Details

sample440.0ms

Algorithm

intervals

Results

244.0ms	90×	body	10240	exit
119.0ms	76×	body	1280	valid
44.0ms	60×	body	640	valid
9.0ms	28×	body	320	valid
9.0ms	78×	body	80	valid
3.0ms	14×	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 (0.0%)

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: 35.5b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
40.9b	(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)

series64.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(sin (expm1 a))
1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify109.0ms

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	2680	148
8	5001	148

prune116.0ms

Filtered

30 candidates to 21 candidates (70.0%)

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: 34.6b

Counts

31 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a))
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(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)

series122.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(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)

simplify246.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	34	413
1	63	335
2	140	333
3	584	333
4	4641	333
5	5001	333

prune200.0ms

Filtered

44 candidates to 31 candidates (70.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	38	16	54

Merged error: 34.6b

Counts

54 → 16

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))))
40.9b	(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)

series316.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (expm1 (sin (expm1 a))))
104.0ms	(cbrt (expm1 (sin (expm1 a))))
106.0ms	(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)

simplify91.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	39	474
1	69	412
2	146	406
3	479	395
4	2429	395
5	5001	395

prune266.0ms

Filtered

52 candidates to 36 candidates (69.2%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	39	13	52
Fresh	0	13	13
Picked	0	1	1
Done	1	1	2
Total	40	28	68

Merged error: 34.2b

Counts

68 → 28

localize20.0ms

Local error

Found 4 expressions with local error:

40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
40.9b	(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)

simplify96.0ms

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	1672	300
8	5001	300

prune156.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	1	24	25
Picked	0	1	1
Done	0	2	2
Total	36	32	68

Merged error: 34.2b

Counts

68 → 32

regimes502.0ms

Accuracy

0% (1.2b remaining)

Error of 34.0b against oracle of 32.8b and baseline of 34.0b

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

6.9s	2544×	body	10240	exit
3.9s	2326×	body	1280	valid
1.1s	1637×	body	640	valid
286.0ms	854×	body	320	valid
275.0ms	2707×	body	80	valid
102.0ms	474×	body	160	valid
5.0ms	1×	body	5120	valid
2.0ms	1×	body	2560	valid