Details

sample4.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.844116%

Guaranteed chance to sample good point: 45.302502%

Results

74.0ms	134×	body	1280	valid
46.0ms	43×	body	1280	nan
19.0ms	42×	body	640	valid
17.0ms	117×	body	80	overflowed
14.0ms	20×	body	640	nan
12.0ms	8×	body	1280	invalid
7.0ms	24×	body	320	valid
6.0ms	10×	body	640	invalid
5.0ms	12×	body	320	nan
4.0ms	44×	body	80	valid
2.0ms	12×	body	160	valid
1.0ms	6×	body	160	nan
1.0ms	3×	body	320	invalid
1.0ms	3×	body	160	invalid
1.0ms	11×	body	80	nan
1.0ms	5×	body	80	invalid

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

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: 32.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow x (/ 1.0 n))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite18.0ms

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))
12.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series53.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(pow x (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify44.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (37.0ms)

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

prune144.0ms

Filtered

47 candidates to 57 candidates (-21.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Merged error: 22.9b

Counts

58 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite42.0ms

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:

11.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
47.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	505	1633
1	1560	1564
2	5001	1489

prune550.0ms

Filtered

93 candidates to 109 candidates (-17.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	106	9	115

Merged error: 22.9b

Counts

115 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
32×	`*-un-lft-identity`
24×	`sqr-pow`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

16.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
16.0ms	(- (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)))
9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series188.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
38.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
46.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
67.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify142.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	280	1408
1	785	1348
2	3548	1316
3	5001	1316

prune845.0ms

Filtered

92 candidates to 108 candidates (-17.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	110	7	117

Merged error: 22.8b

Counts

117 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
52×	`unpow-prod-down`
43×	`difference-of-squares`
34×	`*-un-lft-identity`
26×	`sqr-pow`
13×	`distribute-lft-out--`
12×	`sqrt-prod` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 104

Calls

4 calls:

9.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms	(- (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)))
13.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

series217.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
39.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
37.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
104.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow (sqrt x) (/ 1.0 n)))

simplify58.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	498	1650
1	1591	1585
2	5002	1556

prune1.1s

Filtered

93 candidates to 116 candidates (-24.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	112	4	116
Fresh	1	4	5
Picked	1	0	1
Done	1	0	1
Total	115	8	123

Merged error: 22.8b

Counts

123 → 8

regimes400.0ms

Accuracy

84.5% (1.6b remaining)

Error of 23.9b against oracle of 22.3b and baseline of 32.8b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	145
1	93	145
2	96	145
3	96	145

end0.0ms

sample11.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 30.844116%

Guaranteed chance to sample good point: 45.302502%

Results

2.0s	3737×	body	1280	valid
1.2s	1064×	body	1280	nan
712.0ms	1606×	body	640	valid
623.0ms	4118×	body	80	overflowed
605.0ms	895×	body	640	nan
213.0ms	697×	body	320	valid
185.0ms	443×	body	320	nan
173.0ms	256×	body	640	invalid
143.0ms	1601×	body	80	valid
128.0ms	99×	body	1280	invalid
76.0ms	181×	body	320	invalid
70.0ms	359×	body	160	valid
45.0ms	205×	body	160	nan
29.0ms	469×	body	80	nan
24.0ms	104×	body	160	invalid
19.0ms	162×	body	80	invalid

Details

sample4.4s

simplify33.0ms

prune3.0ms

localize8.0ms

rewrite18.0ms

series53.0ms

simplify44.0ms

prune144.0ms

localize13.0ms

rewrite42.0ms

series263.0ms

simplify56.0ms

prune550.0ms

localize16.0ms

rewrite57.0ms

series188.0ms

simplify142.0ms

prune845.0ms

localize28.0ms

rewrite46.0ms

series217.0ms

simplify58.0ms

prune1.1s

regimes400.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample11.1s

Profiling