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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
16×	`pow1` `add-sqr-sqrt` `prod-diff`
14×	`add-cube-cbrt` `log-pow`
11×	`log-prod`
4×	`log-div` `fma-neg` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 65

Calls

2 calls:

3.0ms	(log (+ N 1.0))
8.0ms	(- (log (+ N 1.0)) (log N))

series135.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify124.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (118.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	343

prune131.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	2	72

Merged error: 0.1b

Counts

72 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`log-prod`
7×	`add-exp-log` `distribute-lft-out`
4×	`add-cbrt-cube` `associate-/l*`
3×	`pow1` `associate-/r*`
2×	`expm1-log1p-u` `div-exp` `rem-log-exp` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 64

Calls

2 calls:

5.0ms	(/ (+ N 1.0) N)
5.0ms	(log (/ (+ N 1.0) N))

series129.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
84.0ms	(log (/ (+ N 1.0) N))

simplify109.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	243	383
1	808	358
2	3663	347
3	5001	344

prune123.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	67	5	72

Merged error: 0.1b

Counts

72 → 5

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
0.6b	(/ 1 (pow N 2))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
11×	`add-exp-log`
8×	`associate-/r*`
6×	`div-exp`
4×	`add-cbrt-cube` `unpow2` `sqr-pow`
3×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `clear-num` `fma-udef` `div-inv` `inv-pow`

Counts

2 → 69

Calls

2 calls:

1.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
5.0ms	(/ 1 (pow N 2))

series54.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(fma (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5) (/ 1.0 N))
17.0ms	(/ 1 (pow N 2))

simplify33.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	208	384
1	789	315
2	5001	269

prune109.0ms

Filtered

75 candidates to 34 candidates (45.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	74	6	80

Merged error: 0.1b

Counts

80 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
27×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `cube-prod` `associate-/r*`
7×	`add-exp-log`
4×	`cube-mult` `unpow3` `add-cbrt-cube` `sqr-pow`
3×	`div-exp` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 77

Calls

2 calls:

1.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
5.0ms	(/ 0.3333333333333333 (pow N 3))

series77.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(fma (/ 1 N) (- 1.0 (/ 0.5 N)) (/ 0.3333333333333333 (pow N 3)))
35.0ms	(/ 0.3333333333333333 (pow N 3))

simplify39.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	231	411
1	1092	387
2	5002	378

prune146.0ms

Filtered

83 candidates to 48 candidates (57.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	84	5	89

Merged error: 0.1b

Counts

89 → 5

regimes24.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.8b

bsearch29.0ms

Steps

Iters	Range		Point
8	7328.433068492625	2697524.489058797	7940.225109591849

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	9
1	21	9

end0.0ms

sample1.2s

Algorithm

intervals

Results

421.0ms	1774×	body	1280	valid
191.0ms	1307×	body	640	valid
182.0ms	7833×	body	80	nan
167.0ms	4021×	body	80	valid
56.0ms	586×	body	320	valid
18.0ms	312×	body	160	valid