Details

analyze123.0ms (1.1%)

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)

sample2.0s (17.5%)

Results

2.0s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% 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

0.5b

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)

localize49.0ms (0.4%)

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))))
✓	0.3b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series129.0ms (1.1%)

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

rewrite36.0ms (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)
6.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify101.0ms (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 (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	223	8	231
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	225	8	233

Error

0.0b

Counts

233 → 8

Alt Table

Status	Error	Program
	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)))))
	0.7b	(/.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))))
	0.5b	(/.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)))))
	0.6b	(.f32 (sqrt.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)))) (sqrt.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)))))
	0.7b	(.f32 (/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
▶	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))))))
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))))

Compiler

Compiled 9173 to 4927 computations (46.3% saved)

localize94.0ms (0.8%)

Local error

Found 4 expressions with local error:

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

series63.0ms (0.5%)

Counts

4 → 36

Calls

4 calls:

32.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
27.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
3.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`pow1_binary32`
42×	`log-pow_binary32`
32×	`add-sqr-sqrt_binary32`
31×	`*-un-lft-identity_binary32`
28×	`swap-sqr_binary32`

Counts

4 → 181

Calls

4 calls:

10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
10.0ms	(.f32 (.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (.f32 alpha alpha))) (log.f32 (*.f32 alpha alpha)))
7.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
4.0ms	(*.f32 (PI.f32) (PI.f32))

simplify148.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

520×	`distribute-rgt-in_binary32`
466×	`distribute-lft-in_binary32`
392×	`fma-def_binary32`
389×	`fma-neg_binary32`
325×	`*-commutative_binary32`

Counts

217 → 218

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3094
1	367	2456
2	1195	2224
3	3763	2176
4	4968	2176
5	5169	2176

prune427.0ms (3.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	216	2	218
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	217	9	226

Error

0.0b

Counts

226 → 9

Alt Table

Status	Error	Program
▶	0.4b	(cbrt.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 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))))))
	0.8b	(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)))))
	0.7b	(/.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))))
	0.5b	(/.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)))))
	0.6b	(.f32 (sqrt.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)))) (sqrt.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)))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (cbrt.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
✓	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))))))
	0.5b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.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))))))
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))))

Compiler

Compiled 18345 to 8560 computations (53.3% saved)

localize98.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 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 (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))

series517.0ms (4.5%)

Counts

1 → 24

Calls

1 calls:

517.0ms

(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha -2) 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)))))

rewrite270.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

438×	`add-cbrt-cube_binary32`
438×	`add-exp-log_binary32`
313×	`cbrt-unprod_binary32`
313×	`prod-exp_binary32`
62×	`cbrt-undiv_binary32`

Counts

1 → 167

Calls

1 calls:

62.0ms

(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha -2) 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)))))

simplify377.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary32`
320×	`distribute-rgt-in_binary32`
319×	`distribute-lft-in_binary32`
270×	`*-commutative_binary32`
182×	`associate-/r*_binary32`

Counts

191 → 202

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	935	34009
1	2723	20110
2	5067	20110

prune855.0ms (7.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	331	3	334
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	334	9	343

Error

Counts

343 → 9

Alt Table

Status	Error	Program
	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)))))
	0.7b	(/.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))))
	10.3b	(cbrt.f32 (log.f32 (exp.f32 (/.f32 (.f32 (fma.f32 alpha alpha -1) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1)) (.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 (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 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (-.f32 (.f32 alpha alpha) 1) (*.f32 cosTheta cosTheta)))))
	0.6b	(.f32 (sqrt.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)))) (sqrt.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	(cbrt.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.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))))))
✓	0.4b	(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))))))
	0.7b	(/.f32 (.f32 (cbrt.f32 (-.f32 (.f32 alpha alpha) 1)) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))) (/.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))) (cbrt.f32 (-.f32 (.f32 alpha alpha) 1))))
▶	0.4b	(cbrt.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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))))))

Compiler

Compiled 37775 to 20424 computations (45.9% saved)

localize113.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (log.f32 (*.f32 alpha alpha)))
✓	0.5b	(pow.f32 (log.f32 (/.f32 1 alpha)) 2)
	1.0b	(*.f32 (PI.f32) (PI.f32))

series1.6s (13.4%)

Counts

3 → 44

Calls

3 calls:

1.5s

(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (*.f32 alpha alpha) 1)) (*.f32 (*.f32 (*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)) (*.f32 (*.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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)))))

55.0ms

(*.f32 (*.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (log.f32 (*.f32 alpha alpha)))

23.0ms

(pow.f32 (log.f32 (/.f32 1 alpha)) 2)

rewrite269.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

739×	`add-exp-log_binary32`
554×	`prod-exp_binary32`
445×	`add-cbrt-cube_binary32`
316×	`cbrt-unprod_binary32`
98×	`div-exp_binary32`

Counts

3 → 255

Calls

3 calls:

41.0ms

(/.f32 (*.f32 (fma.f32 (*.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (*.f32 alpha alpha) 1)) (*.f32 (*.f32 (*.f32 (*.f32 (PI.f32) (PI.f32)) (PI.f32)) (*.f32 (*.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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)))))

7.0ms

(*.f32 (*.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (log.f32 (*.f32 alpha alpha)))

2.0ms

(pow.f32 (log.f32 (/.f32 1 alpha)) 2)

simplify591.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

471×	`*-commutative_binary32`
278×	`fma-def_binary32`
277×	`associate-/r*_binary32`
273×	`associate-+r+_binary32`
214×	`associate-*r/_binary32`

Counts

299 → 310

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1457	47651
1	4215	30620
2	4971	30521
3	4949	30521

prune1.3s (11%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	338	2	340
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	340	9	349

Error

Counts

349 → 9

Alt Table

Status	Error	Program
	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)))))
	0.7b	(/.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))))
	10.3b	(cbrt.f32 (log.f32 (exp.f32 (/.f32 (.f32 (fma.f32 alpha alpha -1) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1)) (.f32 (.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 (log.f32 alpha) 3))) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3))))))
	0.5b	(cbrt.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 5) (cbrt.f32 (PI.f32))) (PI.f32)) (.f32 (.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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 (-.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)))))
	0.6b	(.f32 (sqrt.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)))) (sqrt.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)))))
	0.4b	(cbrt.f32 (cbrt.f32 (/.f32 (pow.f32 (.f32 (fma.f32 alpha alpha -1) (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1)) 3) (.f32 (pow.f32 (pow.f32 (+.f32 1 (.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)))) 3) 3) (.f32 (pow.f32 (pow.f32 (*.f32 2 (log.f32 alpha)) 3) 3) (pow.f32 (pow.f32 (PI.f32) 3) 3))))))
✓	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))))))
✓	0.4b	(cbrt.f32 (/.f32 (.f32 (fma.f32 (.f32 alpha alpha) (fma.f32 alpha alpha -2) 1) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (PI.f32) (PI.f32)) (PI.f32)) (.f32 (.f32 4 (pow.f32 (log.f32 (/.f32 1 alpha)) 2)) (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))))))

Compiler

Compiled 47743 to 30917 computations (35.2% saved)

regimes1.8s (15.5%)

Accuracy

Total 0.4b remaining (96%)

Threshold costs 0.4b (96%)

Counts

246 → 1

Compiler

Compiled 53409 to 33953 computations (36.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	113
1	39	113
2	40	113
3	38	113

end263.0ms (2.3%)

Compiler: Compiled 602 to 369 computations (38.7% saved)

Details

analyze123.0ms (1.1%)

sample2.0s (17.5%)

simplify48.0ms (0.4%)

prune4.0ms (0%)

localize49.0ms (0.4%)

series129.0ms (1.1%)

rewrite36.0ms (0.3%)

simplify101.0ms (0.9%)

prune321.0ms (2.8%)

localize94.0ms (0.8%)

series63.0ms (0.5%)

rewrite43.0ms (0.4%)

simplify148.0ms (1.3%)

prune427.0ms (3.7%)

localize98.0ms (0.8%)

series517.0ms (4.5%)

rewrite270.0ms (2.3%)

simplify377.0ms (3.2%)

prune855.0ms (7.4%)

localize113.0ms (1%)

series1.6s (13.4%)

rewrite269.0ms (2.3%)

simplify591.0ms (5.1%)

prune1.3s (11%)

regimes1.8s (15.5%)

simplify4.0ms (0%)

end263.0ms (2.3%)

Profiling