Details

sample249.0ms

Algorithm

intervals

Results

52.0ms	110×	body	1280	valid
49.0ms	77×	body	1280	nan
31.0ms	74×	body	640	nan
27.0ms	48×	body	10240	exit
25.0ms	73×	body	640	valid
15.0ms	40×	body	320	nan
11.0ms	234×	body	80	nan
7.0ms	32×	body	320	valid
5.0ms	104×	body	80	valid
2.0ms	14×	body	160	nan
1.0ms	11×	body	160	valid

simplify34.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize8.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`*-un-lft-identity`
6×	`sqr-pow`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 24

Calls

1 calls:

10.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series276.0ms

Counts

1 → 3

Calls

1 calls:

276.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify74.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	222	326
1	594	313
2	2745	307
3	5003	307

prune84.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
33×	`*-un-lft-identity`
24×	`sqr-pow`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 97

Calls

4 calls:

10.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

580.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify127.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	362	1439
1	973	1385
2	4399	1363
3	5001	1363

prune425.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
48×	`unpow-prod-down`
37×	`*-un-lft-identity`
34×	`difference-of-squares`
20×	`sqr-pow`
16×	`sqrt-prod`
10×	`distribute-lft-out--` `add-log-exp`
8×	`distribute-lft-out`
7×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 97

Calls

4 calls:

13.0ms	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series4.5s

Counts

4 → 12

Calls

4 calls:

3.2s	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
288.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
745.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	443	1514
1	1251	1434
2	5001	1418

prune576.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (sqrt (+ x 1.0)) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
48×	`unpow-prod-down`
37×	`*-un-lft-identity`
34×	`difference-of-squares`
20×	`sqr-pow`
16×	`sqrt-prod`
10×	`distribute-lft-out--` `add-log-exp`
8×	`distribute-lft-out`
7×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`cbrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 97

Calls

4 calls:

13.0ms	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
15.0ms	(- (pow (sqrt (+ x 1.0)) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))

series4.5s

Counts

4 → 12

Calls

4 calls:

3.2s	(cbrt (+ (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n))))
290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
763.0ms	(- (pow (sqrt (+ x 1.0)) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ (/ 1.0 n) 2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	489	1612
1	1381	1528
2	5001	1512

prune674.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

regimes238.0ms

Accuracy

81.9% (2.0b remaining)

Error of 24.0b against oracle of 22.1b and baseline of 33.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	75	80
1	75	80

end0.0ms

sample7.0s

Algorithm

intervals

Results

1.9s	3923×	body	1280	valid
1.3s	2258×	body	1280	nan
745.0ms	1811×	body	640	nan
675.0ms	1446×	body	10240	exit
613.0ms	1792×	body	640	valid
283.0ms	6286×	body	80	nan
277.0ms	466×	body	160	valid
230.0ms	918×	body	320	nan
196.0ms	891×	body	320	valid
168.0ms	3191×	body	80	valid
76.0ms	478×	body	160	nan