Details

sample42.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
6.0ms	274×	body	80	nan
5.0ms	135×	body	80	valid
5.0ms	36×	body	640	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

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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:

4.0ms	(- (log (+ N 1.0)) (log N))
2.0ms	(log (+ N 1.0))

series134.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify51.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	172	120
1	496	114
2	1763	110
3	5001	102

prune42.0ms

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

localize4.0ms

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))

series126.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(/ (+ N 1.0) N)
79.0ms	(log (/ (+ N 1.0) N))

simplify45.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	130	85
1	381	81
2	1473	78
3	5002	76

prune32.0ms

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)))

series149.0ms

Counts

2 → 6

Calls

2 calls:

32.0ms	(/ N (+ N 1.0))
116.0ms	(log (/ N (+ N 1.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	149	103
1	470	97
2	1964	92
3	5001	88

prune39.0ms

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

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (/ 1 N) (- (/ 0.5 N) 1.0) (/ (- 0.3333333333333333) (pow N 3)))
0.2b	(/ (- 0.3333333333333333) (pow N 3))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`neg-mul-1`
2×	`times-frac` `unpow3` `associate-/r*` `sqr-pow`
1×	`neg-sub0` `frac-2neg` `div-sub` `distribute-frac-neg` `clear-num` `fma-udef` `div-inv` `associate-/l*`

Counts

2 → 11

Calls

2 calls:

1.0ms	(fma (/ 1 N) (- (/ 0.5 N) 1.0) (/ (- 0.3333333333333333) (pow N 3)))
3.0ms	(/ (- 0.3333333333333333) (pow N 3))

series77.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma (/ 1 N) (- (/ 0.5 N) 1.0) (/ (- 0.3333333333333333) (pow N 3)))
38.0ms	(/ (- 0.3333333333333333) (pow N 3))

simplify36.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	84	63
1	252	62
2	1119	59
3	5002	53

prune35.0ms

Filtered

17 candidates to 13 candidates (76.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Merged error: 0.0b

Counts

19 → 2

regimes17.0ms

Accuracy

100% (0.0b remaining)

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

bsearch30.0ms

Steps

Iters	Range		Point
9	357.20278190505735	4524963932.878733	8891.449503616011

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	12
1	26	12

end0.0ms

sample1.2s

Algorithm

intervals

Results

410.0ms	1739×	body	1280	valid
189.0ms	1276×	body	640	valid
187.0ms	7959×	body	80	nan
165.0ms	4092×	body	80	valid
56.0ms	591×	body	320	valid
18.0ms	302×	body	160	valid