Details

sample42.0ms

Algorithm

intervals

Results

14.0ms	59×	body	1280	valid
5.0ms	127×	body	80	valid
5.0ms	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

localize10.0ms

Local error

Found 2 expressions with local error:

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

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:

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

series133.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
93.0ms	(- (log (+ N 1.0)) (log N))

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	5002	102

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))

series132.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ N 1.0) N)
81.0ms	(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

prune40.0ms

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)))

series158.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(/ N (+ N 1.0))
118.0ms	(log (/ N (+ N 1.0)))

simplify60.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (57.0ms)

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

prune40.0ms

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (* 0.3333333333333333 (/ 1 (pow N 3))))
0.1b	(* 0.3333333333333333 (/ 1 (pow N 3)))
0.3b	(/ 1 (pow N 3))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`associate-*r/`
4×	`associate-/r*`
3×	`clear-num`
2×	`frac-2neg` `unpow3` `un-div-inv` `div-inv` `sqr-pow`
1×	`pow-to-exp` `rec-exp` `pow-flip` `associate-r` `*-commutative` `fma-udef` `inv-pow`

Counts

3 → 18

Calls

3 calls:

1.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (* 0.3333333333333333 (/ 1 (pow N 3))))
7.0ms	(* 0.3333333333333333 (/ 1 (pow N 3)))
3.0ms	(/ 1 (pow N 3))

series110.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (* 0.3333333333333333 (/ 1 (pow N 3))))
36.0ms	(* 0.3333333333333333 (/ 1 (pow N 3)))
31.0ms	(/ 1 (pow N 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	83	65
1	292	58
2	1444	52
3	5002	52

prune44.0ms

Filtered

27 candidates to 15 candidates (55.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	26	4	30

Merged error: 0.1b

Counts

30 → 4

regimes20.0ms

Accuracy

100% (0.0b remaining)

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

bsearch32.0ms

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

429.0ms	1774×	body	1280	valid
199.0ms	1307×	body	640	valid
186.0ms	7833×	body	80	nan
165.0ms	4021×	body	80	valid
59.0ms	586×	body	320	valid
19.0ms	312×	body	160	valid