calls:

132.0ms	alpha
28.0ms	cosTheta

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 267 to 159 computations (40.4% saved)

regimes85.0ms (0.1%)

Counts

16 → 1

Calls

Call 1

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

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

Calls

2 calls:

34.0ms	cosTheta
29.0ms	alpha

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 213 to 130 computations (39% saved)

regimes77.0ms (0.1%)

Counts

10 → 1

Calls

Call 1

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

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

Calls

2 calls:

38.0ms	alpha
35.0ms	cosTheta

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 115 to 67 computations (41.7% saved)

regimes55.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

27.0ms	cosTheta
25.0ms	alpha

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 87 to 52 computations (40.2% saved)

regimes59.0ms (0.1%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

2 calls:

34.0ms	alpha
22.0ms	cosTheta

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 73 to 44 computations (39.7% saved)

regimes63.0ms (0.1%)

Counts

5 → 1

Calls

Call 1

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

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

Calls

2 calls:

40.0ms	cosTheta
21.0ms	alpha

Results

Error	Segments	Branch
10.6b	1	`cosTheta`
10.6b	1	`alpha`

Compiler

Compiled 48 to 32 computations (33.3% saved)

regimes29.0ms (0%)

Accuracy

Total -0.0b remaining (-0.4%)

Threshold costs -0.0b (-0.4%)

Counts

4 → 1

Calls

Call 1

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

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

Calls

2 calls:

20.0ms	alpha
7.0ms	cosTheta

Results

Error	Segments	Branch
11.1b	1	`cosTheta`
11.1b	1	`alpha`

Compiler

Compiled 36 to 25 computations (30.6% saved)

simplify46.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	787

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (-.f32 (/.f32 (+.f32 -1 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) 0) (PI.f32)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 (+.f32 1 (.f32 (+.f32 (.f32 alpha alpha) -1) (.f32 cosTheta cosTheta))) (log.f32 (.f32 alpha alpha)))) (PI.f32))
(/.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 -1 (.f32 alpha alpha)) (.f32 (PI.f32) (+.f32 1 (.f32 (+.f32 -1 (.f32 alpha alpha)) (.f32 cosTheta cosTheta))))) (/.f32 1/2 (log.f32 alpha)))
(/.f32 (/.f32 (/.f32 (+.f32 (.f32 alpha alpha) -1) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta)))) (.f32 (PI.f32) 2))
(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (*.f32 (neg.f32 cosTheta) cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 cosTheta (.f32 (+.f32 (*.f32 alpha alpha) -1) cosTheta))))
(/.f32 (/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha)) (+.f32 1 (.f32 -1 (.f32 cosTheta cosTheta))))
(.f32 (/.f32 1 (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))) (/.f32 -1/2 (log.f32 alpha)))
(.f32 (/.f32 1 (PI.f32)) (/.f32 -1/2 (.f32 (log.f32 alpha) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 (/.f32 -1/2 (log.f32 alpha)) (-.f32 1 (*.f32 cosTheta cosTheta))) (PI.f32))
(/.f32 -1/2 (.f32 (log.f32 alpha) (.f32 (PI.f32) (-.f32 1 (*.f32 cosTheta cosTheta)))))
(/.f32 (/.f32 -1/2 (PI.f32)) (log.f32 alpha))
(/.f32 -1/2 (*.f32 (log.f32 alpha) (PI.f32)))

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

Compiler

Compiled 287 to 205 computations (28.6% saved)

soundness848.0ms (1.1%)

Algorithm

2×	egg-herbie

Rules

1478×	`rational_best-simplify-108`
1204×	`rational_best-simplify-52`
1178×	`rational_best-simplify-48`
880×	`rational_best-simplify-54`
852×	`rational_best-simplify-49`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	73
1	35	73
2	89	73
3	297	73
4	1045	73
5	4460	73
0	662	26990
1	1994	24660
2	7740	24168

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 200 to 96 computations (52% saved)

end332.0ms (0.4%)

Compiler: Compiled 259 to 136 computations (47.5% saved)