Details

sample72.0ms

Algorithm

intervals

Results

29.0ms	593×	body	80	nan
21.0ms	358×	body	80	valid

simplify1.9s

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	803	16
6	3283	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize17.0ms

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))

rewrite42.0ms

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:

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))

series527.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(* (/ 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))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.1s

Counts

169 → 169

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	369	2880
1	974	2712
2	3438	2532
done	5000	2523

prune449.0ms

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	(/ (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))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
38×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
26×	`add-exp-log`
19×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`pow-prod-down` `pow-exp` `associate-/r*`
5×	`div-exp` `associate-/l*`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `frac-2neg` `associate-l` `clear-num` `*-commutative` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

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

series418.0ms

Counts

3 → 9

Calls

3 calls:

245.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
32.0ms	(* (* 2.0 PI) n)
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify825.0ms

Counts

127 → 127

Iterations

Useful iterations: done (821.0ms)

Iter	Nodes	Cost
0	290	2643
1	717	2495
2	2521	2351
done	5000	2345

prune326.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
19×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-l` `*-commutative` `inv-pow`

Counts

4 → 296

Calls

4 calls:

13.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
5.0ms	(/ (sqrt k) (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:

323.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
417.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
148.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify898.0ms

Counts

308 → 308

Iterations

Useful iterations: done (887.0ms)

Iter	Nodes	Cost
0	589	8352
1	1512	7595
done	5000	7094

prune596.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite289.0ms

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`
101×	`add-exp-log`
86×	`div-inv`
59×	`associate-/r*`
58×	`div-exp`
34×	`associate-/l*`
33×	`div-sub` `associate-/r/` `pow-sub`
23×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`pow1` `prod-exp`
15×	`pow-exp`
9×	`cbrt-undiv`
7×	`rec-exp` `1-exp`
6×	`pow-prod-down`
5×	`pow-to-exp` `pow-flip`
4×	`expm1-log1p-u` `sqrt-pow1` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `pow1/2` `clear-num`
1×	`associate-l` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 1792

Calls

4 calls:

55.0ms	(/ (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1 (sqrt (sqrt k)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series641.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(/ (/ 1 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
143.0ms	(/ 1 (sqrt (sqrt k)))
32.0ms	(* (* 2.0 PI) n)
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify751.0ms

Counts

1804 → 1804

Iterations

Useful iterations: done (643.0ms)

Iter	Nodes	Cost
0	1945	80657
done	5000	80642

prune6.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	22	23
done	22	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	20329×	body	80	nan
705.0ms	11817×	body	80	valid
0.0ms	2×	body	160	nan