Details

sample42.0ms

Algorithm

intervals

Results

12.0ms	52×	body	1280	valid
5.0ms	237×	body	80	nan
5.0ms	130×	body	80	valid
5.0ms	34×	body	640	valid
2.0ms	26×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.6b	(log (+ N 1.0))
3.9b	(- (log (+ N 1.0)) (log N))

rewrite20.0ms

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:

4.0ms	(log (+ N 1.0))
14.0ms	(- (log (+ N 1.0)) (log N))

series132.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(log (+ N 1.0))
88.0ms	(- (log (+ N 1.0)) (log N))

simplify123.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (117.0ms)

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

prune128.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
3.8b	(log (/ (+ N 1.0) N))

rewrite29.0ms

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:

21.0ms	(/ (+ N 1.0) N)
6.0ms	(log (/ (+ N 1.0) N))

series123.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(/ (+ N 1.0) N)
80.0ms	(log (/ (+ N 1.0) N))

simplify103.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (97.0ms)

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

prune121.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ N 1.0) N))
0.1b	(sqrt (/ (+ N 1.0) N))
3.8b	(log (sqrt (/ (+ N 1.0) N)))
3.8b	(log (sqrt (/ (+ N 1.0) N)))

rewrite38.0ms

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:

10.0ms	(sqrt (/ (+ N 1.0) N))
10.0ms	(sqrt (/ (+ N 1.0) N))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

series316.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(sqrt (/ (+ N 1.0) N))
45.0ms	(sqrt (/ (+ N 1.0) N))
113.0ms	(log (sqrt (/ (+ N 1.0) N)))
119.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify65.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 3 (54.0ms)

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

prune323.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ N 1.0) N)
0.1b	(sqrt (/ (+ N 1.0) N))
3.8b	(log (/ (+ N 1.0) N))
3.8b	(log (sqrt (/ (+ N 1.0) N)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity`
49×	`times-frac`
41×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
35×	`log-prod`
32×	`sqrt-prod`
13×	`distribute-lft-out`
10×	`add-exp-log`
8×	`pow1`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`rem-log-exp` `associate-/r*`
2×	`rem-sqrt-square` `log-div` `sqrt-pow1` `pow1/2` `sqrt-div` `div-exp` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `clear-num` `flip-+`

Counts

4 → 127

Calls

4 calls:

18.0ms	(/ (+ N 1.0) N)
13.0ms	(sqrt (/ (+ N 1.0) N))
6.0ms	(log (/ (+ N 1.0) N))
7.0ms	(log (sqrt (/ (+ N 1.0) N)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ (+ N 1.0) N)
46.0ms	(sqrt (/ (+ N 1.0) N))
82.0ms	(log (/ (+ N 1.0) N))
114.0ms	(log (sqrt (/ (+ N 1.0) N)))

simplify146.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	377	883
1	1125	826
2	4899	799
3	5001	798

prune327.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes23.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.7b

bsearch33.0ms

Steps

Iters	Range		Point
8	26.826342714152005	112870.16560235518	6381.7936198495445

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	22
1	36	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

414.0ms	1763×	body	1280	valid
189.0ms	8191×	body	80	nan
188.0ms	1275×	body	640	valid
166.0ms	4026×	body	80	valid
61.0ms	641×	body	320	valid
18.0ms	295×	body	160	valid