Details

sample220.0ms

Algorithm

intervals

Results

58.0ms	89×	body	1280	valid
33.0ms	45×	body	10240	exit
29.0ms	53×	body	640	valid
15.0ms	22×	body	1280	nan
14.0ms	29×	body	320	valid
13.0ms	152×	body	80	valid
10.0ms	172×	body	80	nan
9.0ms	16×	body	640	nan
4.0ms	13×	body	320	nan
2.0ms	10×	body	160	valid
2.0ms	9×	body	160	nan

simplify1.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	34	13
3	81	13
4	238	13
5	1224	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize19.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite145.0ms

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:

8.0ms	(pow x (/ 1.0 n))
117.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
15.0ms	(pow (+ x 1.0) (/ 1.0 n))

series820.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(pow x (/ 1.0 n))
478.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
222.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.3s

Counts

88 → 88

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	190	1337
1	546	1246
2	2105	1206
done	5001	1204

prune431.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
0.7b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
52×	`unpow-prod-down`
46×	`*-un-lft-identity`
36×	`cbrt-prod`
27×	`difference-of-squares`
26×	`pow-unpow`
23×	`add-cube-cbrt`
21×	`sqr-pow`
18×	`times-frac`
15×	`cube-prod`
9×	`distribute-lft-out--`
6×	`pow1` `add-exp-log` `add-log-exp`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`cube-div` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow-exp` `flip--` `div-inv`
1×	`cube-mult` `sub-neg` `pow1/3` `diff-log` `unpow3` `rem-cbrt-cube`

Counts

4 → 126

Calls

4 calls:

107.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
5.0ms	(pow x (/ 1.0 n))
103.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.0s

Counts

4 → 12

Calls

4 calls:

373.0ms	(cbrt (pow (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))) 3))
98.0ms	(pow x (/ 1.0 n))
357.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
212.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.0s

Counts

138 → 138

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	261	2940
1	798	2513
2	3762	2414
done	5001	2412

prune594.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

localize24.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
28×	`unpow-prod-down`
26×	`pow-unpow`
20×	`add-cube-cbrt`
18×	`times-frac` `difference-of-squares`
14×	`sqr-pow`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`add-cbrt-cube` `distribute-lft-out`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

4 → 104

Calls

4 calls:

132.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
127.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
18.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.3s

Counts

4 → 12

Calls

4 calls:

449.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
374.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
219.0ms	(pow (+ x 1.0) (/ 1.0 n))
220.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify937.0ms

Counts

116 → 116

Iterations

Useful iterations: done (930.0ms)

Iter	Nodes	Cost
0	149	2052
1	403	1930
2	1425	1854
done	5000	1838

prune841.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

localize46.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
1.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.8b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.8b	(pow (+ x 1.0) (/ 1.0 n))

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
101×	`add-sqr-sqrt`
99×	`pow-unpow`
92×	`*-un-lft-identity`
84×	`add-cube-cbrt`
19×	`unpow-prod-down`
12×	`difference-of-squares`
10×	`sqr-pow`
9×	`sqrt-prod` `div-inv`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 169

Calls

4 calls:

131.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
17.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
30.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
17.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.2s

Counts

4 → 12

Calls

4 calls:

515.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (sqrt (pow x (/ 1.0 n))))
211.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
258.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
208.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.3s

Counts

181 → 181

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	264	2884
1	839	2629
2	3283	2563
done	5002	2560

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.3b

regimes228.0ms

Accuracy

85.4% (1.3b remaining)

Error of 21.7b against oracle of 20.4b and baseline of 29.2b

bsearch207.0ms

Steps

Iters	Range		Point
6	32715339.804033544	132929981.28964968	56897569.69187657
5	-1333.496421940221	-527.3133570883257	-1313.1390827564153

simplify26.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	44	113
1	57	89
2	63	89
3	64	89
done	64	89

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.5s	3173×	body	1280	valid
1.5s	1211×	body	10240	exit
916.0ms	1586×	body	640	valid
821.0ms	619×	body	640	nan
545.0ms	616×	body	1280	nan
487.0ms	4838×	body	80	valid
442.0ms	5208×	body	80	nan
357.0ms	827×	body	320	valid
195.0ms	350×	body	320	nan
101.0ms	424×	body	160	valid
79.0ms	202×	body	160	nan