Details

sample140.0ms

Algorithm

intervals

Results

57.0ms	685×	body	80	nan
37.0ms	370×	body	80	valid

simplify3.8s

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

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))

rewrite160.0ms

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:

63.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
28.0ms	(* (* 2.0 PI) n)
42.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series805.0ms

Counts

4 → 12

Calls

4 calls:

436.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
69.0ms	(/ 1.0 (sqrt k))
67.0ms	(* (* 2.0 PI) n)
232.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

161 → 161

Iterations

Useful iterations: 2 (1.1s)

Iter	Nodes	Cost
0	361	2800
1	931	2635
2	3047	2471
done	5000	2471

prune635.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

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))

rewrite74.0ms

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:

10.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
18.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series640.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1.0 (sqrt k))
392.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
119.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
75.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.6s

Counts

162 → 162

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	316	2486
1	752	2260
2	2229	2160
done	5000	2107

prune824.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize27.0ms

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))

rewrite555.0ms

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` `unpow-prod-down` `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 → 307

Calls

4 calls:

134.0ms	(* (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))))
345.0ms	(* (/ 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)))))
14.0ms	(/ 1.0 (sqrt k))
16.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.7s

Counts

4 → 12

Calls

4 calls:

552.0ms	(* (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)))))
42.0ms	(/ 1.0 (sqrt k))
87.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

319 → 319

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	464	11011
1	1223	8028
2	4112	7464
done	5000	6576

prune969.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize53.0ms

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 (/ 1 n) (* -0.5 (- 1.0 k)))))
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 (/ 1 n) (* -0.5 (- 1.0 k))))))
0.2b	(/ 1.0 (sqrt k))
0.7b	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

rewrite621.0ms

Algorithm

rewrite-expression-head

Rules

1204×	`add-exp-log`
937×	`prod-exp`
490×	`pow-exp`
200×	`div-exp`
196×	`pow-to-exp`
49×	`rec-exp` `1-exp`
45×	`times-frac`
40×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`add-cbrt-cube`
27×	`associate-l`
24×	`div-sub`
21×	`sqrt-prod`
15×	`cbrt-unprod`
14×	`unpow-prod-down`
12×	`pow-sub`
10×	`associate-*l/`
8×	`pow1`
6×	`frac-times` `associate-r/` `associate-/r`
4×	`cbrt-undiv` `unpow-prod-up` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r` `*-commutative` `sqr-pow`
1×	`pow-unpow` `pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `inv-pow`

Counts

4 → 439

Calls

4 calls:

146.0ms	(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (/ 1 n) (* -0.5 (- 1.0 k)))))
372.0ms	(* (/ 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 (/ 1 n) (* -0.5 (- 1.0 k))))))
8.0ms	(/ 1.0 (sqrt k))
19.0ms	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

series1.7s

Counts

4 → 12

Calls

4 calls:

500.0ms	(* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (* (pow (* 2.0 PI) (/ (/ (- 1.0 k) 2.0) 2)) (pow (/ 1 n) (* -0.5 (- 1.0 k)))))
1.1s	(* (/ 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 (/ 1 n) (* -0.5 (- 1.0 k))))))
44.0ms	(/ 1.0 (sqrt k))
100.0ms	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

simplify2.7s

Counts

451 → 451

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	553	17091
1	1275	12144
2	3946	11464
done	5000	10460

prune865.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes213.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	38
1	28	38
done	28	38

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.6s	21032×	body	80	nan
1.6s	11948×	body	80	valid
0.0ms	2×	body	160	nan