Details

sample227.0ms

Algorithm

intervals

Results

67.0ms	123×	body	1280	valid
35.0ms	31×	body	1280	nan
31.0ms	58×	body	640	valid
18.0ms	121×	body	80	overflowed
17.0ms	25×	body	640	nan
12.0ms	39×	body	320	valid
10.0ms	205×	body	80	nan
9.0ms	93×	body	80	valid
6.0ms	14×	body	320	nan
2.0ms	10×	body	160	valid
1.0ms	4×	body	160	nan

simplify33.0ms

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: 33.1b

Counts

2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

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:

9.0ms

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

series272.0ms

Counts

1 → 3

Calls

1 calls:

272.0ms

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

simplify78.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (17.0ms)

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

prune67.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	24	3	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	3	28

Merged error: 22.0b

Counts

28 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow x (/ 1.0 n)))
0.0b	(sqrt (+ x 1.0))
0.0b	(sqrt (+ x 1.0))
3.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
31×	`sqrt-prod`
16×	`unpow-prod-down` `difference-of-squares`
14×	`*-un-lft-identity`
10×	`sqr-pow`
8×	`add-cube-cbrt`
6×	`pow1` `add-log-exp`
5×	`rem-sqrt-square`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`sqrt-pow1` `pow1/2`
2×	`flip3-+` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 80

Calls

4 calls:

2.0ms	(sqrt (pow x (/ 1.0 n)))
3.0ms	(sqrt (+ x 1.0))
3.0ms	(sqrt (+ x 1.0))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

series609.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(sqrt (pow x (/ 1.0 n)))
29.0ms	(sqrt (+ x 1.0))
29.0ms	(sqrt (+ x 1.0))
471.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify121.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	427	872
1	1246	831
2	4886	817
3	5001	817

prune259.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	92	3	95

Merged error: 22.0b

Counts

95 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))))
3.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))
3.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))
3.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
64×	`sqrt-prod` `difference-of-squares`
48×	`unpow-prod-down`
32×	`sqr-pow`
20×	`cbrt-prod`
13×	`*-un-lft-identity`
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 → 117

Calls

4 calls:

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

series3.1s

Counts

4 → 12

Calls

4 calls:

1.7s	(cbrt (- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n)))))
475.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))
475.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))
469.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (sqrt (pow x (/ 1.0 n))))

simplify69.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	555	2584
1	1860	2507
2	5001	2446

prune487.0ms

Filtered

129 candidates to 90 candidates (69.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	129	3	132

Merged error: 22.0b

Counts

132 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
0.5b	(log (- (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)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
30×	`unpow-prod-down` `log-prod`
27×	`*-un-lft-identity` `difference-of-squares`
18×	`sqr-pow`
15×	`exp-sum`
9×	`distribute-lft-out--`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-div` `exp-prod`
3×	`flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out`
2×	`exp-diff` `log-pow`
1×	`sub-neg` `diff-log` `rem-log-exp` `rem-exp-log`

Counts

3 → 79

Calls

3 calls:

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

series1.0s

Counts

3 → 9

Calls

3 calls:

286.0ms	(exp (log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
460.0ms	(log (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify127.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	362	1122
1	962	1069
2	4463	1041
3	5001	1035

prune208.0ms

Filtered

88 candidates to 69 candidates (78.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	87	4	91

Merged error: 22.0b

Counts

91 → 4

regimes157.0ms

Accuracy

82.2% (2.0b remaining)

Error of 23.9b against oracle of 21.9b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	73
1	63	73

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.1s	3879×	body	1280	valid
1.2s	1067×	body	1280	nan
816.0ms	1775×	body	640	valid
639.0ms	900×	body	640	nan
621.0ms	4045×	body	80	overflowed
314.0ms	3137×	body	80	valid
301.0ms	6208×	body	80	nan
284.0ms	898×	body	320	valid
190.0ms	439×	body	320	nan
85.0ms	424×	body	160	valid
54.0ms	233×	body	160	nan