Details

sample458.0ms

Algorithm

intervals

Results

242.0ms	87×	body	10240	exit
144.0ms	87×	body	1280	valid
35.0ms	50×	body	640	valid
14.0ms	85×	body	80	valid
9.0ms	25×	body	320	valid
2.0ms	9×	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: 34.6b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (expm1 a))
0.0b	(expm1 (sin (expm1 a)))
0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
40.0b	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

rewrite5.0ms

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:

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

series166.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(sin (expm1 a))
96.0ms	(expm1 (sin (expm1 a)))
2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
2.0ms	(fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)

simplify127.0ms

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

prune216.0ms

Filtered

51 candidates to 39 candidates (76.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	38	13	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	13	52

Merged error: 33.4b

Counts

52 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(atan2 (expm1 (sin (expm1 a))) (atan a))
0.3b	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.3b	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
40.0b	(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-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u`
3×	`log-prod`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 48

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 (expm1 (sin (expm1 a))) (atan a))
35.0ms	(exp (atan2 (expm1 (sin (expm1 a))) (atan a)))
2.0ms	(log (exp (atan2 (expm1 (sin (expm1 a))) (atan a))))
3.0ms	(fmod (log (exp (atan2 (expm1 (sin (expm1 a))) (atan a)))) a)

simplify103.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 7 (97.0ms)

Iter	Nodes	Cost
0	67	490
1	97	429
2	125	429
3	179	429
4	329	429
5	851	429
6	3887	429
7	5002	425

prune253.0ms

Filtered

60 candidates to 41 candidates (68.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	52	8	60
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	58	15	73

Merged error: 33.1b

Counts

73 → 15

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.0b	(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)

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

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

series365.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
117.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
118.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
7.0ms	(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)

simplify66.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	68	771
1	139	685
2	402	679
3	1680	679
4	5001	676

prune357.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

20 alts after pruning (20 fresh and 0 done)

	Pruned	Kept	Total
New	53	7	60
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	55	20	75

Merged error: 33.1b

Counts

75 → 20

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
0.7b	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
40.0b	(fmod (log (pow (exp (* (log1p (expm1 (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)

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
1.0ms	(fmod (log (pow (exp (* (log1p (expm1 (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)

series371.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
119.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
119.0ms	(cbrt (atan2 (expm1 (sin (expm1 a))) (atan a)))
9.0ms	(fmod (log (pow (exp (* (log1p (expm1 (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)

simplify39.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	69	819
1	126	729
2	255	723
3	831	723
4	5002	723

prune301.0ms

Filtered

60 candidates to 46 candidates (76.7%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	56	4	60
Fresh	3	16	19
Picked	0	1	1
Done	0	0	0
Total	59	21	80

Merged error: 33.1b

Counts

80 → 21

regimes313.0ms

Accuracy

0% (1.6b remaining)

Error of 33.7b against oracle of 32.1b and baseline of 33.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	16	26

end0.0ms

sample13.4s

Algorithm

intervals

Results

7.4s	2710×	body	10240	exit
3.9s	2336×	body	1280	valid
1.1s	1636×	body	640	valid
303.0ms	2792×	body	80	valid
270.0ms	783×	body	320	valid
96.0ms	444×	body	160	valid
24.0ms	5×	body	5120	valid
8.0ms	4×	body	2560	valid