Details

sample137.0ms

Algorithm

intervals

Results

47.0ms	106×	body	1280	valid
15.0ms	47×	body	640	valid
13.0ms	29×	body	640	nan
10.0ms	18×	body	1280	nan
9.0ms	35×	body	10240	exit
7.0ms	187×	body	80	nan
7.0ms	154×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	12×	body	320	nan
1.0ms	9×	body	160	valid
1.0ms	7×	body	160	nan

simplify2.1s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite116.0ms

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))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))

series487.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
149.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify895.0ms

Counts

158 → 158

Iterations

Useful iterations: done (889.0ms)

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

prune342.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

89×	`*-un-lft-identity`
78×	`unpow-prod-down`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
56×	`prod-diff`
39×	`pow-unpow`
27×	`times-frac`
25×	`sqr-pow`
12×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 180

Calls

4 calls:

96.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series727.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
143.0ms	(pow (+ x 1.0) (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.2s

Counts

192 → 192

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	234	5202
1	537	3939
2	1315	3391
3	4464	3017
done	5000	3017

prune571.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.7b

localize27.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
112×	`pow-unpow`
100×	`*-un-lft-identity`
92×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`unpow-prod-down`
10×	`div-inv`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `sqr-pow`

Counts

4 → 180

Calls

4 calls:

13.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series601.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
144.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
153.0ms	(pow (+ x 1.0) (/ 1.0 n))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.3s

Counts

192 → 192

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	197	2440
1	502	2212
2	1290	2176
3	3674	2164
done	5001	2160

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 18.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
1.3b	(pow (+ x 1.0) (/ 1.0 n))
1.3b	(pow (+ x 1.0) (/ 1.0 n))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
112×	`pow-unpow`
100×	`*-un-lft-identity`
92×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`unpow-prod-down`
10×	`div-inv`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out` `add-log-exp` `sqr-pow`

Counts

4 → 180

Calls

4 calls:

14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
14.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
13.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series588.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
146.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
151.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify2.3s

Counts

192 → 192

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	197	2440
1	502	2212
2	1290	2176
3	3674	2164
done	5001	2160

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.7b

regimes172.0ms

Accuracy

84.4% (1.4b remaining)

Error of 22.1b against oracle of 20.7b and baseline of 29.6b

bsearch1.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	191
1	61	191
done	61	191

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3194×	body	1280	valid
543.0ms	1608×	body	640	valid
473.0ms	1142×	body	10240	exit
289.0ms	635×	body	1280	nan
249.0ms	4614×	body	80	valid
211.0ms	665×	body	640	nan
186.0ms	845×	body	320	valid
177.0ms	4987×	body	80	nan
65.0ms	461×	body	160	valid
63.0ms	348×	body	320	nan
21.0ms	196×	body	160	nan