Details

sample217.0ms

Algorithm

intervals

Results

62.0ms	130×	body	1280	valid
37.0ms	62×	body	1280	nan
23.0ms	57×	body	640	nan
22.0ms	54×	body	640	valid
19.0ms	44×	body	5120	exit
9.0ms	40×	body	320	valid
9.0ms	191×	body	80	nan
8.0ms	30×	body	320	nan
5.0ms	94×	body	80	valid
2.0ms	14×	body	160	valid
2.0ms	10×	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: 31.8b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.0b	(pow (+ x 1.0) (/ 1.0 n))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

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:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
14.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series492.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

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

prune206.0ms

Filtered

88 candidates to 70 candidates (79.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	5	89

Merged error: 20.3b

Counts

89 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite40.0ms

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:

9.0ms	(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)))

series1.4s

Counts

4 → 12

Calls

4 calls:

580.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify117.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	362	1439
1	973	1385
2	4399	1363
3	5001	1363

prune369.0ms

Filtered

109 candidates to 93 candidates (85.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	109	5	114

Merged error: 20.3b

Counts

114 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
40×	`unpow-prod-down`
36×	`difference-of-squares`
35×	`*-un-lft-identity`
24×	`sqr-pow`
19×	`log-pow`
18×	`exp-prod`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
7×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `log-prod` `flip3--` `diff-log` `flip--`
1×	`rem-log-exp`

Counts

4 → 102

Calls

4 calls:

14.0ms	(log (exp (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)))
10.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts

4 → 12

Calls

4 calls:

591.0ms	(log (exp (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
301.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
292.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
291.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify125.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	397	1359
1	1021	1291
2	4472	1269
3	5001	1269

prune428.0ms

Filtered

114 candidates to 96 candidates (84.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	113	6	119

Merged error: 20.3b

Counts

119 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.3b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite45.0ms

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:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

292.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
289.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
288.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	222	1304
1	594	1252
2	2745	1228
3	5003	1228

prune479.0ms

Filtered

108 candidates to 92 candidates (85.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	108	6	114

Merged error: 20.3b

Counts

114 → 6

regimes233.0ms

Accuracy

83.5% (1.8b remaining)

Error of 23.6b against oracle of 21.8b and baseline of 32.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	64	111
1	64	111

end0.0ms

sample7.0s

Algorithm

intervals

Results

1.9s	3885×	body	1280	valid
1.5s	2078×	body	1280	nan
730.0ms	1719×	body	640	nan
684.0ms	1406×	body	5120	exit
635.0ms	1782×	body	640	valid
281.0ms	6036×	body	80	nan
248.0ms	911×	body	320	nan
219.0ms	917×	body	320	valid
173.0ms	3082×	body	80	valid
72.0ms	448×	body	160	nan
66.0ms	443×	body	160	valid