Details

sample424.0ms

Algorithm

intervals

Results

226.0ms	83×	body	10240	exit
127.0ms	76×	body	1280	valid
39.0ms	56×	body	640	valid
9.0ms	90×	body	80	valid
5.0ms	16×	body	320	valid
4.0ms	18×	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: 33.0b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
37.9b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

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:

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

series5.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
3.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify111.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	31	212
1	35	181
2	43	181
3	54	181
4	91	181
5	185	181
6	781	181
7	2678	181
8	5001	181

prune121.0ms

Filtered

30 candidates to 21 candidates (70.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	17	13	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	18	13	31

Merged error: 31.8b

Counts

31 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`exp-prod`
5×	`pow1` `add-exp-log` `add-log-exp`
4×	`log-pow` `add-cbrt-cube`
3×	`log-prod`
2×	`rem-log-exp`
1×	`rem-exp-log`

Counts

4 → 41

Calls

4 calls:

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

series38.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(expm1 (sin (expm1 a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify98.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 7 (93.0ms)

Iter	Nodes	Cost
0	63	414
1	92	353
2	121	353
3	180	353
4	339	353
5	863	353
6	3892	353
7	5001	349

prune191.0ms

Filtered

53 candidates to 33 candidates (62.3%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	42	11	53
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	48	18	66

Merged error: 31.6b

Counts

66 → 18

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (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` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`exp-prod`
1×	`rem-exp-log`

Counts

4 → 32

Calls

4 calls:

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

series39.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify74.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	430
1	60	361
2	78	361
3	118	361
4	218	361
5	534	361
6	2578	361
7	5001	361

prune273.0ms

Filtered

44 candidates to 33 candidates (75.0%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	35	9	44
Fresh	0	17	17
Picked	1	0	1
Done	0	0	0
Total	36	26	62

Merged error: 31.3b

Counts

62 → 26

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
37.9b	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (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 (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
1.0ms	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)

series129.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
2.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
6.0ms	(fmod (log (pow (exp (* (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) (cbrt (atan2 (expm1 (sin (expm1 a))) (atan a))))) a)

simplify64.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (58.0ms)

Iter	Nodes	Cost
0	76	637
1	157	539
2	420	415
3	1711	415
4	5001	414

prune212.0ms

Filtered

44 candidates to 33 candidates (75.0%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	40	4	44
Fresh	0	25	25
Picked	0	1	1
Done	0	0	0
Total	40	30	70

Merged error: 31.2b

Counts

70 → 30

regimes406.0ms

Accuracy

0% (1.8b remaining)

Error of 33.9b against oracle of 32.1b and baseline of 33.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	45
1	21	45

end0.0ms

sample12.9s

Algorithm

intervals

Results

7.0s	2588×	body	10240	exit
3.7s	2213×	body	1280	valid
1.2s	1708×	body	640	valid
296.0ms	2731×	body	80	valid
295.0ms	881×	body	320	valid
102.0ms	459×	body	160	valid
12.0ms	6×	body	2560	valid
9.0ms	2×	body	5120	valid