Details

sample75.0ms

Algorithm

intervals

Results

31.0ms	593×	body	80	nan
21.0ms	358×	body	80	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	113	16
4	291	16
5	793	16
6	3009	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series524.0ms

Counts

4 → 12

Calls

4 calls:

313.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
34.0ms	(* (* 2.0 PI) n)
38.0ms	(/ 1.0 (sqrt k))
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.0s

Counts

161 → 161

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	361	2800
1	943	2635
2	3230	2459
done	5001	2447

prune423.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 86

Calls

3 calls:

7.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
6.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series460.0ms

Counts

3 → 9

Calls

3 calls:

285.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
36.0ms	(* (* 2.0 PI) n)
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify861.0ms

Counts

95 → 95

Iterations

Useful iterations: done (858.0ms)

Iter	Nodes	Cost
0	264	1828
1	710	1695
2	2456	1527
done	5001	1520

prune250.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
0.2b	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-exp-log`
78×	`times-frac`
48×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
38×	`div-exp` `prod-exp`
23×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`sqrt-prod`
16×	`pow1`
15×	`pow-exp`
12×	`associate-/r*`
9×	`associate-/l*`
7×	`cbrt-undiv` `rec-exp` `1-exp` `div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp` `associate-*r/` `cbrt-unprod`
4×	`add-log-exp`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`unpow-prod-down` `pow-flip` `associate-l` `*-commutative` `inv-pow` `sqr-pow`

Counts

4 → 170

Calls

4 calls:

14.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
6.0ms	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series920.0ms

Counts

4 → 12

Calls

4 calls:

324.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
423.0ms	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
31.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.4s

Counts

182 → 182

Iterations

Useful iterations: 2 (677.0ms)

Iter	Nodes	Cost
0	466	4335
1	1252	3944
2	4151	3556
done	5000	3556

prune380.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(/ 1.0 (sqrt (sqrt k)))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite271.0ms

Algorithm

rewrite-expression-head

Rules

4409×	`times-frac`
2853×	`sqrt-prod`
1811×	`add-sqr-sqrt` `*-un-lft-identity`
1805×	`add-cube-cbrt`
289×	`unpow-prod-down` `sqr-pow`
86×	`div-inv`
61×	`add-exp-log`
59×	`associate-/r*`
34×	`associate-/l*`
33×	`div-sub` `associate-/r/` `pow-sub`
29×	`div-exp`
23×	`add-cbrt-cube`
19×	`pow-unpow`
15×	`pow1`
12×	`prod-exp`
9×	`cbrt-undiv` `pow-exp`
6×	`pow-prod-down`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

4 → 1764

Calls

4 calls:

51.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1.0 (sqrt (sqrt k)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series658.0ms

Counts

4 → 12

Calls

4 calls:

317.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
165.0ms	(/ 1.0 (sqrt (sqrt k)))
36.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify719.0ms

Counts

1776 → 1776

Iterations

Useful iterations: done (612.0ms)

Iter	Nodes	Cost
0	1996	80258
done	5000	80243

prune6.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes108.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	18
1	20	18
done	20	18

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	20329×	body	80	nan
714.0ms	11817×	body	80	valid
0.0ms	2×	body	160	nan