Details

sample415.0ms

Algorithm

intervals

Results

225.0ms	86×	body	10240	exit
109.0ms	63×	body	1280	valid
41.0ms	57×	body	640	valid
10.0ms	30×	body	320	valid
10.0ms	95×	body	80	valid
7.0ms	11×	body	160	valid

simplify3.0ms

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

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
37.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-udef`
1×	`expm1-log1p` `sin-diff`

Counts

4 → 39

Calls

4 calls:

0.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(sin (expm1 a))
0.0ms	(expm1 (sin (expm1 a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

series159.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
64.0ms	(sin (expm1 a))
91.0ms	(expm1 (sin (expm1 a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify121.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	108	302
1	242	264
2	720	264
3	2934	264
4	5001	264

prune202.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 31.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.7b	(fmod (* (* (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)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (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)

series348.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
111.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
120.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (* (* (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)

simplify92.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	42	714
1	72	632
2	149	626
3	483	611
4	2459	611
5	5002	611

prune258.0ms

Filtered

60 candidates to 45 candidates (75.0%)

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 31.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.7b	(fmod (* (* (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)
37.7b	(fmod (* (* (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)
37.7b	(fmod (* (* (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)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (* (* (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)
0.0ms	(fmod (* (* (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)
0.0ms	(fmod (* (* (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)

series124.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(fmod (* (* (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)
5.0ms	(fmod (* (* (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)
3.0ms	(fmod (* (* (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)

simplify92.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	42	990
1	72	848
2	149	846
3	483	801
4	2459	801
5	5002	801

prune318.0ms

Filtered

52 candidates to 42 candidates (80.8%)

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 31.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
37.7b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
37.7b	(fmod (* (* (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)
37.7b	(fmod (* (* (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)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
0.0ms	(fmod (* (* (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)
0.0ms	(fmod (* (* (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)

series120.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)
3.0ms	(fmod (* (* (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)
3.0ms	(fmod (* (* (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)

simplify90.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	52	810
1	83	698
2	162	396
3	488	396
4	2464	396
5	5001	396

prune257.0ms

Filtered

52 candidates to 41 candidates (78.8%)

Pruning

27 alts after pruning (25 fresh and 2 done)

Merged error: 30.9b

regimes348.0ms

Accuracy

0% (1.9b remaining)

Error of 33.9b against oracle of 32.0b and baseline of 33.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	12	22

end0.0ms

sample12.6s

Algorithm

intervals

Results

6.6s	2561×	body	10240	exit
4.0s	2301×	body	1280	valid
1.2s	1692×	body	640	valid
269.0ms	797×	body	320	valid
268.0ms	2746×	body	80	valid
97.0ms	458×	body	160	valid
14.0ms	3×	body	5120	valid
6.0ms	3×	body	2560	valid