Details

sample229.0ms

Algorithm

intervals

Results

80.0ms	680×	body	80	nan
51.0ms	380×	body	80	valid

simplify4.0s

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	853	16
6	3196	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 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))

rewrite132.0ms

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:

58.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
26.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series751.0ms

Counts

4 → 12

Calls

4 calls:

468.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
63.0ms	(* (* 2.0 PI) n)
47.0ms	(/ 1.0 (sqrt k))
173.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.6s

Counts

169 → 169

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3131	2550
done	5000	2540

prune865.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite134.0ms

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

Counts

4 → 221

Calls

4 calls:

39.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
26.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
38.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series531.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
200.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
229.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.7s

Counts

233 → 233

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	332	3588
1	854	3308
2	2490	3202
done	5002	3197

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize57.0ms

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))

rewrite108.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 179

Calls

4 calls:

19.0ms	(* n PI)
14.0ms	(/ 1.0 (sqrt k))
42.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
20.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

series535.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* n PI)
57.0ms	(/ 1.0 (sqrt k))
214.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
223.0ms	(pow (* 2.0 (* n PI)) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

191 → 191

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	398	2712
1	1018	2503
2	2797	2409
done	5001	2403

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

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))

rewrite112.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 177

Calls

4 calls:

14.0ms	(* n PI)
13.0ms	(/ 1.0 (sqrt k))
57.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
11.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

series488.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* n PI)
77.0ms	(/ 1.0 (sqrt k))
240.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
148.0ms	(pow (* n PI) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

189 → 189

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	401	2593
1	1023	2390
2	2853	2297
done	5000	2291

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes208.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	11915×	body	80	valid
2.4s	20479×	body	80	nan