Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample236.0ms

Algorithm

intervals

Results

73.0ms	114×	body	1280	valid
52.0ms	46×	body	1280	nan
26.0ms	55×	body	640	valid
19.0ms	28×	body	640	nan
15.0ms	81×	body	80	overflowed
8.0ms	10×	body	640	invalid
6.0ms	20×	body	320	valid
6.0ms	60×	body	80	valid
4.0ms	9×	body	320	nan
4.0ms	3×	body	1280	invalid
2.0ms	6×	body	160	nan
2.0ms	4×	body	320	invalid
2.0ms	7×	body	160	valid
1.0ms	8×	body	80	invalid
1.0ms	15×	body	80	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

prune3.0ms

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: 31.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
13×	`unpow-prod-down` `pow-unpow`
10×	`add-cube-cbrt`
9×	`times-frac` `difference-of-squares`
7×	`sqr-pow`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`add-cbrt-cube`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv` `distribute-lft-out`

Counts

2 → 51

Calls

2 calls:

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

series52.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(pow x (/ 1.0 n))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	476	520
1	1648	503
2	5001	478

prune138.0ms

Filtered

47 candidates to 57 candidates (-21.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	52	5	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	5	58

Merged error: 22.2b

Counts

58 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
0.0b	(pow (sqrt x) (/ 1.0 n))
0.0b	(pow (sqrt x) (/ 1.0 n))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
41×	`unpow-prod-down`
39×	`pow-unpow`
31×	`add-cube-cbrt`
27×	`times-frac`
22×	`sqrt-prod`
16×	`difference-of-squares`
11×	`sqr-pow`
10×	`pow1`
9×	`pow-pow`
7×	`add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out--`
3×	`pow-to-exp` `sqrt-pow1` `pow1/2` `pow-exp` `sqrt-pow2` `div-inv`
2×	`distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 132

Calls

4 calls:

6.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))
4.0ms	(pow (sqrt x) (/ 1.0 n))
16.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(pow (sqrt (+ x 1.0)) (/ 1.0 n))
45.0ms	(pow (sqrt x) (/ 1.0 n))
40.0ms	(pow (sqrt x) (/ 1.0 n))
107.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify55.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	509	1212
1	1779	1175
2	5001	1159

prune389.0ms

Filtered

102 candidates to 144 candidates (-41.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	144	5	149

Merged error: 22.2b

Counts

149 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (cbrt x))
0.5b	(cbrt x)
0.5b	(cbrt x)
2.6b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (* (pow (fabs (cbrt x)) (/ 1.0 n)) (pow (sqrt (cbrt x)) (/ 1.0 n))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

10×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`rem-sqrt-square` `sqrt-pow1`
1×	`sub-neg` `flip3--` `pow1/2` `diff-log` `flip--`

Counts

4 → 52

Calls

4 calls:

2.0ms	(sqrt (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
7.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (* (pow (fabs (cbrt x)) (/ 1.0 n)) (pow (sqrt (cbrt x)) (/ 1.0 n))))

series155.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(sqrt (cbrt x))
23.0ms	(cbrt x)
21.0ms	(cbrt x)
90.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (* (pow (fabs (cbrt x)) (/ 1.0 n)) (pow (sqrt (cbrt x)) (/ 1.0 n))))

simplify43.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	462	638
1	1601	588
2	5001	534

prune227.0ms

Filtered

52 candidates to 64 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	63	6	69

Merged error: 22.1b

Counts

69 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (sqrt x) (/ 1.0 n)))
0.3b	(cbrt (pow (sqrt x) (/ 1.0 n)))
0.3b	(cbrt (pow (sqrt x) (/ 1.0 n)))
1.9b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

40×	`unpow-prod-down`
37×	`add-sqr-sqrt`
30×	`cbrt-prod`
22×	`*-un-lft-identity`
21×	`sqrt-prod`
16×	`difference-of-squares`
13×	`add-cube-cbrt`
11×	`sqr-pow`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

3.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
3.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
5.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
12.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
36.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
34.0ms	(cbrt (pow (sqrt x) (/ 1.0 n)))
104.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify42.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	356	1110
1	1167	1051
2	5001	1037

prune367.0ms

Filtered

75 candidates to 98 candidates (-30.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	98	6	104

Merged error: 22.1b

Counts

104 → 6

regimes306.0ms

Accuracy

84.5% (1.6b remaining)

Error of 24.1b against oracle of 22.5b and baseline of 32.9b

bsearch1.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	55
1	68	55
2	71	55
3	71	55

end0.0ms

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

sample7.1s

Algorithm

intervals

Results

2.2s	3762×	body	1280	valid
1.3s	1153×	body	1280	nan
745.0ms	1587×	body	640	valid
665.0ms	894×	body	640	nan
489.0ms	2559×	body	80	overflowed
233.0ms	494×	body	320	nan
226.0ms	670×	body	320	valid
156.0ms	222×	body	640	invalid
156.0ms	106×	body	1280	invalid
154.0ms	1597×	body	80	valid
83.0ms	384×	body	160	valid
70.0ms	163×	body	320	invalid
52.0ms	215×	body	160	nan
34.0ms	100×	body	160	invalid
33.0ms	511×	body	80	nan
29.0ms	221×	body	80	invalid

Details

analyze1.1s

sample236.0ms

simplify34.0ms

prune3.0ms

localize8.0ms

rewrite14.0ms

series52.0ms

simplify43.0ms

prune138.0ms

localize15.0ms

rewrite34.0ms

series246.0ms

simplify55.0ms

prune389.0ms

localize22.0ms

rewrite12.0ms

series155.0ms

simplify43.0ms

prune227.0ms

localize16.0ms

rewrite25.0ms

series209.0ms

simplify42.0ms

prune367.0ms

regimes306.0ms

bsearch1.0ms

simplify3.0ms

end0.0ms

analyze1.1s

sample7.1s

Profiling