Details

sample185.0ms

Algorithm

intervals

Results

54.0ms	91×	body	1280	valid
26.0ms	53×	body	640	valid
23.0ms	32×	body	10240	exit
10.0ms	170×	body	80	nan
10.0ms	18×	body	640	nan
9.0ms	131×	body	80	valid
9.0ms	27×	body	320	valid
6.0ms	11×	body	1280	nan
4.0ms	13×	body	320	nan
3.0ms	18×	body	160	valid
1.0ms	8×	body	160	nan

simplify3.7s

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: 31.1b

localize10.0ms

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))

rewrite186.0ms

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:

8.0ms	(pow x (/ 1.0 n))
152.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series737.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(pow x (/ 1.0 n))
399.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
244.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.4s)

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

prune528.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 21.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1.0 n) 2))
1.7b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`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` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

15.0ms	(pow x (/ (/ 1.0 n) 2))
139.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
24.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
19.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series939.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(pow x (/ (/ 1.0 n) 2))
424.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
217.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
202.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify2.0s

Counts

281 → 281

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	378	7611
1	958	5824
2	2417	5145
done	5000	4547

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1.0 n) 2))
1.7b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`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` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

8.0ms	(pow x (/ (/ 1.0 n) 2))
136.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
20.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
23.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

86.0ms	(pow x (/ (/ 1.0 n) 2))
469.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
225.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
232.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify1.9s

Counts

281 → 281

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	378	7611
1	958	5824
2	2417	5145
done	5000	4547

prune1.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ (/ 1.0 n) 2))
1.7b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
2.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

198×	`times-frac`
171×	`*-un-lft-identity`
156×	`add-sqr-sqrt`
144×	`add-cube-cbrt`
129×	`pow-unpow`
77×	`unpow-prod-down`
56×	`prod-diff`
25×	`sqr-pow`
12×	`div-inv`
11×	`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` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 269

Calls

4 calls:

10.0ms	(pow x (/ (/ 1.0 n) 2))
151.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
20.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
15.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

series983.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow x (/ (/ 1.0 n) 2))
413.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))
226.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
240.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))

simplify1.8s

Counts

281 → 281

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	378	7611
1	958	5824
2	2417	5145
done	5000	4547

prune1.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.6b

regimes244.0ms

Accuracy

83.8% (1.4b remaining)

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

bsearch210.0ms

Steps

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

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	39	98
1	51	76
done	51	76

end0.0ms

sample8.8s

Algorithm

intervals

Results

2.6s	3138×	body	1280	valid
1.5s	1634×	body	640	valid
1.0s	4732×	body	80	valid
815.0ms	1160×	body	10240	exit
612.0ms	643×	body	1280	nan
506.0ms	656×	body	640	nan
369.0ms	5002×	body	80	nan
362.0ms	827×	body	320	valid
114.0ms	361×	body	320	nan
97.0ms	436×	body	160	valid
37.0ms	199×	body	160	nan