Details

analyze160.0ms (0.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	28.1%	71.9%	0
0%	28.1%	71.9%	1
0%	28.1%	71.9%	2
0%	28.1%	71.9%	3
3.5%	24.6%	71.9%	4
5.3%	22.8%	71.9%	5
10.5%	17.5%	71.9%	6
14%	14%	71.9%	7
19.1%	9%	71.9%	8
24.6%	3.5%	71.9%	9
25.1%	3%	71.9%	10
25.8%	2.3%	71.9%	11
26.3%	1.8%	71.9%	12
26.6%	1.5%	71.9%	13
26.9%	1.2%	71.9%	14

Compiler

Compiled 43 to 28 computations (34.9% saved)

sample1.9s (7%)

Results

1.1s	6737×	body	128	valid
375.0ms	662×	body	1024	valid
208.0ms	498×	body	512	valid
85.0ms	310×	body	256	valid
32.0ms	49×	body	2048	valid

Compiler

Compiled 118 to 76 computations (35.6% saved)

simplify42.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

817×	`distribute-rgt-in_binary64`
748×	`distribute-lft-in_binary64`
245×	`+-commutative_binary64`
193×	`associate-+l+_binary64`
184×	`fma-def_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	16	43
1	34	39
2	112	37
3	520	37
4	2735	37
5	4514	37

Stop Event

1×	node limit

Counts

1 → 2

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

12.5b

Counts

3 → 2

Alt Table

Status	Error	Program
	26.2b	(/.f64 (+.f64 (/.f64 (/.f64 (.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)
▶	12.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

Status

Error

Program

26.2b

(/.f64 (+.f64 (/.f64 (/.f64 (*.f64 (+.f64 alpha beta) (-.f64 beta alpha)) (+.f64 (+.f64 alpha beta) (*.f64 2 i))) (+.f64 (+.f64 (+.f64 alpha beta) (*.f64 2 i)) 2)) 1) 2)

▶

12.5b

(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)

Compiler

Compiled 180 to 109 computations (39.4% saved)

localize18.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))
✓	0.0b	(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))
✓	1.8b	(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

series255.0ms (1%)

Counts

3 → 108

Calls

3 calls:

167.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

55.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

32.0ms

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

rewrite49.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

180×	`add-sqr-sqrt_binary64`
172×	`log1p-expm1-u_binary64`
172×	`expm1-log1p-u_binary64`
171×	`add-cbrt-cube_binary64`
167×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	65
1	349	65

Stop Event

1×	node limit

Counts

3 → 89

Calls

3 calls:

46.0ms

(/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2)))

46.0ms

(/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))

46.0ms

(fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1)

simplify117.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

778×	`associate-/l*_binary64`
365×	`+-commutative_binary64`
282×	`associate-+r+_binary64`
265×	`fma-def_binary64`
218×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	883	10939
1	3352	10904

Stop Event

1×	node limit

Counts

197 → 218

prune413.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	4	218
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	215	5	220

Error

0.1b

Counts

220 → 5

Alt Table

Status	Error	Program
	51.8b	(/.f64 (-.f64 (+.f64 (/.f64 2 alpha) (fma.f64 2 (/.f64 beta alpha) (/.f64 i (/.f64 alpha 4)))) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)
	49.5b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
▶	12.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
✓	12.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
	53.4b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) i) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 i (/.f64 (pow.f64 alpha 3) i)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 beta (/.f64 (pow.f64 alpha 3) i)) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 15803 to 9836 computations (37.8% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
✓	0.1b	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))
✓	1.6b	(-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))
✓	1.7b	(+.f64 (pow.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1)

series17.0s (63.4%)

Counts

4 → 144

Calls

4 calls:

15.4s	(+.f64 (pow.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1)
1.1s	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
283.0ms	(-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))
155.0ms	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))

rewrite46.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

256×	`add-sqr-sqrt_binary64`
252×	`log1p-expm1-u_binary64`
252×	`expm1-log1p-u_binary64`
247×	`add-cbrt-cube_binary64`
239×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	144
1	542	144

Stop Event

1×	node limit

Counts

4 → 69

Calls

4 calls:

43.0ms	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
43.0ms	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))
43.0ms	(-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))
43.0ms	(+.f64 (pow.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1)

simplify602.0ms (2.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7766	113961

Stop Event

1×	node limit

Counts

213 → 165

prune2.4s (9.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	281	1	282
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	282	5	287

Error

0.1b

Counts

287 → 5

Alt Table

Status	Error	Program
	49.6b	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 6 beta) (+.f64 6 (.f64 12 i))) alpha) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
▶	49.5b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	12.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
✓	12.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
	53.4b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) i) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 i (/.f64 (pow.f64 alpha 3) i)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 beta (/.f64 (pow.f64 alpha 3) i)) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 113525 to 79890 computations (29.6% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 2 beta (+.f64 2 (*.f64 i 4)))
✓	0.5b	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

series20.0ms (0.1%)

Counts

2 → 60

Calls

2 calls:

16.0ms	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)
4.0ms	(fma.f64 2 beta (+.f64 2 (*.f64 i 4)))

rewrite47.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

490×	`log-prod_binary64`
201×	`prod-diff_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
164×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	215	21
2	2722	21

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

46.0ms	(fma.f64 2 beta (+.f64 2 (*.f64 i 4)))
46.0ms	(/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha)

simplify54.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

187×	`fma-def_binary64`
30×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
20×	`distribute-rgt-in_binary64`
18×	`associate-/r/_binary64`

Iterations

Useful iterations: 13 (0.0ms)

Iter	Nodes	Cost
0	25	872
1	51	832
2	87	772
3	113	772
4	130	742
5	158	682
6	192	682
7	257	682
8	311	682
9	324	682
10	345	682
11	368	682
12	391	682
13	410	592
14	435	592
15	453	592
16	455	592
17	456	592

Stop Event

1×

saturated

Counts

127 → 85

prune68.0ms (0.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	83	7	90

Error

0.1b

Counts

90 → 7

Alt Table

Status	Error	Program
	49.8b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) 3) alpha) 2)
✓	12.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
▶	49.6b	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 6 beta) (+.f64 6 (.f64 12 i))) alpha) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
✓	49.5b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	12.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
	49.7b	(/.f64 (*.f64 (/.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (cbrt.f64 alpha))) 2)
	53.4b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) i) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 i (/.f64 (pow.f64 alpha 3) i)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 beta (/.f64 (pow.f64 alpha 3) i)) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 2103 to 1515 computations (28% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))))
	0.1b	(*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))
✓	0.8b	(/.f64 (+.f64 (.f64 6 beta) (+.f64 6 (.f64 12 i))) alpha)
	1.6b	(-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1))

series17.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

17.0ms

(/.f64 (+.f64 (*.f64 6 beta) (+.f64 6 (*.f64 12 i))) alpha)

rewrite45.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

414×	`fma-def_binary64`
235×	`fma-neg_binary64`
228×	`expm1-udef_binary64`
228×	`log1p-udef_binary64`
126×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	249	12
2	3438	12

Stop Event

1×	node limit

Counts

1 → 33

Calls

1 calls:

45.0ms

(/.f64 (+.f64 (*.f64 6 beta) (+.f64 6 (*.f64 12 i))) alpha)

simplify33.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

184×	`fma-def_binary64`
31×	`*-commutative_binary64`
20×	`associate-/l*_binary64`
17×	`associate-r_binary64`
16×	`associate-/r*_binary64`

Iterations

Useful iterations: 14 (0.0ms)

Iter	Nodes	Cost
0	23	406
1	46	404
2	75	368
3	93	368
4	109	350
5	137	314
6	171	314
7	232	314
8	283	314
9	295	314
10	313	314
11	334	314
12	345	314
13	360	314
14	384	260
15	439	260
16	452	260
17	455	260

Stop Event

1×

saturated

Counts

57 → 42

prune1.0s (3.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	236	0	236
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	236	7	243

Error

0.1b

Counts

243 → 7

Alt Table

Status	Error	Program
	49.8b	(/.f64 (/.f64 (pow.f64 (cbrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) 3) alpha) 2)
✓	12.5b	(/.f64 (fma.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 (+.f64 alpha beta) 2))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))) 1) 2)
✓	49.6b	(/.f64 (/.f64 (/.f64 (+.f64 (.f64 6 beta) (+.f64 6 (.f64 12 i))) alpha) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (*.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
✓	49.5b	(/.f64 (/.f64 (fma.f64 2 beta (+.f64 2 (*.f64 i 4))) alpha) 2)
✓	12.4b	(/.f64 (/.f64 (+.f64 (pow.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 3) 1) (+.f64 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta))))) (-.f64 1 (.f64 (.f64 (/.f64 (+.f64 alpha beta) (fma.f64 2 i (+.f64 alpha (+.f64 beta 2)))) (/.f64 (-.f64 beta alpha) (+.f64 alpha (fma.f64 2 i beta)))) 1)))) 2)
	49.7b	(/.f64 (*.f64 (/.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (pow.f64 (cbrt.f64 alpha) 2)) (/.f64 (sqrt.f64 (fma.f64 2 beta (fma.f64 i 4 2))) (cbrt.f64 alpha))) 2)
	53.4b	(/.f64 (-.f64 (fma.f64 2 (/.f64 (pow.f64 beta 3) (pow.f64 alpha 3)) (+.f64 (/.f64 2 alpha) (fma.f64 32 (/.f64 (pow.f64 i 3) (pow.f64 alpha 3)) (fma.f64 4 (/.f64 i alpha) (fma.f64 2 (/.f64 beta alpha) (fma.f64 20 (.f64 (/.f64 (.f64 beta beta) (pow.f64 alpha 3)) i) (fma.f64 16 (/.f64 beta (pow.f64 alpha 3)) (fma.f64 48 (.f64 (/.f64 beta (pow.f64 alpha 3)) (.f64 i i)) (fma.f64 32 (/.f64 i (pow.f64 alpha 3)) (fma.f64 48 (/.f64 i (/.f64 (pow.f64 alpha 3) i)) (+.f64 (/.f64 8 (pow.f64 alpha 3)) (fma.f64 48 (/.f64 beta (/.f64 (pow.f64 alpha 3) i)) (.f64 10 (/.f64 (.f64 beta beta) (pow.f64 alpha 3))))))))))))))) (fma.f64 6 (/.f64 beta (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (.f64 alpha alpha)) (+.f64 (/.f64 4 (.f64 alpha alpha)) (fma.f64 12 (/.f64 i (/.f64 alpha (/.f64 i alpha))) (fma.f64 12 (.f64 (/.f64 beta (.f64 alpha alpha)) i) (.f64 2 (/.f64 (.f64 beta beta) (.f64 alpha alpha))))))))) 2)

Compiler

Compiled 57304 to 39818 computations (30.5% saved)

regimes2.1s (7.8%)

Accuracy

Total 1.4b remaining (92.6%)

Threshold costs 0b (0%)

Counts

171 → 2

Compiler

Compiled 67758 to 43691 computations (35.5% saved)

bsearch12.0ms (0%)

Compiler: Compiled 28 to 16 computations (42.9% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
7×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	117
1	56	117
2	64	117
3	68	117
4	70	117

Stop Event

1×

saturated

end283.0ms (1.1%)

Compiler: Compiled 611 to 381 computations (37.6% saved)

Iter	Nodes	Cost
0	25	872
1	51	832
2	87	772
3	113	772
4	130	742
5	158	682
6	192	682
7	257	682
8	311	682
9	324	682
10	345	682
11	368	682
12	391	682
13	410	592
14	435	592
15	453	592
16	455	592
17	456	592

Iter	Nodes	Cost
0	23	406
1	46	404
2	75	368
3	93	368
4	109	350
5	137	314
6	171	314
7	232	314
8	283	314
9	295	314
10	313	314
11	334	314
12	345	314
13	360	314
14	384	260
15	439	260
16	452	260
17	455	260

Iter	Nodes	Cost
0	25	872
1	51	832
2	87	772
3	113	772
4	130	742
5	158	682
6	192	682
7	257	682
8	311	682
9	324	682
10	345	682
11	368	682
12	391	682
13	410	592
14	435	592
15	453	592
16	455	592
17	456	592

Iter	Nodes	Cost
0	23	406
1	46	404
2	75	368
3	93	368
4	109	350
5	137	314
6	171	314
7	232	314
8	283	314
9	295	314
10	313	314
11	334	314
12	345	314
13	360	314
14	384	260
15	439	260
16	452	260
17	455	260

Details

analyze160.0ms (0.6%)

sample1.9s (7%)

simplify42.0ms (0.2%)

prune5.0ms (0%)

localize18.0ms (0.1%)

series255.0ms (1%)

rewrite49.0ms (0.2%)

simplify117.0ms (0.4%)

prune413.0ms (1.5%)

localize23.0ms (0.1%)

series17.0s (63.4%)

rewrite46.0ms (0.2%)

simplify602.0ms (2.2%)

prune2.4s (9.1%)

localize7.0ms (0%)

series20.0ms (0.1%)

rewrite47.0ms (0.2%)

simplify54.0ms (0.2%)

prune68.0ms (0.3%)

localize28.0ms (0.1%)

series17.0ms (0.1%)

rewrite45.0ms (0.2%)

simplify33.0ms (0.1%)

prune1.0s (3.9%)

regimes2.1s (7.8%)

bsearch12.0ms (0%)

simplify4.0ms (0%)

end283.0ms (1.1%)

Profiling

Iter	Nodes	Cost
0	25	872
1	51	832
2	87	772
3	113	772
4	130	742
5	158	682
6	192	682
7	257	682
8	311	682
9	324	682
10	345	682
11	368	682
12	391	682
13	410	592
14	435	592
15	453	592
16	455	592
17	456	592

Iter	Nodes	Cost
0	23	406
1	46	404
2	75	368
3	93	368
4	109	350
5	137	314
6	171	314
7	232	314
8	283	314
9	295	314
10	313	314
11	334	314
12	345	314
13	360	314
14	384	260
15	439	260
16	452	260
17	455	260