Details

sample88.0ms

Algorithm

intervals

Results

31.0ms	613×	body	80	nan
26.0ms	389×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8
done	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
1.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite91.0ms

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:

37.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series543.0ms

Counts

4 → 12

Calls

4 calls:

325.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383
done	5003	1383

prune487.0ms

Pruning

10 alts after pruning (10 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))
0.3b	(* (* 2.0 PI) n)
1.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite64.0ms

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×	`expm1-log1p-u` `pow-pow` `associate-r` `log1p-expm1-u` `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 → 92

Calls

3 calls:

23.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
17.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series466.0ms

Counts

3 → 9

Calls

3 calls:

288.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
39.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify77.0ms

Counts

101 → 101

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	732	973
1	3046	872
2	5001	836
done	5001	836

prune282.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.3b	(* (* 2.0 PI) n)
1.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
46×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
16×	`div-exp` `add-cbrt-cube`
15×	`pow1`
12×	`prod-exp`
9×	`pow-exp` `associate-/l*`
7×	`div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `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`

Counts

4 → 282

Calls

4 calls:

12.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
25.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
17.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series926.0ms

Counts

4 → 12

Calls

4 calls:

419.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
328.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
33.0ms	(* (* 2.0 PI) n)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify65.0ms

Counts

294 → 294

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1582	4271
1	5001	4099
done	5001	4099

prune830.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
1.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 200

Calls

4 calls:

18.0ms	(* (* 2.0 PI) n)
17.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
29.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series366.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)
149.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
143.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify73.0ms

Counts

212 → 212

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	703	1718
1	2797	1652
2	5001	1636
done	5001	1636

prune721.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8
done	15	8

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	20322×	body	80	nan
731.0ms	11899×	body	80	valid
0.0ms	1×	body	160	nan