Details

analyze140.0ms (1.3%)

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)

sample1.9s (18%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify49.0ms (0.5%)

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 (-.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

▶

0.5b

(/.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))))

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)

localize69.0ms (0.7%)

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)
✓	0.4b	(/.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))))
✓	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series146.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

91.0ms	(/.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)))
15.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
9.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite39.0ms (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:

14.0ms	(/.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)
5.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)
5.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

simplify93.0ms (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

prune310.0ms (3%)

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
	0.9b	(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))))
▶	0.4b	(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))))))
	0.9b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (PI.f32) (.f32 (cbrt.f32 (log.f32 (.f32 alpha alpha))) (cbrt.f32 (log.f32 (.f32 alpha alpha))))) (cbrt.f32 (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(/.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))))
	0.5b	(-.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)))
	0.7b	(/.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))))
	0.6b	(.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)))
	0.5b	(.f32 (/.f32 (fma.f32 alpha alpha -1) (.f32 (.f32 2 (.f32 (PI.f32) (log.f32 alpha))) (+.f32 1 (.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 cosTheta 6))))) (+.f32 (.f32 1 1) (-.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta) (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta)) (.f32 1 (.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)))))

Compiler

Compiled 9259 to 4997 computations (46% saved)

localize95.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.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 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
✓	0.6b	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
✓	1.0b	(*.f32 (PI.f32) (PI.f32))

series441.0ms (4.2%)

Counts

4 → 48

Calls

4 calls:

411.0ms	(/.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)))))
25.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
5.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
0.0ms	(*.f32 (PI.f32) (PI.f32))

rewrite431.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Rules

712×	`add-cbrt-cube_binary32`
712×	`add-exp-log_binary32`
519×	`cbrt-unprod_binary32`
519×	`prod-exp_binary32`
93×	`cbrt-undiv_binary32`

Counts

4 → 395

Calls

4 calls:

91.0ms	(/.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)))))
11.0ms	(.f32 (log.f32 (.f32 alpha alpha)) (log.f32 (*.f32 alpha alpha)))
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
3.0ms	(*.f32 (PI.f32) (PI.f32))

simplify452.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

597×	`fma-def_binary32`
494×	`distribute-rgt-in_binary32`
303×	`*-commutative_binary32`
173×	`unswap-sqr_binary32`
167×	`associate-/r*_binary32`

Counts

443 → 450

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1015	41028
1	2713	22276
2	4956	22276

prune961.0ms (9.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	446	4	450
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	451	8	459

Error

Counts

459 → 8

Alt Table

Status	Error	Program
	0.5b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1))) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (fma.f32 alpha alpha 1) (fma.f32 alpha alpha 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)))))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 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 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (.f32 (PI.f32) (PI.f32))) (cbrt.f32 (.f32 (PI.f32) (PI.f32)))) (cbrt.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	(cbrt.f32 (exp.f32 (log.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (.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))))))
	0.7b	(/.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))))
	0.7b	(/.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 (.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))))))
	0.6b	(.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)))

Compiler

Compiled 46993 to 24229 computations (48.4% saved)

localize86.0ms (0.8%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
	0.6b	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
✓	0.7b	(pow.f32 (log.f32 alpha) 3)
✓	1.0b	(pow.f32 (PI.f32) 3)

series73.0ms (0.7%)

Counts

3 → 20

Calls

3 calls:

43.0ms	(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
29.0ms	(pow.f32 (log.f32 alpha) 3)
0.0ms	(pow.f32 (PI.f32) 3)

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary32`
21×	`prod-exp_binary32`
12×	`associate-l_binary32`
12×	`*-un-lft-identity_binary32`
12×	`add-sqr-sqrt_binary32`

Counts

3 → 89

Calls

3 calls:

7.0ms	(.f32 (pow.f32 (PI.f32) 3) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
2.0ms	(pow.f32 (log.f32 alpha) 3)
2.0ms	(pow.f32 (PI.f32) 3)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

777×	`fma-def_binary32`
614×	`*-commutative_binary32`
367×	`exp-prod_binary32`
362×	`log-prod_binary32`
274×	`swap-sqr_binary32`

Counts

109 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	116	1383
1	255	1313
2	1125	1225
3	2440	1212
4	4601	1212
5	4914	1212

prune319.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	187	3	190
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	191	7	198

Error

Counts

198 → 7

Alt Table

Status	Error	Program
	0.5b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1))) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (fma.f32 alpha alpha 1) (fma.f32 alpha alpha 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)))))
	0.7b	(/.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	(cbrt.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 1 (.f32 (.f32 (.f32 (pow.f32 (.f32 (cbrt.f32 (PI.f32)) (cbrt.f32 (PI.f32))) 3) (pow.f32 (cbrt.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)))))
✓	0.4b	(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))))))
	0.6b	(.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)))
	0.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha -1) (+.f32 1 alpha)) (-.f32 alpha 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 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)))))
▶	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 1 (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 8 (pow.f32 (log.f32 alpha) 3))) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))))

Compiler

Compiled 10059 to 6532 computations (35.1% saved)

localize96.0ms (0.9%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
	0.6b	(.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (*.f32 alpha alpha) 1))
	0.7b	(pow.f32 (log.f32 alpha) 3)
✓	1.0b	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

series540.0ms (5.2%)

Counts

2 → 12

Calls

2 calls:

540.0ms	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
0.0ms	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-exp-log_binary32`
35×	`prod-exp_binary32`
25×	`pow-exp_binary32`
20×	`unpow-prod-down_binary32`
15×	`pow-to-exp_binary32`

Counts

2 → 72

Calls

2 calls:

8.0ms	(.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 8 (pow.f32 (log.f32 alpha) 3)))
3.0ms	(pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3))

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

547×	`fma-def_binary32`
511×	`unswap-sqr_binary32`
439×	`distribute-rgt-neg-out_binary32`
425×	`*-commutative_binary32`
350×	`distribute-lft-neg-out_binary32`

Counts

84 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	125	1705
1	274	1378
2	876	1358
3	1913	1325
4	3876	1325
5	4576	1325
6	4988	1325
7	5033	1325

prune376.0ms (3.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	202	1	203
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	203	7	210

Error

Counts

210 → 7

Alt Table

Status	Error	Program
	0.5b	(cbrt.f32 (/.f32 (.f32 (.f32 (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1)) (-.f32 (.f32 (.f32 alpha alpha) (.f32 alpha alpha)) (.f32 1 1))) (-.f32 (.f32 alpha alpha) 1)) (.f32 (.f32 (fma.f32 alpha alpha 1) (fma.f32 alpha alpha 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)))))
	0.7b	(/.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 (.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	(cbrt.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 1 (.f32 (.f32 (expm1.f32 (log1p.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)))) (.f32 8 (pow.f32 (log.f32 alpha) 3))) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))))
	0.6b	(.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)))
	0.5b	(cbrt.f32 (.f32 (.f32 (.f32 (.f32 (fma.f32 alpha alpha -1) (+.f32 1 alpha)) (-.f32 alpha 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 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)))))
✓	0.4b	(cbrt.f32 (.f32 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) (-.f32 (.f32 alpha alpha) 1)) (-.f32 (.f32 alpha alpha) 1)) (/.f32 1 (.f32 (.f32 (pow.f32 (pow.f32 (PI.f32) (sqrt.f32 3)) (sqrt.f32 3)) (.f32 8 (pow.f32 (log.f32 alpha) 3))) (pow.f32 (fma.f32 cosTheta (.f32 cosTheta (fma.f32 alpha alpha -1)) 1) 3)))))

Compiler

Compiled 11288 to 7648 computations (32.2% saved)

regimes3.4s (32.2%)

Accuracy

Total 0.4b remaining (94.8%)

Threshold costs 0.4b (94.8%)

Counts

431 → 1

Compiler

Compiled 87160 to 59073 computations (32.2% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary32`
1×	`+-commutative_binary32`
1×	`sub-neg_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	90
1	40	90
2	41	90
3	39	90

end244.0ms (2.3%)

Compiler: Compiled 469 to 325 computations (30.7% saved)

Details

analyze140.0ms (1.3%)

sample1.9s (18%)

simplify49.0ms (0.5%)

prune4.0ms (0%)

localize69.0ms (0.7%)

series146.0ms (1.4%)

rewrite39.0ms (0.4%)

simplify93.0ms (0.9%)

prune310.0ms (3%)

localize95.0ms (0.9%)

series441.0ms (4.2%)

rewrite431.0ms (4.1%)

simplify452.0ms (4.3%)

prune961.0ms (9.2%)

localize86.0ms (0.8%)

series73.0ms (0.7%)

rewrite14.0ms (0.1%)

simplify84.0ms (0.8%)

prune319.0ms (3.1%)

localize96.0ms (0.9%)

series540.0ms (5.2%)

rewrite15.0ms (0.1%)

simplify116.0ms (1.1%)

prune376.0ms (3.6%)

regimes3.4s (32.2%)

simplify4.0ms (0%)

end244.0ms (2.3%)

Profiling