Details

sample394.0ms

Algorithm

intervals

Results

211.0ms	78×	body	10240	exit
116.0ms	73×	body	1280	valid
27.0ms	42×	body	640	valid
15.0ms	98×	body	80	valid
10.0ms	29×	body	320	valid
3.0ms	14×	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: 31.6b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(expm1 (sin (expm1 a)))
36.3b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 14

Calls

2 calls:

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

series4.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify103.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	137
1	26	117
2	32	117
3	40	117
4	68	117
5	142	117
6	643	117
7	2176	117
8	5001	117

prune93.0ms

Filtered

20 candidates to 14 candidates (70.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	10	10	20
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	11	21

Merged error: 30.9b

Counts

21 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
0.4b	(cbrt (expm1 (sin (expm1 a))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite6.0ms

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))))
2.0ms	(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)

series315.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(cbrt (expm1 (sin (expm1 a))))
103.0ms	(cbrt (expm1 (sin (expm1 a))))
107.0ms	(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)

simplify94.0ms

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	479	395
4	2429	395
5	5001	395

prune234.0ms

Filtered

52 candidates to 36 candidates (69.2%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	40	12	52
Fresh	2	7	9
Picked	1	0	1
Done	0	1	1
Total	43	20	63

Merged error: 30.5b

Counts

63 → 20

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`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 → 49

Calls

4 calls:

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

series320.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
105.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
103.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (cbrt (expm1 (sin (expm1 a))))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (atan a)) a)

simplify124.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 6 (118.0ms)

Iter	Nodes	Cost
0	53	760
1	78	666
2	131	660
3	300	660
4	1009	660
5	3347	633
6	5001	624

prune295.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	50	11	61
Fresh	3	15	18
Picked	1	0	1
Done	0	1	1
Total	54	27	81

Merged error: 30.2b

Counts

81 → 27

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
0.7b	(cbrt (cbrt (expm1 (sin (expm1 a)))))
36.3b	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

27×	`cbrt-prod`
10×	`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 → 49

Calls

4 calls:

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

series323.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
111.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
104.0ms	(cbrt (cbrt (expm1 (sin (expm1 a)))))
3.0ms	(fmod (atan2 (* (* (cbrt (expm1 (sin (expm1 a)))) (* (* (cbrt (cbrt (expm1 (sin (expm1 a))))) (cbrt (cbrt (expm1 (sin (expm1 a)))))) (cbrt (cbrt (expm1 (sin (expm1 a))))))) (cbrt (expm1 (sin (expm1 a))))) (atan a)) a)

simplify126.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 6 (119.0ms)

Iter	Nodes	Cost
0	54	760
1	75	666
2	125	660
3	290	660
4	1001	660
5	3337	633
6	5001	624

prune185.0ms

Filtered

61 candidates to 39 candidates (63.9%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	3	22	25
Picked	0	1	1
Done	0	1	1
Total	60	28	88

Merged error: 30.1b

Counts

88 → 28

regimes466.0ms

Accuracy

0% (1.5b remaining)

Error of 33.5b against oracle of 32.0b 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

sample12.7s

Algorithm

intervals

Results

6.9s	2554×	body	10240	exit
3.8s	2240×	body	1280	valid
1.1s	1662×	body	640	valid
294.0ms	2794×	body	80	valid
292.0ms	873×	body	320	valid
97.0ms	429×	body	160	valid
4.0ms	2×	body	2560	valid