Details

sample351.0ms

Algorithm

intervals

Results

163.0ms	59×	body	5120	exit
120.0ms	68×	body	1280	valid
33.0ms	46×	body	640	valid
11.0ms	30×	body	320	valid
11.0ms	97×	body	80	valid
3.0ms	15×	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

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: 31.8b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(sin (expm1 a))
36.5b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite4.0ms

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

series67.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
1.0ms	(expm1 (sin (expm1 a)))
61.0ms	(sin (expm1 a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify120.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	39	248
1	44	212
2	54	212
3	68	212
4	114	212
5	228	212
6	919	212
7	3184	212
8	5001	212

prune157.0ms

Filtered

40 candidates to 28 candidates (70.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	26	14	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	14	41

Merged error: 30.8b

Counts

41 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

2.0ms	(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)

series91.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(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

52 → 52

Iterations

Useful iterations: 7 (93.0ms)

Iter	Nodes	Cost
0	63	401
1	92	342
2	121	342
3	180	342
4	339	342
5	863	342
6	3913	342
7	5001	338

prune198.0ms

Filtered

52 candidates to 33 candidates (63.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	46	6	52
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	49	17	66

Merged error: 30.6b

Counts

66 → 17

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.5b	(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:

31.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
3.0ms	(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	2589	361
7	5001	361

prune270.0ms

Filtered

44 candidates to 33 candidates (75.0%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	37	7	44
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	39	22	61

Merged error: 30.3b

Counts

61 → 22

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
36.5b	(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)
36.5b	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)
36.5b	(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`
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 (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)
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)

series121.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan 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)
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)

simplify68.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	76	637
1	157	539
2	420	415
3	1717	415
4	5001	414

prune228.0ms

Filtered

44 candidates to 33 candidates (75.0%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	38	6	44
Fresh	0	21	21
Picked	1	0	1
Done	0	0	0
Total	39	27	66

Merged error: 30.2b

Counts

66 → 27

regimes370.0ms

Accuracy

0% (1.8b remaining)

Error of 33.5b against oracle of 31.7b and baseline of 33.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	66
1	26	66

end0.0ms

sample13.1s

Algorithm

intervals

Results

7.1s	2570×	body	5120	exit
3.8s	2224×	body	1280	valid
1.2s	1666×	body	640	valid
317.0ms	862×	body	320	valid
316.0ms	2796×	body	80	valid
102.0ms	446×	body	160	valid
19.0ms	4×	body	5120	valid
4.0ms	2×	body	2560	valid