Details

analyze148.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0.6%	99.4%	0
0%	0.6%	99.4%	1
0%	0.6%	99.4%	2
0.3%	0.3%	99.4%	3
0.3%	0.3%	99.4%	4
0.5%	0.2%	99.4%	5
0.5%	0.2%	99.4%	6
0.6%	0.1%	99.4%	7
0.6%	0.1%	99.4%	8
0.6%	0%	99.4%	9
0.6%	0%	99.4%	10
0.6%	0%	99.4%	11
0.6%	0%	99.4%	12
0.6%	0%	99.4%	13
0.6%	0%	99.4%	14

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample1.8s (21.1%)

Results

1.7s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify47.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-/l*_binary32`
462×	`associate-l_binary32`
382×	`associate-*l/_binary32`
363×	`associate-r_binary32`
360×	`distribute-lft-in_binary32`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	33
1	45	31
2	160	31
3	661	31
4	2791	31
5	4866	31
6	4978	31

prune4.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.4b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
▶	0.4b	(/.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

0.4b

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

▶

0.4b

(/.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 145 to 87 computations (40% saved)

localize45.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series129.0ms (1.5%)

Counts

4 → 84

Calls

4 calls:

78.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
28.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
13.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary32`
22×	`add-exp-log_binary32`
21×	`pow1_binary32`
18×	`add-sqr-sqrt_binary32`
15×	`associate-r_binary32`

Counts

4 → 111

Calls

4 calls:

11.0ms	(/.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))))
7.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
7.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
6.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

633×	`associate-l_binary32`
535×	`times-frac_binary32`
508×	`associate-/r*_binary32`
299×	`associate-/l*_binary32`
183×	`fma-def_binary32`

Counts

195 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	419	5485
1	1280	4813
2	5382	4813

prune330.0ms (3.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	222	9	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	224	9	233

Error

0.0b

Counts

233 → 9

Alt Table

Status	Error	Program
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.9b	(.f32 (.f32 (cbrt.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))))) (cbrt.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)))))) (cbrt.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))))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (cbrt.f32 (fma.f32 alpha alpha -1))) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.8b	(exp.f32 (log.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))))
	0.5b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.4b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (.f32 alpha alpha)))) (.f32 (.f32 (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))))
▶	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))

Compiler

Compiled 9257 to 4985 computations (46.1% saved)

localize45.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
	0.2b	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	3.2b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series111.0ms (1.3%)

Counts

2 → 36

Calls

2 calls:

86.0ms

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

24.0ms

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

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary32`
10×	`pow1_binary32`
7×	`add-cbrt-cube_binary32`
7×	`*-un-lft-identity_binary32`
7×	`add-sqr-sqrt_binary32`

Counts

2 → 57

Calls

2 calls:

9.0ms

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

3.0ms

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

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

467×	`associate-r_binary32`
452×	`associate-/r*_binary32`
414×	`times-frac_binary32`
406×	`associate-l_binary32`
265×	`associate-/l*_binary32`

Counts

93 → 121

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	360	4112
1	1120	3692
2	5116	3692

prune254.0ms (3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	205	4	209
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	210	8	218

Error

Counts

218 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))
	0.7b	(exp.f32 (log.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))))
	0.5b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
▶	0.4b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 8315 to 4531 computations (45.5% saved)

localize56.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
✓	0.3b	(/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.3b	(/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	3.2b	(pow.f32 (*.f32 alpha alpha) (PI.f32))

series331.0ms (3.9%)

Counts

3 → 72

Calls

3 calls:

156.0ms

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

90.0ms

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

84.0ms

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

rewrite51.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary32`
44×	`associate-/r/_binary32`
44×	`associate-*r/_binary32`
38×	`times-frac_binary32`
35×	`*-un-lft-identity_binary32`

Counts

3 → 158

Calls

3 calls:

12.0ms

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

6.0ms

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

5.0ms

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

simplify338.0ms (4%)

Algorithm

1×	egg-herbie

Rules

497×	`times-frac_binary32`
483×	`fma-def_binary32`
267×	`fma-neg_binary32`
205×	`*-commutative_binary32`
190×	`sub-neg_binary32`

Counts

230 → 329

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	710	24186
1	2181	17663
2	4809	17657
3	4983	17657

prune668.0ms (7.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	381	0	381
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	381	8	389

Error

Counts

389 → 8

Alt Table

Status	Error	Program
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))
	0.7b	(exp.f32 (log.f32 (/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))))
▶	0.5b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (cbrt.f32 (fma.f32 alpha alpha -1)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
✓	0.4b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32)))) (/.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))

Compiler

Compiled 31602 to 17082 computations (45.9% saved)

localize58.0ms (0.7%)

Local error

Found 4 expressions with local error:

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

series295.0ms (3.5%)

Counts

4 → 68

Calls

4 calls:

214.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
37.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32))
34.0ms	(/.f32 1/2 (log.f32 alpha))
9.0ms	(*.f32 cosTheta (fma.f32 alpha alpha -1))

rewrite148.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary32`
258×	`add-sqr-sqrt_binary32`
242×	`*-un-lft-identity_binary32`
241×	`add-cube-cbrt_binary32`
163×	`associate-r_binary32`

Counts

4 → 333

Calls

4 calls:

44.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
7.0ms	(*.f32 cosTheta (fma.f32 alpha alpha -1))
5.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32))
2.0ms	(/.f32 1/2 (log.f32 alpha))

simplify231.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

763×	`times-frac_binary32`
411×	`fma-def_binary32`
314×	`*-commutative_binary32`
210×	`associate-*r/_binary32`
157×	`associate-/r*_binary32`

Counts

401 → 518

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	920	15055
1	2674	14650
2	4979	14650

prune912.0ms (10.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	515	3	518
Fresh	3	2	5
Picked	0	1	1
Done	0	2	2
Total	518	8	526

Error

Counts

526 → 8

Alt Table

Status	Error	Program
✓	0.5b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (pow.f32 (.f32 alpha alpha) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (cbrt.f32 (PI.f32)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.4b	(cbrt.f32 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (/.f32 (/.f32 (/.f32 1/8 (pow.f32 (log.f32 alpha) 3)) (pow.f32 (PI.f32) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.4b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.6b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (/.f32 1 (/.f32 (PI.f32) (/.f32 1/2 (log.f32 alpha)))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.6b	(.f32 (-.f32 (.f32 alpha alpha) 1) (/.f32 (.f32 (/.f32 (sqrt.f32 1/2) (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32)))) (/.f32 (/.f32 (sqrt.f32 1/2) (log.f32 alpha)) (cbrt.f32 (PI.f32)))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.6b	(/.f32 (-.f32 (pow.f32 (.f32 alpha alpha) 3) (pow.f32 1 3)) (.f32 (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (+.f32 (pow.f32 alpha 4) (fma.f32 alpha alpha 1))))

Compiler

Compiled 24552 to 14832 computations (39.6% saved)

regimes2.1s (24.9%)

Accuracy

Total 0.4b remaining (95.6%)

Threshold costs 0.4b (95.6%)

Counts

339 → 1

Compiler

Compiled 48440 to 31895 computations (34.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary32`
2×	`+-commutative_binary32`
1×	`sub-neg_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	35
1	24	35
2	25	35
3	23	35

end148.0ms (1.8%)

Compiler: Compiled 308 to 203 computations (34.1% saved)

Details

analyze148.0ms (1.7%)

sample1.8s (21.1%)

simplify47.0ms (0.6%)

prune4.0ms (0%)

localize45.0ms (0.5%)

series129.0ms (1.5%)

rewrite37.0ms (0.4%)

simplify93.0ms (1.1%)

prune330.0ms (3.9%)

localize45.0ms (0.5%)

series111.0ms (1.3%)

rewrite15.0ms (0.2%)

simplify69.0ms (0.8%)

prune254.0ms (3%)

localize56.0ms (0.7%)

series331.0ms (3.9%)

rewrite51.0ms (0.6%)

simplify338.0ms (4%)

prune668.0ms (7.9%)

localize58.0ms (0.7%)

series295.0ms (3.5%)

rewrite148.0ms (1.8%)

simplify231.0ms (2.7%)

prune912.0ms (10.8%)

regimes2.1s (24.9%)

simplify3.0ms (0%)

end148.0ms (1.8%)

Profiling