Details

sample89.0ms

Algorithm

intervals

Results

34.0ms	681×	body	80	nan
23.0ms	397×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8
done	5001	8

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)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite91.0ms

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:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
36.0ms	(/ 1.0 (sqrt k))
39.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify95.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344
done	5002	1344

prune435.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`add-exp-log` `pow-unpow`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`associate-/r*`
6×	`pow-prod-down` `prod-exp` `associate-/l*`
4×	`add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
6.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (* 2.0 PI) n)
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series253.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1.0 (sqrt k))
42.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
143.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify59.0ms

Counts

144 → 144

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	563	883
1	2197	815
2	5001	791
done	5001	791

prune460.0ms

Pruning

8 alts after pruning (8 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	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
1.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
143×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
122×	`pow-unpow`
103×	`add-cube-cbrt`
91×	`add-exp-log`
64×	`prod-exp`
36×	`pow-exp`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r` `div-inv`
6×	`unpow-prod-down` `pow-pow` `associate-l` `pow-sub`
5×	`swap-sqr`
4×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`pow2` `frac-times` `associate-r/` `associate-l/` `pow-sqr` `pow-prod-up`

Counts

4 → 234

Calls

4 calls:

17.0ms	(* (* 2.0 PI) n)
41.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
28.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series516.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
196.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
140.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
147.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify103.0ms

Counts

246 → 246

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	875	2384
1	3640	2189
2	5002	2154
done	5002	2154

prune764.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

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)))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) n)
1.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite92.0ms

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:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
20.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series552.0ms

Counts

4 → 12

Calls

4 calls:

335.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
45.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify94.0ms

Counts

161 → 161

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344
done	5002	1344

prune542.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes144.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8
done	16	8

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	21027×	body	80	nan
713.0ms	11976×	body	80	valid
0.0ms	3×	body	160	nan