Details

analyze130.0ms (1.4%)

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)

sample1.8s (20%)

Results

1.8s

8256×

body

128

valid

Compiler

Compiled 108 to 70 computations (35.2% saved)

simplify59.0ms (0.6%)

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)

localize47.0ms (0.5%)

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)))

series126.0ms (1.4%)

Counts

4 → 84

Calls

4 calls:

76.0ms	(/.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))))
27.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
13.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
10.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

rewrite345.0ms (3.7%)

Algorithm

4×	egg-rewrite

Rules

83×	`egg`
51×	`egg`
44×	`egg`
38×	`egg`

Counts

4 → 216

Calls

4 calls:

113.0ms	(.f32 (.f32 (-.f32 (*.f32 alpha alpha) 1) cosTheta) cosTheta)
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))))
83.0ms	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))
53.0ms	(.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	115	10
2	1269	10
3	4972	10
4	5080	10
0	14	33
1	310	31
2	4242	31
3	4972	31
0	7	8
1	148	8
2	1655	8
3	5214	8
0	8	11
1	169	11
2	1924	11
3	4991	11
4	4949	11
5	4943	11

simplify100.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

335×	`associate-/r*_binary32`
303×	`cancel-sign-sub-inv_binary32`
267×	`associate-r_binary32`
258×	`fma-neg_binary32`
223×	`sub-neg_binary32`

Counts

300 → 270

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	264	3015
1	865	2707
2	3733	2705
3	4989	2705

prune432.0ms (4.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	261	9	270
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	263	9	272

Error

Counts

272 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1)))
	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.7b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (*.f32 (PI.f32) (log.f32 alpha))))))))
▶	0.5b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)))

Compiler

Compiled 10099 to 5269 computations (47.8% saved)

localize139.0ms (1.5%)

Local error

Found 4 expressions with local error:

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

series616.0ms (6.7%)

Counts

3 → 60

Calls

3 calls:

429.0ms

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

183.0ms

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

3.0ms

(pow.f32 (fma.f32 alpha alpha -1) 3)

rewrite227.0ms (2.5%)

Algorithm

3×	egg-rewrite

Rules

59×	`egg`
46×	`egg`
37×	`egg`

Counts

3 → 142

Calls

3 calls:

82.0ms

(pow.f32 (fma.f32 alpha alpha -1) 3)

77.0ms

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

64.0ms

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	27
1	291	27
2	3028	27
3	5031	27
0	6	8
1	119	8
2	1181	8
3	4716	8
4	5961	8
0	17	37
1	338	34
2	3733	34
3	4973	34

simplify200.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary32`
799×	`times-frac_binary32`
340×	`*-commutative_binary32`
199×	`+-commutative_binary32`
181×	`associate-r_binary32`

Counts

202 → 232

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	787	11302
1	2638	11110
2	5041	11110

prune560.0ms (6.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	287	9	296

Error

Counts

296 → 9

Alt Table

Status	Error	Program
	0.6b	(/.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1)))
▶	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.7b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (*.f32 (PI.f32) (log.f32 alpha))))))))
✓	0.5b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)))

Compiler

Compiled 19561 to 12951 computations (33.8% saved)

localize51.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.2b	(/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))))
✓	0.3b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series131.0ms (1.4%)

Counts

3 → 48

Calls

3 calls:

76.0ms

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

35.0ms

(/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

20.0ms

(log.f32 (*.f32 alpha alpha))

rewrite201.0ms (2.2%)

Algorithm

3×	egg-rewrite

Rules

102×	`egg`
46×	`egg`
39×	`egg`

Counts

3 → 187

Calls

3 calls:

112.0ms

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

46.0ms

(/.f32 1 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))))

39.0ms

(log.f32 (*.f32 alpha alpha))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	300	31
2	3643	31
3	4962	31
4	5285	31
0	8	13
1	156	13
2	1711	13
3	5123	13
0	4	6
1	76	6
2	806	6
3	4902	6

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Rules

355×	`associate-/r*_binary32`
300×	`cancel-sign-sub-inv_binary32`
266×	`associate-r_binary32`
247×	`fma-neg_binary32`
224×	`times-frac_binary32`

Counts

235 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	2530
1	849	2357
2	3781	2355
3	5025	2355

prune316.0ms (3.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	290	0	290
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	290	9	299

Error

Counts

299 → 9

Alt Table

Status	Error	Program
▶	0.6b	(/.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1)))
✓	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.7b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (*.f32 (PI.f32) (log.f32 alpha))))))))
✓	0.5b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)))

Compiler

Compiled 10294 to 5454 computations (47% saved)

localize67.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(log.f32 (*.f32 alpha alpha))
✓	0.3b	(/.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1)))
✓	0.4b	(.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1))
	0.4b	(.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))

series313.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

175.0ms

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

138.0ms

(*.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1))

rewrite161.0ms (1.7%)

Algorithm

2×	egg-rewrite

Rules

66×	`egg`
46×	`egg`

Counts

2 → 112

Calls

2 calls:

89.0ms

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

69.0ms

(*.f32 (*.f32 (*.f32 (PI.f32) (log.f32 (*.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	286	31
2	3138	31
3	5342	31
0	19	40
1	388	40
2	4603	40
3	5310	40

simplify159.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

591×	`associate-/r*_binary32`
417×	`associate-l_binary32`
352×	`times-frac_binary32`
277×	`fma-def_binary32`
204×	`associate-/l*_binary32`

Counts

160 → 177

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	412	6974
1	1365	6025
2	4968	6025
3	5094	6025

prune380.0ms (4.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	282	0	282
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	282	9	291

Error

Counts

291 → 9

Alt Table

Status	Error	Program
✓	0.6b	(/.f32 (+.f32 (pow.f32 alpha 4) -1) (.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (*.f32 cosTheta cosTheta) 1)) (fma.f32 alpha alpha 1)))
✓	0.5b	(.f32 (/.f32 1 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha)))) (/.f32 (fma.f32 alpha alpha -1) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))
	0.7b	(.f32 (/.f32 (+.f32 alpha 1) (PI.f32)) (/.f32 (+.f32 alpha -1) (.f32 (log.f32 (.f32 alpha alpha)) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1))))
	0.8b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (.f32 (log.f32 (.f32 alpha alpha)) (pow.f32 (cbrt.f32 (PI.f32)) 2)) (cbrt.f32 (PI.f32))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.7b	(pow.f32 (sqrt.f32 (/.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)))) 2)
	0.7b	(.f32 (+.f32 alpha 1) (.f32 (+.f32 alpha -1) (/.f32 1 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)))))
	0.7b	(/.f32 (-.f32 (.f32 alpha alpha) 1) (.f32 (.f32 (pow.f32 (cbrt.f32 (PI.f32)) 2) (.f32 (cbrt.f32 (PI.f32)) (log.f32 (.f32 alpha alpha)))) (+.f32 1 (.f32 (.f32 (-.f32 (.f32 alpha alpha) 1) cosTheta) cosTheta))))
	0.9b	(-.f32 (fma.f32 3 (.f32 (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (pow.f32 cosTheta 4)) (fma.f32 2 (/.f32 (.f32 (.f32 cosTheta cosTheta) (.f32 alpha alpha)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (fma.f32 (/.f32 (pow.f32 cosTheta 4) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 6) (PI.f32)) (/.f32 (.f32 alpha alpha) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))))) (+.f32 (/.f32 (/.f32 1/2 (log.f32 alpha)) (PI.f32)) (+.f32 (fma.f32 (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (log.f32 alpha))) (/.f32 (pow.f32 alpha 4) (PI.f32)) (/.f32 (pow.f32 cosTheta 4) (.f32 2 (.f32 (PI.f32) (log.f32 alpha))))) (fma.f32 3 (/.f32 (.f32 (pow.f32 alpha 4) (pow.f32 cosTheta 4)) (.f32 2 (.f32 (PI.f32) (log.f32 alpha)))) (/.f32 (.f32 cosTheta cosTheta) (.f32 2 (*.f32 (PI.f32) (log.f32 alpha))))))))
✓	0.5b	(cbrt.f32 (/.f32 (pow.f32 (fma.f32 alpha alpha -1) 3) (pow.f32 (.f32 (.f32 (PI.f32) (log.f32 (.f32 alpha alpha))) (fma.f32 (fma.f32 alpha alpha -1) (.f32 cosTheta cosTheta) 1)) 3)))

Compiler

Compiled 13531 to 8178 computations (39.6% saved)

regimes2.3s (25.1%)

Accuracy

Total 0.4b remaining (93.2%)

Threshold costs 0.4b (93.2%)

Counts

358 → 1

Compiler

Compiled 43218 to 28982 computations (32.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	23	37
2	24	37
3	22	37

end208.0ms (2.3%)

Compiler: Compiled 395 to 249 computations (37% saved)

Details

analyze130.0ms (1.4%)

sample1.8s (20%)

simplify59.0ms (0.6%)

prune4.0ms (0%)

localize47.0ms (0.5%)

series126.0ms (1.4%)

rewrite345.0ms (3.7%)

simplify100.0ms (1.1%)

prune432.0ms (4.7%)

localize139.0ms (1.5%)

series616.0ms (6.7%)

rewrite227.0ms (2.5%)

simplify200.0ms (2.2%)

prune560.0ms (6.1%)

localize51.0ms (0.6%)

series131.0ms (1.4%)

rewrite201.0ms (2.2%)

simplify90.0ms (1%)

prune316.0ms (3.4%)

localize67.0ms (0.7%)

series313.0ms (3.4%)

rewrite161.0ms (1.7%)

simplify159.0ms (1.7%)

prune380.0ms (4.1%)

regimes2.3s (25.1%)

simplify3.0ms (0%)

end208.0ms (2.3%)

Profiling