Details

analyze124.0ms (1.2%)

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 (0.9%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
7.0ms	256×	pre	128	true

Compiler

Compiled 69 to 45 computations (34.8% saved)

simplify46.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	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)))
▶	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 (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)))

▶

0.5b

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

localize46.0ms (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)))

series128.0ms (1.2%)

Counts

4 → 84

Calls

4 calls:

75.0ms	(/.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))))
30.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
12.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite37.0ms (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:

10.0ms	(/.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))))
8.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
7.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

simplify97.0ms (0.9%)

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

prune321.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	221	10	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	223	10	233

Error

0.0b

Counts

233 → 10

Alt Table

Status	Error	Program
	0.6b	(/.f32 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)))
	0.7b	(/.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 (+.f32 alpha 1) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 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))))
	0.6b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	10.3b	(/.f32 -1/2 (.f32 (-.f32 1 (pow.f32 cosTheta 2)) (.f32 (PI.f32) (log.f32 alpha))))
	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)))
	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.7b	(.f32 (sqrt.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))))) (sqrt.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))))))

Compiler

Compiled 9163 to 4949 computations (46% saved)

localize68.0ms (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 (16.8%)

Counts

4 → 48

Calls

4 calls:

1.7s	(/.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)))
35.0ms	(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:

12.0ms	(/.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 (PI.f32) 3)
2.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)

simplify405.0ms (3.8%)

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

prune658.0ms (6.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	234	7	241

Error

Counts

241 → 7

Alt Table

Status	Error	Program
	0.6b	(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	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.7b	(/.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))))
	1.2b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (.f32 (cbrt.f32 3) (cbrt.f32 3))) (cbrt.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) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))

Compiler

Compiled 26056 to 20253 computations (22.3% saved)

localize68.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	0.4b	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
✓	0.5b	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series138.0ms (1.3%)

Counts

4 → 48

Calls

4 calls:

75.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
32.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
30.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite45.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`pow1_binary32`
42×	`log-pow_binary32`
22×	`add-sqr-sqrt_binary32`
21×	`associate-r_binary32`
21×	`*-un-lft-identity_binary32`

Counts

4 → 155

Calls

4 calls:

15.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
9.0ms	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
7.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Rules

551×	`associate-l_binary32`
516×	`associate-/r*_binary32`
496×	`times-frac_binary32`
243×	`associate-/l*_binary32`
182×	`fma-def_binary32`

Counts

203 → 228

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	411	6724
1	1237	4967
2	5006	4967

prune265.0ms (2.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	228	7	235

Error

Counts

235 → 7

Alt Table

Status	Error	Program
	0.6b	(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))))
✓	0.5b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (cbrt.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 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	0.6b	(/.f32 (+.f32 alpha 1) (/.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.6b	(-.f32 (/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1))) (/.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
	0.7b	(/.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))))
	1.2b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (.f32 (cbrt.f32 3) (cbrt.f32 3))) (cbrt.f32 3)) (pow.f32 (.f32 2 (log.f32 alpha)) 3)) (pow.f32 (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))

Compiler

Compiled 11331 to 5368 computations (52.6% saved)

localize100.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))
✓	0.4b	(/.f32 (+.f32 alpha 1) (/.f32 (cbrt.f32 (.f32 (pow.f32 (PI.f32) 3) (pow.f32 (.f32 2 (log.f32 alpha)) 3))) (/.f32 (+.f32 alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
	1.0b	(pow.f32 (PI.f32) 3)

series281.0ms (2.7%)

Counts

2 → 36

Calls

2 calls:

228.0ms

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

53.0ms

(*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3))

rewrite333.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

1004×	`times-frac_binary32`
652×	`*-un-lft-identity_binary32`
438×	`add-sqr-sqrt_binary32`
368×	`add-cube-cbrt_binary32`
142×	`distribute-lft-out_binary32`

Counts

2 → 482

Calls

2 calls:

19.0ms

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

6.0ms

(*.f32 (pow.f32 (PI.f32) 3) (pow.f32 (*.f32 2 (log.f32 alpha)) 3))

simplify570.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

519×	`associate-/r/_binary32`
512×	`fma-def_binary32`
205×	`*-commutative_binary32`
155×	`distribute-rgt-in_binary32`
150×	`distribute-lft-in_binary32`

Counts

518 → 685

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1179	40187
1	3284	39737
2	5085	39737

prune1.3s (12.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	748	1	749
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	750	6	756

Error

Counts

756 → 6

Alt Table

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

Compiler

Compiled 45027 to 32175 computations (28.5% saved)

regimes1.9s (18.3%)

Accuracy

Total 0.4b remaining (94.1%)

Threshold costs 0.4b (94.1%)

Counts

307 → 1

Compiler

Compiled 44747 to 31491 computations (29.6% saved)

simplify3.0ms (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)

sample1.6s (15%)

Algorithm

1×

intervals

Results

799.0ms	8000×	body	128	valid
210.0ms	8000×	pre	128	true

Compiler

Compiled 303 to 212 computations (30% saved)

Details

analyze124.0ms (1.2%)

sample93.0ms (0.9%)

simplify46.0ms (0.4%)

prune4.0ms (0%)

localize46.0ms (0.4%)

series128.0ms (1.2%)

rewrite37.0ms (0.3%)

simplify97.0ms (0.9%)

prune321.0ms (3%)

localize68.0ms (0.6%)

series1.8s (16.8%)

rewrite55.0ms (0.5%)

simplify405.0ms (3.8%)

prune658.0ms (6.2%)

localize68.0ms (0.6%)

series138.0ms (1.3%)

rewrite45.0ms (0.4%)

simplify107.0ms (1%)

prune265.0ms (2.5%)

localize100.0ms (0.9%)

series281.0ms (2.7%)

rewrite333.0ms (3.1%)

simplify570.0ms (5.4%)

prune1.3s (12.3%)

regimes1.9s (18.3%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.6s (15%)

Profiling