Details

sample77.0ms

Algorithm

intervals

Results

32.0ms	650×	body	80	nan
22.0ms	379×	body	80	valid

simplify3.0s

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	299	16
5	846	16
6	3058	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite41.0ms

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×	`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 → 149

Calls

4 calls:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series556.0ms

Counts

4 → 12

Calls

4 calls:

334.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
38.0ms	(/ 1.0 (sqrt k))
37.0ms	(* (* 2.0 PI) n)
147.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

161 → 161

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	361	2800
1	943	2643
2	3235	2475
done	5000	2463

prune427.0ms

Pruning

11 alts after pruning (11 fresh and 0 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)
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))

rewrite52.0ms

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×	`div-sub` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
16.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series362.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
149.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.2s

Counts

204 → 204

Iterations

Useful iterations: 2 (406.0ms)

Iter	Nodes	Cost
0	241	3252
1	695	3014
2	2269	2898
done	5000	2898

prune695.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
151×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
115×	`add-cube-cbrt`
18×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`div-inv`
6×	`pow-prod-down` `prod-exp` `associate-/r*`
4×	`unpow-prod-down` `pow-pow` `div-sub` `pow-exp` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 211

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) n)
10.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (sqrt k))
35.0ms	(* (* 2.0 PI) n)
62.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
141.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.2s

Counts

223 → 223

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	413	3101
1	1103	2844
2	3246	2756
done	5000	2751

prune842.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)
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))

rewrite49.0ms

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×	`div-sub` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
6.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
13.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series353.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
36.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
145.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.0s

Counts

204 → 204

Iterations

Useful iterations: 2 (410.0ms)

Iter	Nodes	Cost
0	241	3252
1	695	3014
2	2269	2898
done	5000	2898

prune686.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes145.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	40
1	24	40
done	24	40

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	20670×	body	80	nan
699.0ms	11971×	body	80	valid
0.0ms	3×	body	160	nan