Details

sample198.0ms

Algorithm

intervals

Results

70.0ms	103×	body	1280	valid
23.0ms	44×	body	640	valid
18.0ms	40×	body	10240	exit
12.0ms	34×	body	320	valid
11.0ms	137×	body	80	valid
10.0ms	174×	body	80	nan
10.0ms	18×	body	1280	nan
9.0ms	18×	body	640	nan
4.0ms	13×	body	320	nan
2.0ms	11×	body	160	valid
1.0ms	8×	body	160	nan

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	1264
4	252
3	86
2	35
1	17
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(pow (+ x 1.0) (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite156.0ms

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:

6.0ms	(pow x (/ 1.0 n))
16.0ms	(pow (+ x 1.0) (/ 1.0 n))
124.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series708.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(pow x (/ 1.0 n))
186.0ms	(pow (+ x 1.0) (/ 1.0 n))
431.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.9s

Counts

158 → 158

Iterations

Iter	Nodes
done	5000
2	2866
1	738
0	270

prune879.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize89.0ms

Local error

Found 4 expressions with local error:

1.4b	(pow (+ x 1.0) (/ 1.0 n))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite370.0ms

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:

17.0ms	(pow (+ x 1.0) (/ 1.0 n))
100.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
112.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
124.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.6s

Counts

4 → 12

Calls

4 calls:

236.0ms	(pow (+ x 1.0) (/ 1.0 n))
451.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
469.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
402.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify2.1s

Counts

312 → 312

Iterations

Iter	Nodes
done	5000
2	2187
1	601
0	233

prune1.5s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize114.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite427.0ms

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×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--`

Counts

4 → 360

Calls

4 calls:

89.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
102.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
105.0ms	(- (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)))

series1.5s

Counts

4 → 12

Calls

4 calls:

413.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
390.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
353.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
361.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify1.8s

Counts

372 → 372

Iterations

Iter	Nodes
done	5000
2	1421
1	426
0	185

prune3.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

localize121.0ms

Local error

Found 4 expressions with local error:

3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
3.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
4.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite411.0ms

Algorithm

rewrite-expression-head

Rules

270×	`unpow-prod-down`
245×	`prod-diff`
233×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
146×	`add-cube-cbrt`
92×	`sqr-pow`
73×	`sqrt-prod`
39×	`difference-of-squares`
35×	`fma-neg` `distribute-lft-out`
12×	`add-log-exp`
10×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `log1p-expm1-u` `flip--`

Counts

4 → 385

Calls

4 calls:

107.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
81.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
106.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
84.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.7s

Counts

4 → 12

Calls

4 calls:

417.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
393.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
382.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
536.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify2.5s

Counts

397 → 397

Iterations

Iter	Nodes
done	5001
2	2801
1	800
0	347

prune4.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.0b

regimes376.0ms

Accuracy

85.4% (1.3b remaining)

Error of 22.0b against oracle of 20.7b and baseline of 29.5b

bsearch2.0ms

simplify32.0ms

Iterations

Iter	Nodes
done	74
2	74
1	70
0	51

end0.0ms

sample8.7s

Algorithm

intervals

Results

2.6s	3152×	body	1280	valid
1.1s	1605×	body	640	valid
976.0ms	1162×	body	10240	exit
940.0ms	4956×	body	80	nan
700.0ms	848×	body	320	valid
629.0ms	637×	body	1280	nan
494.0ms	4648×	body	80	valid
354.0ms	632×	body	640	nan
165.0ms	491×	body	160	valid
111.0ms	313×	body	320	nan
42.0ms	199×	body	160	nan