Details

sample216.0ms

Algorithm

intervals

Results

61.0ms	116×	body	1280	valid
35.0ms	63×	body	640	valid
28.0ms	29×	body	1280	nan
18.0ms	30×	body	640	nan
17.0ms	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

simplify2.0s

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	209	13
5	656	13
6	3057	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

localize12.0ms

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)))

series41.0ms

Counts

1 → 3

Calls

1 calls:

41.0ms

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

simplify1.1s

Counts

27 → 27

Iterations

Useful iterations: 3 (314.0ms)

Iter	Nodes	Cost
0	117	719
1	283	684
2	751	644
3	2543	580
done	5001	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 (* x n))

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 (* x n))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(/ 1.0 (* x n))

simplify6.5s

Counts

24 → 24

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	47	185
1	104	182
2	334	152
3	1211	152
4	3183	152
done	5001	152

prune49.0ms

Filtered

16 candidates to 24 candidates (-50.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	18	6	24
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	18	9	27

Merged error: 24.7b

Counts

27 → 9

localize5.0ms

Local error

Found 1 expressions with local error:

0.3b	(* (/ 1 x) (/ 1.0 n))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
25×	`times-frac`
23×	`add-exp-log`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
13×	`associate-r` `associate-l` `add-cbrt-cube`
8×	`div-exp` `prod-exp`
6×	`unswap-sqr`
4×	`cbrt-undiv` `cbrt-unprod`
3×	`pow1`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `add-log-exp`

Counts

1 → 56

Calls

1 calls:

11.0ms

(* (/ 1 x) (/ 1.0 n))

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* (/ 1 x) (/ 1.0 n))

simplify2.6s

Counts

59 → 59

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	116	633
1	330	517
2	906	423
3	3483	423
done	5000	423

prune96.0ms

Filtered

33 candidates to 59 candidates (-78.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	52	7	59
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	55	13	68

Merged error: 24.7b

Counts

68 → 13

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ 1 x))
0.1b	(sqrt (/ 1 x))
0.3b	(* (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (/ 1.0 n)))
0.3b	(* (sqrt (/ 1 x)) (/ 1.0 n))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-sqr-sqrt`
58×	`sqrt-prod`
57×	`times-frac`
45×	`*-un-lft-identity`
41×	`add-cube-cbrt`
32×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
15×	`pow1`
14×	`associate-r`
12×	`sqrt-div`
8×	`unswap-sqr`
7×	`prod-exp` `cbrt-unprod`
6×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `associate-*r/`
5×	`div-inv`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`cbrt-undiv` `pow-flip` `pow1/2` `div-exp` `*-commutative` `inv-pow`

Counts

4 → 149

Calls

4 calls:

3.0ms	(sqrt (/ 1 x))
3.0ms	(sqrt (/ 1 x))
14.0ms	(* (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (/ 1.0 n)))
12.0ms	(* (sqrt (/ 1 x)) (/ 1.0 n))

series29.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (/ 1 x))
3.0ms	(sqrt (/ 1 x))
10.0ms	(* (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (/ 1.0 n)))
14.0ms	(* (sqrt (/ 1 x)) (/ 1.0 n))

simplify756.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	223	1967
1	566	1598
2	1758	1466
done	5001	1466

prune241.0ms

Filtered

110 candidates to 161 candidates (-46.4%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	154	7	161
Fresh	3	7	10
Picked	1	0	1
Done	0	2	2
Total	158	16	174

Merged error: 24.7b

Counts

174 → 16

regimes515.0ms

Accuracy

84.8% (1.6b remaining)

Error of 23.5b against oracle of 21.9b and baseline of 32.7b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	21	52
1	28	40
done	28	40

end0.0ms

sample7.0s

Algorithm

intervals

Results

2.1s	3937×	body	1280	valid
1.0s	1072×	body	1280	nan
828.0ms	1767×	body	640	valid
573.0ms	3907×	body	80	overflowed
565.0ms	888×	body	640	nan
294.0ms	3002×	body	80	valid
291.0ms	5963×	body	80	nan
267.0ms	873×	body	320	valid
183.0ms	446×	body	320	nan
79.0ms	419×	body	160	valid
40.0ms	187×	body	160	nan

Details

sample216.0ms

simplify2.0s

prune3.0ms

localize12.0ms

rewrite11.0ms

series41.0ms

simplify1.1s

prune72.0ms

localize4.0ms

rewrite5.0ms

series4.0ms

simplify6.5s

prune49.0ms

localize5.0ms

rewrite13.0ms

series3.0ms

simplify2.6s

prune96.0ms

localize8.0ms

rewrite39.0ms

series29.0ms

simplify756.0ms

prune241.0ms

regimes515.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample7.0s

Profiling