Details

sample44.0ms

Algorithm

intervals

Results

14.0ms	57×	body	1280	valid
7.0ms	288×	body	80	nan
6.0ms	132×	body	80	valid
5.0ms	31×	body	640	valid
2.0ms	22×	body	320	valid
1.0ms	14×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize6.0ms

Local error

Found 2 expressions with local error:

1.7b	(log (+ N 1.0))
3.3b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms

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:

2.0ms	(log (+ N 1.0))
7.0ms	(- (log (+ N 1.0)) (log N))

series137.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(log (+ N 1.0))
97.0ms	(- (log (+ N 1.0)) (log N))

simplify122.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (116.0ms)

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

prune130.0ms

Filtered

71 candidates to 43 candidates (60.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.0b	(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:

7.0ms	(/ (+ N 1.0) N)
3.0ms	(log (/ (+ N 1.0) N))

series128.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(/ (+ N 1.0) N)
83.0ms	(log (/ (+ N 1.0) N))

simplify110.0ms

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

prune123.0ms

Filtered

70 candidates to 50 candidates (71.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
3.1b	(log (sqrt (/ (+ N 1.0) N)))
3.1b	(log (sqrt (/ (+ N 1.0) N)))

rewrite24.0ms

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:

6.0ms	(sqrt (/ (+ N 1.0) N))
5.0ms	(sqrt (/ (+ N 1.0) N))
4.0ms	(log (sqrt (/ (+ N 1.0) N)))
4.0ms	(log (sqrt (/ (+ N 1.0) N)))

series343.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sqrt (/ (+ N 1.0) N))
49.0ms	(sqrt (/ (+ N 1.0) N))
121.0ms	(log (sqrt (/ (+ N 1.0) N)))
125.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify64.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (53.0ms)

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

prune334.0ms

Filtered

138 candidates to 102 candidates (73.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

3.1b	(log (sqrt (/ (+ N 1.0) N)))
3.1b	(log (sqrt (/ (+ N 1.0) N)))
3.1b	(log (sqrt (/ (+ N 1.0) N)))
3.1b	(log (sqrt (/ (+ N 1.0) N)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

76×	`log-prod`
64×	`*-un-lft-identity` `sqrt-prod`
48×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`pow1` `log-pow` `distribute-lft-out`
8×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `sqrt-pow1` `pow1/2` `sqrt-div` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 132

Calls

4 calls:

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

series499.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(log (sqrt (/ (+ N 1.0) N)))
128.0ms	(log (sqrt (/ (+ N 1.0) N)))
121.0ms	(log (sqrt (/ (+ N 1.0) N)))
128.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify59.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	170	1196
1	375	1128
2	1496	1088
3	5001	1076

prune399.0ms

Filtered

144 candidates to 104 candidates (72.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.9b

bsearch18.0ms

Steps

Iters	Range		Point
5	4717.815806685034	11257.791762216355	5578.40769447651

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	18
1	27	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

448.0ms	1800×	body	1280	valid
189.0ms	8031×	body	80	nan
185.0ms	1213×	body	640	valid
173.0ms	4078×	body	80	valid
61.0ms	613×	body	320	valid
19.0ms	296×	body	160	valid