Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	59×	body	1280	valid
6.0ms	127×	body	80	valid
6.0ms	36×	body	640	valid
5.0ms	229×	body	80	nan
2.0ms	21×	body	320	valid
1.0ms	13×	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: 30.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b	(log (+ N 1.0))
5.0b	(- (log (+ N 1.0)) (log N))

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:

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

series148.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(log (+ N 1.0))
99.0ms	(- (log (+ N 1.0)) (log N))

simplify47.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 3 (44.0ms)

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

prune42.0ms

Filtered

15 candidates to 12 candidates (80.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	13	2	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	2	16

Merged error: 0.1b

Counts

16 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
5.1b	(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))

series137.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(/ (+ N 1.0) N)
89.0ms	(log (/ (+ N 1.0) N))

simplify50.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (42.0ms)

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

prune35.0ms

Filtered

18 candidates to 14 candidates (77.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	17	1	18
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	17	3	20

Merged error: 0.1b

Counts

20 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ N (+ N 1.0))
5.0b	(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)))

series165.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(/ N (+ N 1.0))
130.0ms	(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

prune46.0ms

Filtered

18 candidates to 16 candidates (88.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	18	3	21

Merged error: 0.1b

Counts

21 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
0.1b	(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
0.6b	(/ 0.3333333333333333 (pow N 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

50×	`frac-add`
36×	`frac-times`
25×	`flip3--` `flip--`
24×	`frac-2neg` `clear-num`
22×	`associate-/r*`
12×	`associate-*r/`
11×	`unpow2` `sqr-pow`
6×	`associate-+r+`
5×	`flip3-+` `flip-+`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`+-commutative` `sub-neg` `associate-*l/`
2×	`div-inv`
1×	`associate-+r-` `associate-l` `*-commutative`

Counts

3 → 82

Calls

3 calls:

5.0ms	(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
10.0ms	(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
2.0ms	(/ 0.3333333333333333 (pow N 2))

series98.0ms

Counts

3 → 9

Calls

3 calls:

21.0ms	(+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N)))
47.0ms	(* (/ 1 N) (+ (/ 0.3333333333333333 (pow N 2)) (- 1.0 (/ 0.5 N))))
31.0ms	(/ 0.3333333333333333 (pow N 2))

simplify109.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	869	1332
1	4668	1236
2	5001	1232

prune187.0ms

Filtered

91 candidates to 56 candidates (61.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	91	3	94

Merged error: 0.1b

Counts

94 → 3

regimes18.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.7b

bsearch33.0ms

Steps

Iters	Range		Point
8	7328.433068492625	2697524.489058797	10135.618383580597

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	25	11

end0.0ms

sample1.3s

Algorithm

intervals

Results

443.0ms	1774×	body	1280	valid
203.0ms	1307×	body	640	valid
188.0ms	7833×	body	80	nan
174.0ms	4021×	body	80	valid
62.0ms	586×	body	320	valid
20.0ms	312×	body	160	valid