Details

sample253.0ms

Algorithm

intervals

Results

58.0ms	118×	body	1280	valid
51.0ms	45×	body	1280	nan
32.0ms	75×	body	640	valid
25.0ms	155×	body	80	overflowed
23.0ms	34×	body	640	nan
13.0ms	265×	body	80	nan
10.0ms	25×	body	320	nan
9.0ms	101×	body	80	valid
9.0ms	27×	body	320	valid
2.0ms	10×	body	160	valid
1.0ms	7×	body	160	nan

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 31.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow x (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
3.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series467.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(pow (+ x 1.0) (/ 1.0 n))
61.0ms	(pow x (/ 1.0 n))
266.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune204.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	6	89

Merged error: 22.2b

Counts

89 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ x 1.0) (/ 1.0 n))
0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
0.0b	(pow x (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
29×	`pow-unpow`
27×	`difference-of-squares`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
5×	`add-cbrt-cube`
4×	`distribute-lft-out`
3×	`pow-to-exp` `pow-pow` `pow-exp`
2×	`cube-div` `flip3--` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `diff-log` `unpow3` `rem-cube-cbrt`

Counts

4 → 128

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
4.0ms	(pow x (/ 1.0 n))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series934.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
455.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
55.0ms	(pow x (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify79.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	757	1328
1	3144	1278
2	5001	1272

prune354.0ms

Filtered

140 candidates to 95 candidates (67.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Merged error: 22.2b

Counts

146 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
0.0b	(pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)
0.0b	(pow x (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

157×	`unpow-prod-down`
108×	`add-sqr-sqrt`
84×	`cube-prod`
73×	`*-un-lft-identity`
72×	`cbrt-prod`
63×	`difference-of-squares`
47×	`sqr-pow`
24×	`add-cube-cbrt`
21×	`distribute-lft-out--`
19×	`pow-unpow`
9×	`times-frac`
7×	`pow1` `add-exp-log` `distribute-lft-out`
6×	`cube-div` `add-log-exp`
5×	`add-cbrt-cube`
4×	`cube-mult` `pow-pow` `unpow3`
3×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
2×	`cbrt-div` `rem-cube-cbrt`
1×	`sub-neg` `pow1/3` `diff-log` `div-inv`

Counts

4 → 198

Calls

4 calls:

12.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
19.0ms	(pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)
4.0ms	(pow x (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

471.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
458.0ms	(pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)
62.0ms	(pow x (/ 1.0 n))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify111.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	962	2587
1	3443	2432
2	5002	2414

prune411.0ms

Filtered

210 candidates to 99 candidates (47.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	208	2	210
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	209	9	218

Merged error: 22.2b

Counts

218 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)) 3)
0.0b	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
0.0b	(pow x (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

353×	`unpow-prod-down`
312×	`cbrt-prod`
240×	`cube-prod`
168×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
99×	`difference-of-squares`
75×	`sqr-pow`
36×	`add-cube-cbrt`
33×	`distribute-lft-out--`
19×	`pow-unpow`
11×	`distribute-lft-out`
9×	`times-frac`
8×	`cube-div` `cube-mult` `unpow3`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
5×	`add-cbrt-cube`
4×	`cbrt-div` `pow-pow`
3×	`pow-to-exp` `flip3--` `pow-exp` `flip--`
2×	`rem-cube-cbrt`
1×	`sub-neg` `pow1/3` `diff-log` `div-inv`

Counts

4 → 294

Calls

4 calls:

31.0ms	(pow (cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)) 3)
12.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
4.0ms	(pow x (/ 1.0 n))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.3s

Counts

4 → 12

Calls

4 calls:

456.0ms	(pow (cbrt (pow (cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)) 3)) 3)
458.0ms	(pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3)
62.0ms	(pow x (/ 1.0 n))
284.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify121.0ms

Algorithm

egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	1259	4047
1	3741	3756
2	5001	3722

prune425.0ms

Filtered

306 candidates to 100 candidates (32.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	305	1	306
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	306	9	315

Merged error: 22.2b

Counts

315 → 9

regimes254.0ms

Accuracy

84.2% (1.7b remaining)

Error of 23.7b against oracle of 22.1b and baseline of 32.5b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	40
1	45	40

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.0s	3869×	body	1280	valid
1.2s	1076×	body	1280	nan
800.0ms	1813×	body	640	valid
779.0ms	4108×	body	80	overflowed
623.0ms	915×	body	640	nan
308.0ms	3127×	body	80	valid
296.0ms	6255×	body	80	nan
263.0ms	881×	body	320	valid
175.0ms	437×	body	320	nan
87.0ms	463×	body	160	valid
52.0ms	243×	body	160	nan

Details

sample253.0ms

simplify34.0ms

prune2.0ms

localize12.0ms

rewrite20.0ms

series467.0ms

simplify48.0ms

prune204.0ms

localize11.0ms

rewrite37.0ms

series934.0ms

simplify79.0ms

prune354.0ms

localize18.0ms

rewrite54.0ms

series1.3s

simplify111.0ms

prune411.0ms

localize16.0ms

rewrite79.0ms

series1.3s

simplify121.0ms

prune425.0ms

regimes254.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample7.0s

Profiling