Details

sample223.0ms

Algorithm

intervals

Results

62.0ms	116×	body	1280	valid
32.0ms	63×	body	640	valid
29.0ms	29×	body	1280	nan
24.0ms	30×	body	640	nan
18.0ms	122×	body	80	overflowed
10.0ms	97×	body	80	valid
8.0ms	169×	body	80	nan
7.0ms	21×	body	320	valid
4.0ms	10×	body	320	nan
3.0ms	15×	body	160	valid
1.0ms	6×	body	160	nan

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	216	13
5	719	13
6	3216	13
done	5000	13

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: 33.8b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

2.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite11.0ms

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:

10.0ms

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

series49.0ms

Counts

1 → 3

Calls

1 calls:

49.0ms

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

simplify662.0ms

Counts

27 → 27

Iterations

Useful iterations: 3 (222.0ms)

Iter	Nodes	Cost
0	117	719
1	283	686
2	826	644
3	2502	580
done	5000	580

prune72.0ms

Filtered

23 candidates to 27 candidates (-17.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 24.7b

Counts

28 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

0.8b	(/ 1.0 (* n x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
2×	`cbrt-undiv` `div-exp`
1×	`pow1` `frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv` `add-log-exp`

Counts

1 → 21

Calls

1 calls:

5.0ms

(/ 1.0 (* n x))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(/ 1.0 (* n x))

simplify990.0ms

Counts

24 → 24

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	49	185
1	106	182
2	355	152
3	1310	152
4	3456	152
done	5000	152

prune54.0ms

Filtered

16 candidates to 24 candidates (-50.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	17	7	24
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	17	10	27

Merged error: 24.7b

Counts

27 → 10

localize4.0ms

Local error

Found 1 expressions with local error:

0.2b	(/ (/ 1.0 n) x)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
43×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv`
3×	`cbrt-undiv` `div-exp` `associate-/r*`
1×	`pow1` `frac-2neg` `clear-num` `associate-/l/` `add-log-exp`

Counts

1 → 70

Calls

1 calls:

6.0ms

(/ (/ 1.0 n) x)

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(/ (/ 1.0 n) x)

simplify641.0ms

Counts

73 → 73

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	150	862
1	336	813
2	1017	781
3	3166	781
done	5001	781

prune142.0ms

Filtered

60 candidates to 73 candidates (-21.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	64	9	73
Fresh	4	3	7
Picked	0	1	1
Done	1	1	2
Total	69	14	83

Merged error: 24.7b

Counts

83 → 14

localize6.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (/ (/ 1.0 n) (sqrt x)) (sqrt x))
0.3b	(/ (/ 1.0 n) (sqrt x))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

1557×	`times-frac`
728×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
564×	`sqrt-prod`
95×	`associate-/l*`
58×	`div-inv`
16×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r*`
9×	`cbrt-undiv` `div-exp`
2×	`pow1` `frac-2neg` `clear-num` `associate-/l/` `add-log-exp`

Counts

2 → 709

Calls

2 calls:

30.0ms	(/ (/ (/ 1.0 n) (sqrt x)) (sqrt x))
11.0ms	(/ (/ 1.0 n) (sqrt x))

series16.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(/ (/ (/ 1.0 n) (sqrt x)) (sqrt x))
9.0ms	(/ (/ 1.0 n) (sqrt x))

simplify580.0ms

Counts

715 → 715

Iterations

Useful iterations: done (553.0ms)

Iter	Nodes	Cost
0	840	15787
1	1935	14158
done	5001	13800

prune491.0ms

Filtered

293 candidates to 715 candidates (-144.0%)

Pruning

22 alts after pruning (21 fresh and 1 done)

	Pruned	Kept	Total
New	700	15	715
Fresh	5	6	11
Picked	1	0	1
Done	1	1	2
Total	707	22	729

Merged error: 24.7b

Counts

729 → 22

regimes637.0ms

Accuracy

85.8% (1.5b remaining)

Error of 23.4b against oracle of 21.9b and baseline of 32.7b

bsearch105.0ms

Steps

Iters	Range		Point
7	18.076566431700634	848.6737351236724	837.618174149808
9	-5050.104235080154	-0.0552767792151412	-4984.247920402621

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	65
1	35	65
done	35	65

end0.0ms

sample7.2s

Algorithm

intervals

Results

2.3s	3937×	body	1280	valid
1.1s	1072×	body	1280	nan
833.0ms	1767×	body	640	valid
588.0ms	3907×	body	80	overflowed
578.0ms	888×	body	640	nan
300.0ms	5963×	body	80	nan
290.0ms	3002×	body	80	valid
277.0ms	873×	body	320	valid
180.0ms	446×	body	320	nan
83.0ms	419×	body	160	valid
40.0ms	187×	body	160	nan

Details

sample223.0ms

simplify1.1s

prune3.0ms

localize7.0ms

rewrite11.0ms

series49.0ms

simplify662.0ms

prune72.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify990.0ms

prune54.0ms

localize4.0ms

rewrite10.0ms

series4.0ms

simplify641.0ms

prune142.0ms

localize6.0ms

rewrite111.0ms

series16.0ms

simplify580.0ms

prune491.0ms

regimes637.0ms

bsearch105.0ms

simplify3.0ms

end0.0ms

sample7.2s

Profiling