Details

sample135.0ms

Algorithm

intervals

Results

48.0ms	647×	body	80	nan
48.0ms	384×	body	80	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	2693
5	806
4	285
3	114
2	58
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

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))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite125.0ms

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×	`associate-/r*` `div-exp` `pow-prod-down` `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` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

62.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series818.0ms

Counts

4 → 12

Calls

4 calls:

511.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
46.0ms	(* (* 2.0 PI) n)
43.0ms	(/ 1.0 (sqrt k))
218.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.8s

Counts

161 → 161

Iterations

Iter	Nodes
done	5003
2	3265
1	975
0	353

prune998.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.4b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.4b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite91.0ms

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×	`associate-/r*` `pow-pow` `pow-exp`
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` `clear-num` `frac-2neg` `div-exp` `associate-l` `*-commutative`

Counts

4 → 213

Calls

4 calls:

13.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
33.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
27.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series515.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* 2.0 PI) n)
54.0ms	(/ 1.0 (sqrt k))
196.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
219.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.3s

Counts

225 → 225

Iterations

Iter	Nodes
done	5002
2	2615
1	938
0	328

prune1.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 132

Calls

4 calls:

23.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
5.0ms	(/ 1.0 (sqrt k))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series360.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* 2.0 PI) n)
49.0ms	(/ 1.0 (sqrt k))
51.0ms	(/ 1.0 (sqrt k))
208.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.0s

Counts

144 → 144

Iterations

Iter	Nodes
done	5000
2	1810
1	601
0	236

prune958.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
0.5b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.6b	(cbrt k)
0.6b	(cbrt k)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
133×	`add-sqr-sqrt` `*-un-lft-identity`
127×	`add-cube-cbrt`
84×	`sqrt-prod`
48×	`cbrt-prod`
19×	`pow-unpow`
15×	`add-exp-log`
13×	`associate-/l*`
12×	`div-inv`
10×	`pow1`
9×	`associate-/r*` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`pow-to-exp` `clear-num` `unpow-prod-down` `frac-2neg` `div-sub` `pow-sub` `sqr-pow` `associate-/l/`

Counts

4 → 212

Calls

4 calls:

12.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.0ms	(cbrt k)
1.0ms	(cbrt k)

series1.1s

Counts

4 → 12

Calls

4 calls:

397.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
194.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
253.0ms	(cbrt k)
268.0ms	(cbrt k)

simplify2.4s

Counts

224 → 224

Iterations

Iter	Nodes
done	5000
2	2527
1	939
0	400

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes294.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.1s	20721×	body	80	nan
1.5s	12037×	body	80	valid
1.0ms	6×	body	160	nan