Details

sample210.0ms

Algorithm

intervals

Results

107.0ms	680×	body	80	nan
46.0ms	380×	body	80	valid

simplify3.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	119	16
4	313	16
5	843	16
6	3221	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite150.0ms

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:

63.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
20.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
47.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

972.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
49.0ms	(* (* 2.0 PI) n)
66.0ms	(/ 1.0 (sqrt k))
231.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

161 → 161

Iterations

Useful iterations: 2 (814.0ms)

Iter	Nodes	Cost
0	361	2800
1	931	2635
2	3051	2471
done	5001	2471

prune747.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
150×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
114×	`add-cube-cbrt`
23×	`add-exp-log`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `div-inv`
6×	`pow-pow` `pow-exp` `associate-/r*`
4×	`div-sub` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 213

Calls

4 calls:

27.0ms	(* (* 2.0 PI) n)
12.0ms	(/ 1.0 (sqrt k))
41.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
35.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series558.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (* 2.0 PI) n)
77.0ms	(/ 1.0 (sqrt k))
206.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
235.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.9s

Counts

225 → 225

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	326	3510
1	839	3234
2	2444	3128
done	5000	3080

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n PI)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

135×	`times-frac`
103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
80×	`pow-unpow`
77×	`add-cube-cbrt`
20×	`add-exp-log`
18×	`pow1`
12×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube`
7×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `pow-exp` `associate-/r*` `div-inv`
4×	`add-log-exp`
3×	`div-sub` `associate-r` `associate-l` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

11.0ms	(* n PI)
10.0ms	(/ 1.0 (sqrt k))
47.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
21.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series517.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* n PI)
48.0ms	(/ 1.0 (sqrt k))
217.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
221.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

183 → 183

Iterations

Useful iterations: 2 (887.0ms)

Iter	Nodes	Cost
0	390	2642
1	997	2438
2	2716	2342
done	5002	2342

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt n)
0.6b	(cbrt n)
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

rewrite262.0ms

Algorithm

rewrite-expression-head

Rules

117×	`times-frac`
86×	`add-sqr-sqrt` `*-un-lft-identity`
80×	`pow-unpow`
62×	`add-cube-cbrt`
29×	`pow1` `add-exp-log`
16×	`pow-prod-down` `prod-exp`
12×	`distribute-lft-out--` `difference-of-squares`
9×	`pow-pow` `pow-exp`
6×	`cbrt-prod`
5×	`div-inv`
4×	`add-cbrt-cube` `add-log-exp`
3×	`div-sub`
2×	`pow-to-exp` `unpow-prod-down` `pow1/3` `pow-sub` `sqr-pow`

Counts

4 → 142

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
56.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
193.0ms	(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

311.0ms	(cbrt n)
356.0ms	(cbrt n)
197.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
266.0ms	(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

154 → 154

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	317	2608
1	847	2419
2	2475	2180
done	5000	2057

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	23	40
1	32	38
done	32	38

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.9s	20479×	body	80	nan
1.6s	11915×	body	80	valid