Details

sample232.0ms

Algorithm

intervals

Results

64.0ms	113×	body	1280	valid
40.0ms	36×	body	1280	nan
29.0ms	68×	body	640	valid
21.0ms	151×	body	80	overflowed
15.0ms	22×	body	640	nan
11.0ms	223×	body	80	nan
11.0ms	107×	body	80	valid
10.0ms	34×	body	320	valid
7.0ms	17×	body	320	nan
2.0ms	9×	body	160	valid
1.0ms	4×	body	160	nan

simplify36.0ms

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

prune4.0ms

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: 35.9b

Counts

2 → 1

localize24.0ms

Local error

Found 1 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

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:

19.0ms

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

series306.0ms

Counts

1 → 3

Calls

1 calls:

305.0ms

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

simplify75.0ms

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

prune89.0ms

Filtered

27 candidates to 23 candidates (85.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	22	5	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	5	28

Merged error: 24.2b

Counts

28 → 5

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
32×	`sqrt-prod`
22×	`unpow-prod-down`
16×	`difference-of-squares`
13×	`*-un-lft-identity`
12×	`sqr-pow`
7×	`add-cube-cbrt`
6×	`rem-sqrt-square`
5×	`add-log-exp`
3×	`pow1` `add-exp-log` `add-cbrt-cube`
2×	`sqrt-pow1` `pow1/2` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

3 → 69

Calls

3 calls:

5.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
5.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
16.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series994.0ms

Counts

3 → 9

Calls

3 calls:

242.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
237.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
515.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify100.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	329	834
1	964	806
2	3705	797
3	5001	797

prune269.0ms

Filtered

78 candidates to 60 candidates (76.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 24.1b

Counts

83 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
0.0b	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

134×	`add-sqr-sqrt`
105×	`unpow-prod-down`
88×	`sqrt-prod`
80×	`difference-of-squares`
46×	`cbrt-prod`
44×	`sqr-pow`
40×	`cube-prod`
24×	`*-un-lft-identity`
12×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
4×	`cube-div`
3×	`rem-sqrt-square` `pow-unpow` `flip3--` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3`
1×	`pow-to-exp` `sub-neg` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `diff-log` `pow-exp` `rem-cbrt-cube` `distribute-lft-out` `rem-cube-cbrt`

Counts

4 → 165

Calls

4 calls:

5.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
19.0ms	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
16.0ms	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
13.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

series3.1s

Counts

4 → 12

Calls

4 calls:

250.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
1.8s	(pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3)
512.0ms	(cbrt (pow (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))) 3))
518.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))

simplify121.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1081	3183
1	4909	3099
2	5001	3099

prune546.0ms

Filtered

177 candidates to 92 candidates (52.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	175	2	177
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	176	7	183

Merged error: 24.1b

Counts

183 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
0.0b	(exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
2.1b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))
2.1b	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
56×	`sqrt-prod`
48×	`difference-of-squares`
41×	`unpow-prod-down`
40×	`exp-prod`
26×	`sqr-pow`
21×	`log-pow`
17×	`*-un-lft-identity`
9×	`add-cube-cbrt` `add-log-exp`
5×	`pow1` `log-prod`
4×	`add-exp-log` `exp-sum` `add-cbrt-cube`
3×	`sub-neg` `rem-sqrt-square` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `sqrt-pow1` `pow1/2` `rem-log-exp` `flip--` `distribute-lft-out`

Counts

4 → 116

Calls

4 calls:

5.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
15.0ms	(exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
14.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))
15.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))))

series2.4s

Counts

4 → 12

Calls

4 calls:

249.0ms	(sqrt (pow (+ x 1.0) (/ 1.0 n)))
1.1s	(exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n))))
528.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))
530.0ms	(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow (sqrt x) (/ 1.0 n)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	424	1524
1	1243	1454
2	4379	1440
3	5002	1440

prune422.0ms

Filtered

128 candidates to 89 candidates (69.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	127	8	135

Merged error: 24.1b

Counts

135 → 8

regimes208.0ms

Accuracy

85.7% (1.6b remaining)

Error of 23.6b against oracle of 22.0b and baseline of 33.1b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	50
1	57	50

end0.0ms

sample7.4s

Algorithm

intervals

Results

2.1s	3942×	body	1280	valid
1.4s	1081×	body	1280	nan
814.0ms	1778×	body	640	valid
648.0ms	926×	body	640	nan
616.0ms	4101×	body	80	overflowed
313.0ms	3101×	body	80	valid
305.0ms	6210×	body	80	nan
274.0ms	889×	body	320	valid
177.0ms	434×	body	320	nan
90.0ms	450×	body	160	valid
50.0ms	232×	body	160	nan

Details

sample232.0ms

simplify36.0ms

prune4.0ms

localize24.0ms

rewrite21.0ms

series306.0ms

simplify75.0ms

prune89.0ms

localize13.0ms

rewrite28.0ms

series994.0ms

simplify100.0ms

prune269.0ms

localize16.0ms

rewrite62.0ms

series3.1s

simplify121.0ms

prune546.0ms

localize16.0ms

rewrite54.0ms

series2.4s

simplify119.0ms

prune422.0ms

regimes208.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.4s

Profiling