Details

sample201.0ms

Algorithm

intervals

Results

61.0ms	91×	body	1280	valid
28.0ms	53×	body	640	valid
27.0ms	32×	body	10240	exit
11.0ms	131×	body	80	valid
10.0ms	170×	body	80	nan
10.0ms	18×	body	640	nan
10.0ms	27×	body	320	valid
6.0ms	11×	body	1280	nan
4.0ms	13×	body	320	nan
4.0ms	18×	body	160	valid
2.0ms	8×	body	160	nan

simplify3.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	17	13
2	35	13
3	86	13
4	245	13
5	730	13
6	3688	13
done	5000	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

4.0ms	(pow x (/ 1.0 n))
125.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series755.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(pow x (/ 1.0 n))
448.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
230.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.4s

Counts

158 → 158

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1619	3020
done	5000	2646

prune479.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.7b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
129×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
100×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 244

Calls

4 calls:

8.0ms	(pow x (/ 1.0 n))
152.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
16.0ms	(pow (+ x 1.0) (/ 1.0 n))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.0s

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow x (/ 1.0 n))
508.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
211.0ms	(pow (+ x 1.0) (/ 1.0 n))
221.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.3s

Counts

256 → 256

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	338	9618
1	772	7067
2	1761	5790
done	5000	5124

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.7b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite218.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
129×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
100×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 244

Calls

4 calls:

4.0ms	(pow x (/ 1.0 n))
160.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
14.0ms	(pow (+ x 1.0) (/ 1.0 n))
21.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow x (/ 1.0 n))
553.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
214.0ms	(pow (+ x 1.0) (/ 1.0 n))
236.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.5s

Counts

256 → 256

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	338	9618
1	772	7067
2	1761	5790
done	5000	5124

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.7b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
2.2b	(pow (+ x 1.0) (/ 1.0 n))
2.2b	(pow (+ x 1.0) (/ 1.0 n))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

195×	`sqrt-prod`
129×	`*-un-lft-identity`
118×	`add-sqr-sqrt`
110×	`prod-diff`
100×	`unpow-prod-down`
94×	`add-cube-cbrt`
39×	`pow-unpow`
33×	`sqr-pow`
27×	`times-frac`
16×	`difference-of-squares`
14×	`distribute-lft-out`
11×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 244

Calls

4 calls:

8.0ms	(pow x (/ 1.0 n))
147.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
29.0ms	(pow (+ x 1.0) (/ 1.0 n))
20.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.1s

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow x (/ 1.0 n))
589.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
243.0ms	(pow (+ x 1.0) (/ 1.0 n))
205.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.4s

Counts

256 → 256

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	338	9618
1	772	7067
2	1761	5790
done	5000	5124

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

regimes264.0ms

Accuracy

83.7% (1.4b remaining)

Error of 22.2b against oracle of 20.8b and baseline of 29.3b

bsearch217.0ms

Steps

Iters	Range		Point
6	273697205435.7094	3744461241692.0635	1031392298459.7406
7	-3446.367806925191	-108.09236434424712	-3406.4169782224208

simplify10.0ms

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	40	94
1	52	72
done	52	72

end0.0ms

sample8.9s

Algorithm

intervals

Results

2.7s	3138×	body	1280	valid
1.2s	1160×	body	10240	exit
984.0ms	1634×	body	640	valid
933.0ms	5002×	body	80	nan
611.0ms	4732×	body	80	valid
594.0ms	643×	body	1280	nan
437.0ms	656×	body	640	nan
335.0ms	827×	body	320	valid
122.0ms	361×	body	320	nan
117.0ms	436×	body	160	valid
40.0ms	199×	body	160	nan