Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	51×	body	1280	valid
8.0ms	263×	body	80	nan
7.0ms	144×	body	80	valid
6.0ms	36×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	8×	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: 26.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (log (+ N 1.0)) (log N))
2.9b	(log (+ N 1.0))

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:

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

series137.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (119.0ms)

Iter	Nodes	Cost
0	277	598
1	837	444
2	3748	347
3	5001	345

prune124.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	3	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	3	72

Merged error: 0.0b

Counts

72 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
2.0b	(log (/ (+ N 1.0) N))

rewrite12.0ms

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)
4.0ms	(log (/ (+ N 1.0) N))

series133.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify106.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (99.0ms)

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

prune105.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	68	2	70
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.0b

Counts

73 → 3

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
2.0b	(log (sqrt (/ (+ N 1.0) N)))
2.0b	(log (sqrt (/ (+ N 1.0) N)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

64×	`sqrt-prod`
62×	`*-un-lft-identity`
50×	`times-frac`
44×	`add-sqr-sqrt`
38×	`add-cube-cbrt` `log-prod`
12×	`distribute-lft-out`
10×	`pow1`
6×	`add-exp-log` `log-pow`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqrt-div` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`log-div` `rem-log-exp`

Counts

4 → 126

Calls

4 calls:

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

series338.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (/ (+ N 1.0) N))
49.0ms	(sqrt (/ (+ N 1.0) N))
126.0ms	(log (sqrt (/ (+ N 1.0) N)))
121.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify67.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	205	1000
1	482	936
2	1903	904
3	5001	886

prune290.0ms

Filtered

138 candidates to 102 candidates (73.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	138	3	141

Merged error: 0.0b

Counts

141 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
2.0b	(log (sqrt (/ (+ N 1.0) N)))
2.1b	(log (sqrt (sqrt (/ (+ N 1.0) N))))
2.1b	(log (sqrt (sqrt (/ (+ N 1.0) N))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

102×	`sqrt-prod`
65×	`*-un-lft-identity`
63×	`log-prod`
49×	`times-frac`
44×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
13×	`pow1` `log-pow`
12×	`distribute-lft-out`
10×	`sqrt-pow1`
7×	`add-exp-log`
6×	`pow1/2` `sqrt-div`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`log-div` `rem-log-exp`
2×	`rem-sqrt-square`

Counts

4 → 139

Calls

4 calls:

5.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
7.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

series527.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(sqrt (/ (+ N 1.0) N))
127.0ms	(log (sqrt (/ (+ N 1.0) N)))
177.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))
179.0ms	(log (sqrt (sqrt (/ (+ N 1.0) N))))

simplify91.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	317	1298
1	700	1226
2	2524	1180
3	5002	1167

prune397.0ms

Filtered

151 candidates to 109 candidates (72.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	151	3	154

Merged error: 0.0b

Counts

154 → 3

regimes22.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.3b

bsearch31.0ms

Steps

Iters	Range		Point
8	8.601567399579238	18724.121991280714	6409.532366542444

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	22
1	27	22

end0.0ms

sample1.5s

Algorithm

intervals

Results

498.0ms	1772×	body	1280	valid
257.0ms	8059×	body	80	nan
216.0ms	1206×	body	640	valid
208.0ms	4099×	body	80	valid
71.0ms	591×	body	320	valid
25.0ms	332×	body	160	valid