Details

sample42.0ms

Algorithm

intervals

Results

11.0ms	47×	body	1280	valid
9.0ms	155×	body	80	valid
7.0ms	276×	body	80	nan
4.0ms	24×	body	640	valid
2.0ms	21×	body	320	valid
1.0ms	9×	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: 23.5b

localize6.0ms

Local error

Found 2 expressions with local error:

2.9b	(- (log (+ N 1.0)) (log N))
2.9b	(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:

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

series133.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (log (+ N 1.0)) (log N))
41.0ms	(log (+ N 1.0))

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	345

prune127.0ms

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:

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

series130.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (+ N 1.0) N)
80.0ms	(log (/ (+ N 1.0) N))

simplify102.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (96.0ms)

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

prune128.0ms

Pruning

4 alts after pruning (3 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)
3.9b	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

57×	`log-prod`
56×	`*-un-lft-identity`
49×	`times-frac`
46×	`associate-+r+`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`cbrt-prod`
28×	`sqrt-prod`
11×	`associate-+l+` `distribute-lft-out`
9×	`pow1`
5×	`log-pow`
4×	`add-exp-log` `expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`log-div` `div-inv`
1×	`+-commutative` `associate-+l-` `associate-+r-` `flip3-+` `sum-log` `flip-+`

Counts

4 → 119

Calls

4 calls:

0.0ms	(cbrt N)
0.0ms	(cbrt N)
0.0ms	(cbrt N)
34.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series771.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt N)
183.0ms	(cbrt N)
175.0ms	(cbrt N)
238.0ms	(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify47.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	515	1353
1	1641	1284
2	5001	1181

prune364.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
2.8b	(log (/ (cbrt (+ N 1.0)) (cbrt N)))
2.8b	(log (/ (cbrt (+ N 1.0)) (cbrt N)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

96×	`cbrt-prod`
92×	`log-prod`
84×	`*-un-lft-identity` `times-frac`
60×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log`
6×	`pow1`
4×	`expm1-log1p-u` `rem-log-exp` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `pow1/3` `div-exp` `log-pow` `div-inv`

Counts

4 → 144

Calls

4 calls:

0.0ms	(cbrt N)
0.0ms	(cbrt N)
5.0ms	(log (/ (cbrt (+ N 1.0)) (cbrt N)))
6.0ms	(log (/ (cbrt (+ N 1.0)) (cbrt N)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt N)
183.0ms	(cbrt N)
215.0ms	(log (/ (cbrt (+ N 1.0)) (cbrt N)))
221.0ms	(log (/ (cbrt (+ N 1.0)) (cbrt N)))

simplify41.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	347	1510
1	1027	1458
2	5002	1418

prune488.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.9b

bsearch34.0ms

Steps

Iters	Range		Point
9	7438.015107423713	588165898.4936482	9158.532865351755

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample1.2s

Algorithm

intervals

Results

432.0ms	1782×	body	1280	valid
182.0ms	8072×	body	80	nan
171.0ms	1136×	body	640	valid
169.0ms	4130×	body	80	valid
63.0ms	657×	body	320	valid
18.0ms	295×	body	160	valid