Details

sample142.0ms

Algorithm

intervals

Results

51.0ms	685×	body	80	nan
49.0ms	370×	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	853	16
6	3196	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite141.0ms

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:

52.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
26.0ms	(* (* 2.0 PI) n)
44.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series851.0ms

Counts

4 → 12

Calls

4 calls:

476.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
51.0ms	(/ 1.0 (sqrt k))
68.0ms	(* (* 2.0 PI) n)
256.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

169 → 169

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3137	2550
done	5000	2540

prune679.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
16×	`prod-exp`
13×	`pow-exp`
12×	`sqrt-prod`
10×	`unpow-prod-down`
9×	`pow-to-exp` `sqr-pow`
8×	`pow1` `add-cbrt-cube`
7×	`associate-r`
6×	`div-sub` `associate-/r*` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
23.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series700.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ 1.0 (sqrt k))
401.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
126.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
101.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.6s

Counts

170 → 170

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	324	2568
1	776	2337
2	2305	2250
done	5000	2234

prune780.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
0.2b	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
0.2b	(/ 1.0 (sqrt k))
0.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

576×	`add-exp-log`
481×	`prod-exp`
199×	`pow-exp`
124×	`pow-to-exp`
61×	`div-sub`
54×	`div-exp`
51×	`times-frac`
49×	`add-sqr-sqrt` `*-un-lft-identity`
43×	`add-cube-cbrt`
37×	`pow-sub`
32×	`add-cbrt-cube`
27×	`associate-l`
22×	`frac-times` `associate-*r/`
21×	`sqrt-prod`
19×	`pow-unpow`
15×	`cbrt-unprod`
10×	`associate-*l/`
7×	`pow1`
6×	`associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`associate-r` `*-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 315

Calls

4 calls:

123.0ms	(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
248.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
8.0ms	(/ 1.0 (sqrt k))
14.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

472.0ms	(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0))))
1.0s	(* (/ 1.0 (sqrt k)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow n (/ (- 1.0 k) 2.0)))))
63.0ms	(/ 1.0 (sqrt k))
96.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.6s

Counts

327 → 327

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	472	11175
1	1271	8148
2	4224	7574
done	5000	7564

prune960.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 447

Calls

4 calls:

23.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt (sqrt k)))
40.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series620.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* 2.0 PI) n)
297.0ms	(/ 1.0 (sqrt (sqrt k)))
69.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
200.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

459 → 459

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	566	9021
1	1341	7684
2	3109	7109
done	5000	6936

prune1.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes149.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.4s	21032×	body	80	nan
2.2s	11948×	body	80	valid
0.0ms	2×	body	160	nan