Details

sample283.0ms

Algorithm

intervals

Results

101.0ms	117×	body	1280	valid
31.0ms	46×	body	640	valid
21.0ms	36×	body	10240	exit
21.0ms	25×	body	1280	nan
21.0ms	143×	body	80	valid
19.0ms	33×	body	640	nan
13.0ms	175×	body	80	nan
9.0ms	23×	body	320	valid
3.0ms	14×	body	160	valid
3.0ms	8×	body	320	nan
1.0ms	6×	body	160	nan

simplify3.3s

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

localize18.0ms

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)))

rewrite219.0ms

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))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
196.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series727.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(pow x (/ 1.0 n))
218.0ms	(pow (+ x 1.0) (/ 1.0 n))
422.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

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

prune518.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.0b

localize30.0ms

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)))

rewrite353.0ms

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:

15.0ms	(pow (+ x 1.0) (/ 1.0 n))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
100.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
111.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.6s

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow (+ x 1.0) (/ 1.0 n))
467.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
513.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
433.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify3.5s

Counts

312 → 312

Iterations

Useful iterations: 3 (1.8s)

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

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 20.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite559.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 330

Calls

4 calls:

29.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
163.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
158.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
176.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.4s

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
403.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
421.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
390.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify2.7s

Counts

342 → 342

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	452	14206
1	1072	10106
2	2722	8409
done	5000	7242

prune1.8s

Pruning

6 alts after pruning (6 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)) (pow x (/ 1.0 n)))
0.5b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
0.5b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
0.5b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite642.0ms

Algorithm

rewrite-expression-head

Rules

264×	`unpow-prod-down`
224×	`*-un-lft-identity` `prod-diff`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
88×	`sqr-pow`
36×	`distribute-lft-out` `difference-of-squares`
32×	`fma-neg`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 360

Calls

4 calls:

164.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
164.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
106.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
163.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.5s

Counts

4 → 12

Calls

4 calls:

343.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
367.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
363.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
390.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify1.6s

Counts

372 → 372

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	330	19608
1	727	13323
2	1796	10948
done	5000	9213

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

regimes331.0ms

Accuracy

79% (1.7b remaining)

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

bsearch1.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	229
1	72	229
done	72	229

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.4s	3089×	body	1280	valid
1.2s	1088×	body	10240	exit
896.0ms	4913×	body	80	nan
893.0ms	1629×	body	640	valid
681.0ms	667×	body	1280	nan
502.0ms	4736×	body	80	valid
447.0ms	909×	body	320	valid
441.0ms	665×	body	640	nan
135.0ms	433×	body	160	valid
123.0ms	360×	body	320	nan
78.0ms	186×	body	160	nan