Details

analyze118.0ms (1%)

Algorithm

1×

Search

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

Compiler

Compiled 41 to 27 computations (34.1% saved)

sample93.0ms (0.8%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
6.0ms	256×	pre	128	true

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify48.0ms (0.4%)

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 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.5b	(/.f32 (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)))

Status

Error

Program

▶

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))))

0.5b

(/.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)))

Compiler

Compiled 145 to 87 computations (40% saved)

localize45.0ms (0.4%)

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)))

series132.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

79.0ms	(/.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))))
29.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
14.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite33.0ms (0.3%)

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))))
6.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
5.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify97.0ms (0.8%)

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

prune292.0ms (2.4%)

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
	1.0b	(.f32 (.f32 (cbrt.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)))) (cbrt.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))))) (cbrt.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)))))
	0.8b	(/.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))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 alpha 1) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.4b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (log.f32 (pow.f32 (.f32 alpha alpha) (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (+.f32 (.f32 alpha alpha) 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))))
▶	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	10.9b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 9153 to 4939 computations (46% saved)

localize74.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
✓	0.7b	(pow.f32 (fma.f32 alpha alpha -1) 3)
✓	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
✓	1.0b	(pow.f32 (PI.f32) 3)

series1.8s (15%)

Counts

4 → 48

Calls

4 calls:

1.8s	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
28.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
3.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite55.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

359×	`add-exp-log_binary32`
253×	`prod-exp_binary32`
173×	`pow-exp_binary32`
145×	`pow-to-exp_binary32`
120×	`div-exp_binary32`

Counts

4 → 234

Calls

4 calls:

11.0ms	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
3.0ms	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
2.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)
2.0ms	(pow.f32 (PI.f32) 3)

simplify413.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

365×	`*-commutative_binary32`
319×	`+-commutative_binary32`
302×	`fma-def_binary32`
271×	`associate-+r+_binary32`
251×	`associate-/r*_binary32`

Counts

282 → 231

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1226	23961
1	4248	23692
2	4990	23692
3	4955	23692

prune679.0ms (5.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	3	231
Fresh	4	4	8
Picked	0	1	1
Done	0	0	0
Total	232	8	240

Error

Counts

240 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 alpha 1) (+.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 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.f32 (PI.f32)) 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.6b	(cbrt.f32 (/.f32 (-.f32 (fma.f32 3 (.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (.f32 3 (pow.f32 alpha 4)))) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	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))))
	10.9b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 26096 to 20293 computations (22.2% saved)

localize79.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))
	0.7b	(pow.f32 (fma.f32 alpha alpha -1) 3)
	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
✓	1.0b	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

series2.0s (16.3%)

Counts

2 → 24

Calls

2 calls:

2.0s

(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))

0.0ms

(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

rewrite83.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

558×	`add-exp-log_binary32`
414×	`prod-exp_binary32`
365×	`pow-exp_binary32`
246×	`pow-to-exp_binary32`
192×	`div-exp_binary32`

Counts

2 → 260

Calls

2 calls:

14.0ms

(/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (*.f32 (*.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (*.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))

3.0ms

(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

simplify423.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

359×	`*-commutative_binary32`
328×	`+-commutative_binary32`
304×	`fma-def_binary32`
271×	`associate-+r+_binary32`
251×	`associate-/r*_binary32`

Counts

284 → 179

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1242	28158
1	4215	26378
2	4976	26378

prune826.0ms (6.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	252	2	254
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	254	8	262

Error

Counts

262 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 alpha 1) (+.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 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.8b	(cbrt.f32 (exp.f32 (log.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))))
	0.6b	(cbrt.f32 (/.f32 (-.f32 (fma.f32 3 (.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (.f32 3 (pow.f32 alpha 4)))) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
▶	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)))) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	10.9b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 29346 to 23034 computations (21.5% saved)

localize60.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series285.0ms (2.4%)

Counts

3 → 72

Calls

3 calls:

136.0ms

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

79.0ms

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

69.0ms

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

rewrite66.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`prod-diff_binary32`
45×	`add-exp-log_binary32`
44×	`associate-/r/_binary32`
44×	`associate-*r/_binary32`
38×	`times-frac_binary32`

Counts

3 → 167

Calls

3 calls:

15.0ms

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

9.0ms

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

8.0ms

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

simplify376.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

602×	`times-frac_binary32`
492×	`fma-def_binary32`
275×	`fma-neg_binary32`
211×	`*-commutative_binary32`
193×	`sub-neg_binary32`

Counts

239 → 339

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	725	24615
1	2233	17915
2	4896	17911
3	5052	17911

prune660.0ms (5.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	427	0	427
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	427	8	435

Error

Counts

435 → 8

Alt Table

Status	Error	Program
	0.5b	(.f32 (/.f32 (+.f32 alpha 1) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (-.f32 alpha 1) (+.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 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	0.8b	(cbrt.f32 (exp.f32 (log.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))))
	0.6b	(cbrt.f32 (/.f32 (-.f32 (fma.f32 3 (.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (.f32 3 (pow.f32 alpha 4)))) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.5b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)))) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))
	0.7b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)))) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
✓	0.4b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))
	10.9b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))

Compiler

Compiled 33777 to 17997 computations (46.7% saved)

regimes1.3s (10.7%)

Accuracy

Total 0.4b remaining (96.1%)

Threshold costs 0.4b (96.1%)

Counts

215 → 1

Compiler

Compiled 31016 to 21228 computations (31.6% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	52
1	29	52
2	28	52

end1.0ms (0%)

Compiler: Compiled 36 to 29 computations (19.4% saved)

sample2.0s (16.8%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
212.0ms	8000×	pre	128	true

Compiler

Compiled 352 to 262 computations (25.6% saved)

Details

analyze118.0ms (1%)

sample93.0ms (0.8%)

simplify48.0ms (0.4%)

prune4.0ms (0%)

localize45.0ms (0.4%)

series132.0ms (1.1%)

rewrite33.0ms (0.3%)

simplify97.0ms (0.8%)

prune292.0ms (2.4%)

localize74.0ms (0.6%)

series1.8s (15%)

rewrite55.0ms (0.5%)

simplify413.0ms (3.4%)

prune679.0ms (5.7%)

localize79.0ms (0.7%)

series2.0s (16.3%)

rewrite83.0ms (0.7%)

simplify423.0ms (3.5%)

prune826.0ms (6.9%)

localize60.0ms (0.5%)

series285.0ms (2.4%)

rewrite66.0ms (0.6%)

simplify376.0ms (3.1%)

prune660.0ms (5.5%)

regimes1.3s (10.7%)

simplify4.0ms (0%)

end1.0ms (0%)

sample2.0s (16.8%)

Profiling