Details

sample195.0ms

Algorithm

intervals

Results

73.0ms	117×	body	1280	valid
24.0ms	46×	body	640	valid
16.0ms	36×	body	10240	exit
14.0ms	25×	body	1280	nan
13.0ms	33×	body	640	nan
11.0ms	143×	body	80	valid
10.0ms	175×	body	80	nan
7.0ms	23×	body	320	valid
3.0ms	14×	body	160	valid
2.0ms	8×	body	320	nan
1.0ms	6×	body	160	nan

simplify3.2s

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: 28.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite172.0ms

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:

7.0ms	(pow x (/ 1.0 n))
23.0ms	(pow (+ x 1.0) (/ 1.0 n))
131.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series733.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(pow x (/ 1.0 n))
222.0ms	(pow (+ x 1.0) (/ 1.0 n))
424.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.3s

Counts

158 → 158

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	271	4785
1	647	3566
2	1620	3020
done	5000	2646

prune495.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite403.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

11.0ms	(pow (+ x 1.0) (/ 1.0 n))
155.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
108.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
113.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

206.0ms	(pow (+ x 1.0) (/ 1.0 n))
435.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
400.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
387.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.3s

Counts

312 → 312

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	234	12646
1	537	9161
2	1315	7533
3	4460	6435
done	5000	6435

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite467.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
189×	`prod-diff`
188×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
73×	`sqrt-prod`
71×	`sqr-pow`
30×	`difference-of-squares`
27×	`fma-neg` `distribute-lft-out`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 325

Calls

4 calls:

15.0ms	(pow (+ x 1.0) (/ 1.0 n))
146.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
137.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
151.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

208.0ms	(pow (+ x 1.0) (/ 1.0 n))
423.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
458.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
583.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify1.9s

Counts

337 → 337

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	396	15231
1	885	10677
2	2146	8710
done	5001	7437

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
1.0b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
1.0b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite670.0ms

Algorithm

rewrite-expression-head

Rules

287×	`prod-diff`
282×	`unpow-prod-down`
251×	`*-un-lft-identity`
237×	`add-sqr-sqrt`
219×	`sqrt-prod`
174×	`add-cube-cbrt`
100×	`sqr-pow`
45×	`difference-of-squares`
41×	`fma-neg`
33×	`distribute-lft-out`
12×	`add-log-exp`
6×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 435

Calls

4 calls:

104.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
203.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
154.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
182.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

421.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
581.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
598.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
620.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify1.8s

Counts

447 → 447

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	347	24123
1	758	16655
2	1813	13135
done	5000	11081

prune2.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

regimes351.0ms

Accuracy

79% (1.7b remaining)

Error of 23.0b against oracle of 21.3b and baseline of 29.5b

bsearch2.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	54	249
1	72	249
done	72	249

end0.0ms

sample9.0s

Algorithm

intervals

Results

2.6s	3089×	body	1280	valid
1.1s	1629×	body	640	valid
951.0ms	1088×	body	10240	exit
678.0ms	667×	body	1280	nan
623.0ms	4736×	body	80	valid
541.0ms	360×	body	320	nan
540.0ms	433×	body	160	valid
481.0ms	665×	body	640	nan
421.0ms	4913×	body	80	nan
344.0ms	909×	body	320	valid
39.0ms	186×	body	160	nan