Details

sample161.0ms

Algorithm

intervals

Results

71.0ms	760×	body	80	nan
40.0ms	432×	body	80	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

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))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite195.0ms

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:

80.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
20.0ms	(/ 1.0 (sqrt k))
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series773.0ms

Counts

4 → 12

Calls

4 calls:

460.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
59.0ms	(* (* 2.0 PI) n)
58.0ms	(/ 1.0 (sqrt k))
195.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.5s

Counts

161 → 161

Iterations

Useful iterations: 2 (918.0ms)

Iter	Nodes	Cost
0	361	2800
1	1008	2643
2	4741	2477
done	5000	2477

prune687.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(/ 1.0 (sqrt k))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
157×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
122×	`pow-unpow`
117×	`add-cube-cbrt`
88×	`add-exp-log`
61×	`prod-exp`
36×	`pow-exp`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`pow-to-exp` `div-sub` `sqrt-prod`
10×	`sqr-pow`
9×	`div-inv`
8×	`add-cbrt-cube`
7×	`pow-prod-down`
6×	`unpow-prod-down` `pow-pow` `associate-/r*` `pow-sub`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`add-log-exp` `unswap-sqr`
3×	`associate-/l*`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 255

Calls

4 calls:

74.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
13.0ms	(/ 1.0 (sqrt k))
52.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
47.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series691.0ms

Counts

4 → 12

Calls

4 calls:

253.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
51.0ms	(/ 1.0 (sqrt k))
183.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
203.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.7s

Counts

267 → 267

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	373	5564
1	1101	4679
2	4713	4193
done	5000	4156

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
24×	`sqrt-prod`
20×	`add-exp-log`
16×	`pow1`
12×	`associate-/r*`
8×	`add-cbrt-cube`
6×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`div-inv` `add-log-exp`
2×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `div-exp` `clear-num` `pow-sub` `sqr-pow`

Counts

4 → 150

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt k))
7.0ms	(/ 1.0 (sqrt k))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
48.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series626.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (sqrt k))
75.0ms	(/ 1.0 (sqrt k))
244.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
239.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify983.0ms

Counts

162 → 162

Iterations

Useful iterations: 2 (314.0ms)

Iter	Nodes	Cost
0	208	2140
1	518	1966
2	1841	1854
done	5001	1854

prune929.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt k)
0.6b	(cbrt k)
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

38×	`pow-unpow`
36×	`add-sqr-sqrt` `*-un-lft-identity`
30×	`times-frac`
24×	`add-cube-cbrt`
16×	`pow1` `add-exp-log`
6×	`cbrt-prod` `pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `pow1/3` `div-sub` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 94

Calls

4 calls:

2.0ms	(cbrt k)
2.0ms	(cbrt k)
44.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series911.0ms

Counts

4 → 12

Calls

4 calls:

257.0ms	(cbrt k)
291.0ms	(cbrt k)
178.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
184.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify809.0ms

Counts

106 → 106

Iterations

Useful iterations: done (803.0ms)

Iter	Nodes	Cost
0	143	1440
1	382	1344
2	1411	1260
done	5000	1254

prune844.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes277.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	16	32
1	19	32
done	19	32

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.0s	20591×	body	80	nan
2.1s	11964×	body	80	valid
0.0ms	2×	body	160	nan