Details

sample406.0ms

Algorithm

intervals

Results

219.0ms	83×	body	10240	exit
109.0ms	69×	body	1280	valid
44.0ms	60×	body	640	valid
11.0ms	33×	body	320	valid
9.0ms	78×	body	80	valid
3.0ms	16×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	7

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

3 → 21

Calls

3 calls:

2.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series66.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify108.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	173
1	35	148
2	43	148
3	54	148
4	91	148
5	185	148
6	781	148
7	2678	148
8	5001	148

prune102.0ms

Filtered

30 candidates to 21 candidates (30.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	21	10	31

Merged error: 34.9b

Counts

31 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
0.5b	(cbrt (expm1 (sin (expm1 a))))
41.2b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(cbrt (expm1 (sin (expm1 a))))
1.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

series324.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (expm1 (sin (expm1 a))))
105.0ms	(cbrt (expm1 (sin (expm1 a))))
108.0ms	(cbrt (expm1 (sin (expm1 a))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify89.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	39	474
1	69	412
2	146	406
3	475	395
4	2380	395
5	5001	395

prune209.0ms

Filtered

52 candidates to 36 candidates (30.8%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	40	12	52
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	42	20	62

Merged error: 34.4b

Counts

62 → 20

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series128.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify236.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	34	413
1	63	335
2	140	333
3	565	333
4	4325	333
5	5001	333

prune210.0ms

Filtered

44 candidates to 31 candidates (29.5%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	2	16	18
Picked	0	1	1
Done	0	1	1
Total	40	24	64

Merged error: 34.4b

Counts

64 → 24

localize20.0ms

Local error

Found 4 expressions with local error:

41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
41.2b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
1.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series8.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify94.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	15	352
1	17	300
2	21	300
3	26	300
4	45	300
5	99	300
6	505	300
7	1678	300
8	5001	300

prune128.0ms

Filtered

40 candidates to 28 candidates (30.0%)

Pruning

25 alts after pruning (24 fresh and 1 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	0	21	21
Picked	1	0	1
Done	1	1	2
Total	39	25	64

Merged error: 34.4b

Counts

64 → 25

regimes413.0ms

Accuracy

0% (1.2b remaining)

Error of 33.5b against oracle of 32.3b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	7

end0.0ms

sample12.8s

Algorithm

intervals

Results

7.1s	2613×	body	10240	exit
3.7s	2260×	body	1280	valid
1.1s	1633×	body	640	valid
294.0ms	866×	body	320	valid
289.0ms	2795×	body	80	valid
101.0ms	440×	body	160	valid
14.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid