Details

sample68.0ms

Algorithm

intervals

Results

18.0ms	55×	body	1280	valid
14.0ms	266×	body	80	nan
11.0ms	129×	body	80	valid
11.0ms	48×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	12×	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: 29.8b

localize11.0ms

Local error

Found 2 expressions with local error:

3.3b	(- (log (+ N 1.0)) (log N))
4.0b	(log (+ N 1.0))

rewrite12.0ms

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:

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

series142.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (log (+ N 1.0)) (log N))
44.0ms	(log (+ N 1.0))

simplify127.0ms

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	345

prune145.0ms

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)
3.2b	(log (/ (+ N 1.0) N))

rewrite14.0ms

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:

8.0ms	(/ (+ N 1.0) N)
4.0ms	(log (/ (+ N 1.0) N))

series144.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (+ N 1.0) N)
89.0ms	(log (/ (+ N 1.0) N))

simplify104.0ms

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

prune143.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ N 1.0) N)
0.3b	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
0.4b	(pow (log (/ (+ N 1.0) N)) 3)
3.2b	(log (/ (+ N 1.0) N))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
27×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`times-frac`
16×	`log-prod`
14×	`cbrt-prod`
10×	`pow1` `add-exp-log`
8×	`unpow-prod-down` `cube-prod`
7×	`add-cbrt-cube` `distribute-lft-out`
5×	`log-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow-unpow` `associate-/r*`
2×	`cube-mult` `unpow3` `div-exp` `rem-log-exp` `div-inv` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `log-div` `pow-pow` `frac-2neg` `flip3-+` `pow1/3` `pow-exp` `clear-num` `rem-cbrt-cube` `flip-+` `rem-cube-cbrt`

Counts

4 → 116

Calls

4 calls:

11.0ms	(/ (+ N 1.0) N)
2.0ms	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
2.0ms	(pow (log (/ (+ N 1.0) N)) 3)
4.0ms	(log (/ (+ N 1.0) N))

series379.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ (+ N 1.0) N)
90.0ms	(cbrt (pow (log (/ (+ N 1.0) N)) 3))
145.0ms	(pow (log (/ (+ N 1.0) N)) 3)
89.0ms	(log (/ (+ N 1.0) N))

simplify59.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	502	790
1	2219	746
2	5002	735

prune269.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

3.2b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
4.0b	(log (+ N 1.0))
4.0b	(log (+ N 1.0))
4.0b	(log (+ N 1.0))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

196×	`prod-diff`
140×	`unpow-prod-down` `cube-prod`
118×	`add-sqr-sqrt` `*-un-lft-identity`
94×	`add-cube-cbrt`
81×	`pow1`
77×	`log-pow`
37×	`sqr-pow`
29×	`cube-mult` `unpow3`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
14×	`fma-neg`
12×	`log-prod`
7×	`add-exp-log`
6×	`log-div` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 309

Calls

4 calls:

29.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
2.0ms	(log (+ N 1.0))
2.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))

series341.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))
47.0ms	(log (+ N 1.0))
43.0ms	(log (+ N 1.0))
48.0ms	(log (+ N 1.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	789	4321
1	2843	3063
2	5001	3061

prune388.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes82.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 28.7b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	24	13

end0.0ms

sample2.0s

Algorithm

intervals

Results

580.0ms	1722×	body	1280	valid
408.0ms	8027×	body	80	nan
357.0ms	4156×	body	80	valid
281.0ms	1237×	body	640	valid
96.0ms	585×	body	320	valid
32.0ms	300×	body	160	valid