Details

sample133.0ms

Algorithm

intervals

Results

50.0ms	647×	body	80	nan
46.0ms	384×	body	80	valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5003
6	2792
5	816
4	285
3	114
2	58
1	29
0	13

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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))

rewrite101.0ms

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×	`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` `clear-num` `frac-2neg` `associate-l/` `associate-r/`

Counts

4 → 157

Calls

4 calls:

40.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
14.0ms	(* (* 2.0 PI) n)
5.0ms	(/ 1.0 (sqrt k))
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series786.0ms

Counts

4 → 12

Calls

4 calls:

460.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
56.0ms	(* (* 2.0 PI) n)
67.0ms	(/ 1.0 (sqrt k))
203.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify3.9s

Counts

169 → 169

Iterations

Iter	Nodes
done	5000
2	3343
1	1004
0	361

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

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))

rewrite143.0ms

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

Counts

4 → 221

Calls

4 calls:

26.0ms	(* (* 2.0 PI) n)
10.0ms	(/ 1.0 (sqrt k))
41.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
38.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series543.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* 2.0 PI) n)
47.0ms	(/ 1.0 (sqrt k))
211.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
239.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.8s

Counts

233 → 233

Iterations

Iter	Nodes
done	5002
2	2630
1	951
0	334

prune1.8s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

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))

rewrite90.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 140

Calls

4 calls:

27.0ms	(* (* 2.0 PI) n)
10.0ms	(/ 1.0 (sqrt k))
10.0ms	(/ 1.0 (sqrt k))
35.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series383.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
56.0ms	(/ 1.0 (sqrt k))
66.0ms	(/ 1.0 (sqrt k))
223.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

152 → 152

Iterations

Iter	Nodes
done	5001
2	1862
1	614
0	242

prune992.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize81.0ms

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)

rewrite83.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 220

Calls

4 calls:

30.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
35.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
2.0ms	(cbrt k)
2.0ms	(cbrt k)

series1.2s

Counts

4 → 12

Calls

4 calls:

408.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
251.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
262.0ms	(cbrt k)
251.0ms	(cbrt k)

simplify2.0s

Counts

232 → 232

Iterations

Iter	Nodes
done	5001
2	2615
1	965
0	406

prune1.9s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes234.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample5.8s

Algorithm

intervals

Results

3.0s	20721×	body	80	nan
1.9s	12037×	body	80	valid
1.0ms	6×	body	160	nan