Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	60×	body	1280	valid
6.0ms	139×	body	80	valid
6.0ms	243×	body	80	nan
6.0ms	37×	body	640	valid
1.0ms	14×	body	320	valid
0.0ms	6×	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: 27.8b

localize7.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (log (+ N 1.0)) (log N))
3.2b	(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))

series139.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(- (log (+ N 1.0)) (log N))
46.0ms	(log (+ N 1.0))

simplify128.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (122.0ms)

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

prune138.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (+ N 1.0) N)
1.7b	(log (/ (+ N 1.0) N))

rewrite18.0ms

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:

12.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series131.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(/ (+ N 1.0) N)
85.0ms	(log (/ (+ N 1.0) N))

simplify107.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (101.0ms)

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

prune131.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sqrt (+ N 1.0)) N)
1.7b	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.0b	(log (sqrt (+ N 1.0)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

60×	`*-un-lft-identity`
42×	`times-frac`
39×	`log-prod`
38×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`sqrt-prod`
25×	`associate-+r+`
13×	`distribute-lft-out`
11×	`pow1`
10×	`log-pow`
7×	`associate-+l+` `associate-/l*`
6×	`add-exp-log` `fma-def` `sqrt-div`
5×	`log-div` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`associate-+l-` `sqrt-pow1` `pow1/2` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r-` `frac-2neg` `div-exp` `rem-log-exp` `clear-num` `sum-log`

Counts

3 → 127

Calls

3 calls:

8.0ms	(/ (sqrt (+ N 1.0)) N)
15.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
3.0ms	(log (sqrt (+ N 1.0)))

series394.0ms

Counts

3 → 9

Calls

3 calls:

73.0ms	(/ (sqrt (+ N 1.0)) N)
239.0ms	(+ (log (sqrt (+ N 1.0))) (log (/ (sqrt (+ N 1.0)) N)))
82.0ms	(log (sqrt (+ N 1.0)))

simplify47.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	1060
1	1471	971
2	5002	878

prune313.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))
3.2b	(log (+ N 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

26×	`log-prod`
21×	`*-un-lft-identity`
11×	`add-sqr-sqrt` `add-cube-cbrt`
8×	`associate--l+`
7×	`pow1` `add-exp-log` `distribute-rgt-in` `distribute-lft-in`
6×	`log-div` `associate--r+` `add-log-exp`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `log-pow` `flip-+`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `difference-of-squares`

Counts

4 → 82

Calls

4 calls:

8.0ms	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))
2.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))

series457.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(- (* (log (+ N 1.0)) (log (+ N 1.0))) (* (log N) (log N)))
40.0ms	(log (+ N 1.0))
46.0ms	(log (+ N 1.0))
41.0ms	(log (+ N 1.0))

simplify39.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	413	732
1	1350	654
2	5002	627

prune267.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes24.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.1b

bsearch29.0ms

Steps

Iters	Range		Point
7	1836.721956390875	43768.65998072103	6058.788192135881

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	14
1	25	14

end0.0ms

sample1.3s

Algorithm

intervals

Results

444.0ms	1799×	body	1280	valid
193.0ms	8106×	body	80	nan
186.0ms	1180×	body	640	valid
174.0ms	4126×	body	80	valid
57.0ms	570×	body	320	valid
20.0ms	325×	body	160	valid