Details

sample85.0ms

Algorithm

intervals

Results

30.0ms	631×	body	80	nan
25.0ms	382×	body	80	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

localize13.0ms

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))
1.2b	(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:

39.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
16.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series538.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
32.0ms	(* (* 2.0 PI) n)
41.0ms	(/ 1.0 (sqrt k))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

161 → 161

Iterations

Useful iterations: 2 (490.0ms)

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

prune432.0ms

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	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.1b	(pow n (/ (- 1.0 k) 2.0))

rewrite55.0ms

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×	`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 → 150

Calls

4 calls:

25.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
10.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
7.0ms	(pow n (/ (- 1.0 k) 2.0))

series454.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
41.0ms	(/ 1.0 (sqrt k))
75.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
60.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify914.0ms

Counts

162 → 162

Iterations

Useful iterations: done (909.0ms)

Iter	Nodes	Cost
0	316	2486
1	753	2260
2	2233	2160
done	5000	2107

prune472.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ 1 (sqrt (sqrt k)))
0.5b	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

190×	`add-sqr-sqrt`
171×	`sqrt-prod`
168×	`times-frac`
113×	`*-un-lft-identity`
95×	`add-cube-cbrt`
38×	`add-exp-log`
31×	`associate-r` `associate-l`
28×	`unswap-sqr`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`associate-/r*`
15×	`pow1`
11×	`div-exp` `prod-exp`
6×	`cbrt-undiv` `associate-/l*`
5×	`pow-flip` `div-inv`
4×	`sqrt-pow1` `pow-prod-down` `cbrt-unprod` `add-log-exp`
3×	`rec-exp` `pow-pow` `1-exp` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `pow1/2` `clear-num`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `div-sub` `associate-r/` `associate-l/` `*-commutative` `inv-pow` `pow-sub` `sqr-pow`

Counts

4 → 260

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt (sqrt k)))
10.0ms	(/ 1 (sqrt (sqrt k)))
58.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series490.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ 1.0 (sqrt (sqrt k)))
143.0ms	(/ 1 (sqrt (sqrt k)))
42.0ms	(* (/ 1 (sqrt (sqrt k))) (/ 1.0 (sqrt (sqrt k))))
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.0s

Counts

272 → 272

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	374	3992
1	940	3441
2	2568	2979
done	5000	2958

prune769.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
0.6b	(cbrt k)
0.6b	(cbrt k)
1.2b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite2.8s

Algorithm

rewrite-expression-head

Rules

7451×	`times-frac`
4552×	`add-sqr-sqrt`
4012×	`sqrt-prod`
2885×	`*-un-lft-identity`
2879×	`add-cube-cbrt`
2559×	`cbrt-prod`
2209×	`associate-l`
306×	`unswap-sqr`
76×	`associate-r`
66×	`div-inv`
42×	`add-exp-log`
26×	`add-cbrt-cube`
19×	`pow-unpow`
16×	`cbrt-undiv` `div-exp`
12×	`pow1`
11×	`prod-exp`
9×	`associate-/r/`
8×	`cbrt-unprod`
4×	`pow-prod-down` `add-log-exp`
3×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `div-sub` `associate-r/` `associate-l/` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 2677

Calls

4 calls:

2.3s	(* (/ (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series782.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (/ (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
181.0ms	(cbrt k)
177.0ms	(cbrt k)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.5s

Counts

2689 → 2689

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	1357	74630
1	4469	74238
done	5000	73858

prune12.5s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes131.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	25
1	27	25
done	27	25

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	20389×	body	80	nan
707.0ms	11892×	body	80	valid