Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	54×	body	1280	valid
6.0ms	274×	body	80	nan
6.0ms	36×	body	640	valid
6.0ms	135×	body	80	valid
2.0ms	24×	body	320	valid
0.0ms	7×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 28.3b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

3.2b	(- (log (+ N 1.0)) (log N))
3.2b	(log (+ N 1.0))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`log-div`
2×	`associate--l-` `flip3-+` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

2 → 9

Calls

2 calls:

3.0ms	(- (log (+ N 1.0)) (log N))
2.0ms	(log (+ N 1.0))

series141.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(- (log (+ N 1.0)) (log N))
47.0ms	(log (+ N 1.0))

simplify47.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	159	123
1	447	122
2	1557	113
3	5001	108

prune41.0ms

Filtered

15 candidates to 12 candidates (80.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	13	3	16

Merged error: 0.0b

Counts

16 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.2b	(log (/ (+ N 1.0) N))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log-div`
4×	`associate-/l/`
3×	`clear-num`
2×	`frac-2neg` `flip3-+` `flip-+` `div-inv`
1×	`log-prod` `log-rec`

Counts

2 → 12

Calls

2 calls:

3.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series132.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify43.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	123	89
1	348	88
2	1338	84
3	5001	82

prune37.0ms

Filtered

18 candidates to 14 candidates (77.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	19	2	21

Merged error: 0.0b

Counts

21 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ N (+ N 1.0))
3.1b	(log (/ N (+ N 1.0)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/r/`
3×	`log-div` `log-prod` `clear-num`
2×	`frac-2neg` `flip3-+` `flip-+` `div-inv`
1×	`log-rec`

Counts

2 → 12

Calls

2 calls:

3.0ms	(/ N (+ N 1.0))
3.0ms	(log (/ N (+ N 1.0)))

series160.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ N (+ N 1.0))
124.0ms	(log (/ N (+ N 1.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	140	106
1	424	101
2	1735	94
3	5001	94

prune42.0ms

Filtered

18 candidates to 16 candidates (88.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	18	2	20

Merged error: 0.0b

Counts

20 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N))
0.1b	(/ (/ 0.5 N) N)
0.2b	(/ (- 0.3333333333333333) (pow N 3))
15.8b	(+ (/ (/ 0.5 N) N) (- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

147×	`frac-add`
144×	`frac-sub`
117×	`frac-2neg` `clear-num`
66×	`associate-/l/`
58×	`associate-/r*`
47×	`associate-/l*`
34×	`unpow3`
27×	`neg-mul-1`
26×	`sqr-pow`
24×	`div-inv`
8×	`flip3--` `flip--` `sub-div`
3×	`neg-sub0` `div-sub`
2×	`associate--l-` `associate-+r-` `sub-neg` `associate-+r+` `times-frac`
1×	`+-commutative` `flip3-+` `distribute-frac-neg` `flip-+`

Counts

4 → 195

Calls

4 calls:

6.0ms	(- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N))
3.0ms	(/ (/ 0.5 N) N)
3.0ms	(/ (- 0.3333333333333333) (pow N 3))
13.0ms	(+ (/ (/ 0.5 N) N) (- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N))
28.0ms	(/ (/ 0.5 N) N)
38.0ms	(/ (- 0.3333333333333333) (pow N 3))
37.0ms	(+ (/ (/ 0.5 N) N) (- (/ (- 0.3333333333333333) (pow N 3)) (/ 1.0 N)))

simplify84.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2238	3413
1	5003	3133

prune432.0ms

Filtered

207 candidates to 122 candidates (58.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	207	2	209

Merged error: 0.0b

Counts

209 → 2

regimes14.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.2b

bsearch40.0ms

Steps

Iters	Range		Point
9	357.20278190505735	4524963932.878733	8891.449503616011

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	31	13
2	33	13
3	33	13

end0.0ms

sample1.3s

Algorithm

intervals

Results

434.0ms	1739×	body	1280	valid
202.0ms	7959×	body	80	nan
200.0ms	1276×	body	640	valid
173.0ms	4092×	body	80	valid
60.0ms	591×	body	320	valid
19.0ms	302×	body	160	valid