Details

sample217.0ms

Algorithm

intervals

Results

113.0ms	680×	body	80	nan
48.0ms	380×	body	80	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	119	16
4	313	16
5	843	16
6	3221	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite151.0ms

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:

75.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
38.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series783.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
51.0ms	(* (* 2.0 PI) n)
46.0ms	(/ 1.0 (sqrt k))
217.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

161 → 161

Iterations

Useful iterations: 2 (797.0ms)

Iter	Nodes	Cost
0	361	2800
1	931	2635
2	3051	2471
done	5001	2471

prune727.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite161.0ms

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

Counts

4 → 213

Calls

4 calls:

25.0ms	(* (* 2.0 PI) n)
13.0ms	(/ 1.0 (sqrt k))
60.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
50.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series574.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* 2.0 PI) n)
62.0ms	(/ 1.0 (sqrt k))
217.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
235.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.8s

Counts

225 → 225

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	326	3510
1	839	3234
2	2444	3128
done	5000	3080

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n PI)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

135×	`times-frac`
103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
80×	`pow-unpow`
77×	`add-cube-cbrt`
20×	`add-exp-log`
18×	`pow1`
12×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube`
7×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `pow-exp` `associate-/r*` `div-inv`
4×	`add-log-exp`
3×	`div-sub` `associate-r` `associate-l` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

20.0ms	(* n PI)
13.0ms	(/ 1.0 (sqrt k))
55.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
23.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series523.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* n PI)
44.0ms	(/ 1.0 (sqrt k))
226.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
222.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify1.8s

Counts

183 → 183

Iterations

Useful iterations: 2 (773.0ms)

Iter	Nodes	Cost
0	390	2642
1	997	2438
2	2716	2342
done	5002	2342

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n PI)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.7b	(pow (* n PI) (/ (- 1.0 k) 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

135×	`times-frac`
103×	`add-sqr-sqrt`
101×	`*-un-lft-identity`
80×	`pow-unpow`
77×	`add-cube-cbrt`
17×	`add-exp-log`
15×	`pow1`
12×	`sqrt-prod` `distribute-lft-out--` `difference-of-squares`
8×	`add-cbrt-cube`
6×	`associate-/r*` `div-inv`
5×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp`
4×	`add-log-exp`
3×	`div-sub` `associate-r` `associate-l` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 169

Calls

4 calls:

14.0ms	(* n PI)
12.0ms	(/ 1.0 (sqrt k))
34.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
17.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

series432.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* n PI)
62.0ms	(/ 1.0 (sqrt k))
202.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
134.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

181 → 181

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	393	2527
1	1003	2328
2	2778	2235
done	5000	2233

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes182.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	23	40
1	32	38
done	32	38

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.8s	20479×	body	80	nan
2.1s	11915×	body	80	valid