Details

sample146.0ms

Algorithm

intervals

Results

61.0ms	680×	body	80	nan
39.0ms	380×	body	80	valid

simplify7.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	16
1	41	16
2	145	16
3	1125	16
done	5000	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

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))

rewrite156.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

56.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
11.0ms	(/ 1.0 (sqrt k))
46.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series744.0ms

Counts

4 → 12

Calls

4 calls:

450.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
42.0ms	(* (* 2.0 PI) n)
52.0ms	(/ 1.0 (sqrt k))
200.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.6s

Counts

169 → 169

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	369	2880
1	4100	2706
done	5001	2568

prune738.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

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×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `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 → 221

Calls

4 calls:

20.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
36.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
53.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series516.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* 2.0 PI) n)
48.0ms	(/ 1.0 (sqrt k))
208.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
212.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify10.6s

Counts

233 → 233

Iterations

Useful iterations: done (10.6s)

Iter	Nodes	Cost
0	332	3588
1	2514	3313
done	5001	3212

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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))

rewrite108.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 179

Calls

4 calls:

12.0ms	(* n PI)
11.0ms	(/ 1.0 (sqrt k))
45.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
21.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series511.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* n PI)
69.0ms	(/ 1.0 (sqrt k))
210.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
202.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

191 → 191

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	398	2712
1	2564	2506
done	5001	2419

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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))

rewrite179.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`div-sub`
2×	`pow-to-exp` `unpow-prod-down` `pow1/3` `pow-sub` `sqr-pow`

Counts

4 → 150

Calls

4 calls:

1.0ms	(cbrt n)
1.0ms	(cbrt n)
39.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
131.0ms	(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

330.0ms	(cbrt n)
320.0ms	(cbrt n)
231.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
235.0ms	(pow (* 2.0 (* (* (cbrt n) (cbrt n)) (* (cbrt n) PI))) (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

162 → 162

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	323	2686
1	1701	2496
done	5001	2132

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes222.0ms

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 (6.0ms)

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

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.9s	20479×	body	80	nan
2.2s	11915×	body	80	valid