Details

analyze120.0ms (0.6%)

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)

sample99.0ms (0.5%)

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)

simplify49.0ms (0.2%)

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

prune5.0ms (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)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.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 (0.6%)

Counts

4 → 84

Calls

4 calls:

80.0ms	(/.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)))
14.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite35.0ms (0.2%)

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))))
7.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
6.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify98.0ms (0.5%)

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

prune319.0ms (1.5%)

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
	0.6b	(.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)))
	0.7b	(/.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))))
	0.8b	(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)))))
	0.6b	(/.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (.f32 (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)) (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))))
	0.5b	(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))))))
	0.5b	(/.f32 1 (/.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1))))
	0.5b	(-.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)))
	0.9b	(.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))))))

Compiler

Compiled 9249 to 4983 computations (46.1% saved)

localize73.0ms (0.3%)

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 (8.7%)

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 (0.3%)

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:

10.0ms	(/.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)
1.0ms	(pow.f32 (fma.f32 alpha alpha -1) 3)

simplify432.0ms (2.1%)

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

prune693.0ms (3.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	234	6	240

Error

Counts

240 → 6

Alt Table

Status	Error	Program
	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	(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))))
	0.6b	(.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)))
	0.8b	(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)))))
	0.6b	(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))))
▶	0.5b	(-.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)))

Compiler

Compiled 25998 to 20224 computations (22.2% saved)

localize70.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series559.0ms (2.7%)

Counts

4 → 68

Calls

4 calls:

330.0ms	(-.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)))
163.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
38.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32))
28.0ms	(*.f32 (PI.f32) (log.f32 alpha))

rewrite627.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

2712×	`times-frac_binary32`
1290×	`add-sqr-sqrt_binary32`
1276×	`*-un-lft-identity_binary32`
1274×	`add-cube-cbrt_binary32`
800×	`prod-diff_binary32`

Counts

4 → 1126

Calls

4 calls:

86.0ms	(-.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)))
7.0ms	(/.f32 (.f32 alpha alpha) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (fma.f32 cosTheta (*.f32 cosTheta (fma.f32 alpha alpha -1)) 1)))
5.0ms	(/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32))
3.0ms	(*.f32 (PI.f32) (log.f32 alpha))

simplify4.2s (19.8%)

Algorithm

1×	egg-herbie

Rules

722×	`fma-udef_binary32`
358×	`neg-mul-1_binary32`
356×	`neg-sub0_binary32`
232×	`distribute-neg-frac_binary32`
187×	`fma-def_binary32`

Counts

1194 → 1549

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2398	213832
1	4979	213790
2	4996	213790

prune4.7s (22.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1549	0	1549
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	1549	6	1555

Error

Counts

1555 → 6

Alt Table

Status	Error	Program
	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	(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))))
	0.6b	(.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)))
	0.8b	(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)))))
	0.6b	(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))))
✓	0.5b	(-.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)))

Compiler

Compiled 196750 to 113168 computations (42.5% saved)

localize99.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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 (fma.f32 3 (.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (.f32 3 (pow.f32 alpha 4))))
	0.7b	(pow.f32 (*.f32 2 (log.f32 alpha)) 3)
	1.0b	(pow.f32 (PI.f32) 3)

series2.0s (9.6%)

Counts

2 → 36

Calls

2 calls:

2.0s

(/.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)))

4.0ms

(-.f32 (fma.f32 3 (*.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (*.f32 3 (pow.f32 alpha 4))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-exp-log_binary32`
84×	`prod-exp_binary32`
43×	`pow-exp_binary32`
40×	`div-exp_binary32`
34×	`pow-to-exp_binary32`

Counts

2 → 102

Calls

2 calls:

13.0ms

(/.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)))

7.0ms

(-.f32 (fma.f32 3 (*.f32 alpha alpha) (pow.f32 alpha 6)) (+.f32 1 (*.f32 3 (pow.f32 alpha 4))))

simplify328.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

386×	`*-commutative_binary32`
363×	`+-commutative_binary32`
343×	`fma-def_binary32`
312×	`associate-+r+_binary32`
270×	`associate-/r*_binary32`

Counts

138 → 158

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1296	24583
1	4631	24152
2	4989	24152

prune754.0ms (3.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	222	0	222
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	222	6	228

Error

Counts

228 → 6

Alt Table

Status	Error	Program
	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	(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))))
	0.6b	(.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)))
	0.8b	(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)))))
	0.6b	(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))))
✓	0.5b	(-.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)))

Compiler

Compiled 30522 to 23573 computations (22.8% saved)

regimes1.7s (8.2%)

Accuracy

Total 0.4b remaining (91.2%)

Threshold costs 0.4b (91.2%)

Counts

267 → 1

Compiler

Compiled 39945 to 27486 computations (31.2% 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)

sample1.9s (9.2%)

Algorithm

1×

intervals

Results

988.0ms	8000×	body	128	valid
206.0ms	8000×	pre	128	true

Compiler

Compiled 285 to 202 computations (29.1% saved)

Details

analyze120.0ms (0.6%)

sample99.0ms (0.5%)

simplify49.0ms (0.2%)

prune5.0ms (0%)

localize48.0ms (0.2%)

series132.0ms (0.6%)

rewrite35.0ms (0.2%)

simplify98.0ms (0.5%)

prune319.0ms (1.5%)

localize73.0ms (0.3%)

series1.8s (8.7%)

rewrite55.0ms (0.3%)

simplify432.0ms (2.1%)

prune693.0ms (3.3%)

localize70.0ms (0.3%)

series559.0ms (2.7%)

rewrite627.0ms (3%)

simplify4.2s (19.8%)

prune4.7s (22.2%)

localize99.0ms (0.5%)

series2.0s (9.6%)

rewrite36.0ms (0.2%)

simplify328.0ms (1.6%)

prune754.0ms (3.6%)

regimes1.7s (8.2%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.9s (9.2%)

Profiling