Details

sample45.0ms

Algorithm

intervals

Results

12.0ms	50×	body	1280	valid
6.0ms	39×	body	640	valid
6.0ms	233×	body	80	nan
5.0ms	130×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	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: 29.2b

localize6.0ms

Local error

Found 2 expressions with local error:

1.2b	(log (+ N 1.0))
3.8b	(- (log (+ N 1.0)) (log N))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
11×	`log-prod`
7×	`pow1` `add-sqr-sqrt`
5×	`add-cube-cbrt` `log-pow`
4×	`log-div` `associate--l+` `distribute-lft-out--`
3×	`add-exp-log` `associate--r+`
2×	`associate--l-` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

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

series140.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(log (+ N 1.0))
95.0ms	(- (log (+ N 1.0)) (log N))

simplify52.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	212	281
1	547	264
2	1875	250
3	5001	247

prune103.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (+ N 1.0))
1.2b	(log (+ N 1.0))
1.2b	(log (+ N 1.0))
3.8b	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down` `cube-prod`
23×	`pow1`
19×	`log-pow`
17×	`distribute-lft-out--`
16×	`difference-of-squares`
12×	`log-prod`
8×	`sqr-pow`
7×	`add-exp-log` `add-cube-cbrt`
6×	`log-div` `add-log-exp`
4×	`add-cbrt-cube`
3×	`flip3-+` `rem-log-exp` `flip-+` `distribute-lft-out`
1×	`difference-cubes` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 91

Calls

4 calls:

3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
3.0ms	(log (+ N 1.0))
14.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

series324.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(log (+ N 1.0))
41.0ms	(log (+ N 1.0))
46.0ms	(log (+ N 1.0))
190.0ms	(- (pow (log (+ N 1.0)) 3) (pow (log N) 3))

simplify49.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	480	888
1	1809	857
2	5001	844

prune298.0ms

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)
3.9b	(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×	`div-exp` `rem-log-exp` `div-inv` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `clear-num` `log-pow` `flip-+`

Counts

2 → 60

Calls

2 calls:

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

series137.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (+ N 1.0) N)
86.0ms	(log (/ (+ N 1.0) N))

simplify101.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	233	373
1	773	351
2	3489	339
3	5002	339

prune126.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
5.1b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
55×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
37×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
8×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 107

Calls

4 calls:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
19.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt N)
189.0ms	(cbrt N)
179.0ms	(cbrt N)
248.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify47.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	507	1315
1	1618	1245
2	5001	1128

prune348.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes34.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.1b

bsearch39.0ms

Steps

Iters	Range		Point
8	21.660028671588154	6793.132116615613	4600.683996243076

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	22
1	38	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

427.0ms	1731×	body	1280	valid
190.0ms	1199×	body	640	valid
189.0ms	8115×	body	80	nan
175.0ms	4132×	body	80	valid
60.0ms	600×	body	320	valid
21.0ms	338×	body	160	valid