Details

sample163.0ms

Algorithm

intervals

Results

78.0ms	689×	body	80	nan
37.0ms	394×	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	843	16
6	3221	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

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)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite143.0ms

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:

56.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
11.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* 2.0 PI) n)
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series829.0ms

Counts

4 → 12

Calls

4 calls:

510.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
71.0ms	(/ 1.0 (sqrt k))
42.0ms	(* (* 2.0 PI) n)
206.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.0s

Counts

161 → 161

Iterations

Useful iterations: 2 (836.0ms)

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

prune697.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`pow-to-exp` `div-sub` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 161

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
41.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
12.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series664.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (sqrt k))
437.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
87.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
95.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.6s

Counts

173 → 173

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	325	2550
1	805	2394
2	2331	2288
done	5001	2206

prune870.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
64×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow` `prod-exp`
22×	`associate-l`
21×	`sqrt-prod`
18×	`add-cbrt-cube`
14×	`pow-to-exp` `pow-exp`
11×	`div-exp`
10×	`div-sub` `pow-sub`
8×	`pow1`
6×	`unpow-prod-down` `associate-/r*` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*r/`
4×	`div-inv` `add-log-exp`
3×	`cbrt-undiv` `associate-l/` `associate-/l`
2×	`pow-pow` `sqr-pow`
1×	`frac-2neg` `associate-r` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 170

Calls

4 calls:

13.0ms	(/ 1.0 (sqrt k))
106.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
9.0ms	(pow PI (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ 1.0 (sqrt k))
891.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
73.0ms	(pow PI (/ (- 1.0 k) 2.0))
102.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

182 → 182

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	376	3141
1	1009	2818
2	3212	2638
done	5001	2624

prune879.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite529.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
60×	`times-frac`
56×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`pow-unpow` `prod-exp`
18×	`sqrt-prod`
17×	`pow-exp`
16×	`div-exp`
15×	`add-cbrt-cube`
14×	`unpow-prod-down`
12×	`pow-to-exp`
10×	`sqr-pow`
8×	`pow1`
7×	`associate-r`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
5×	`div-sub` `cbrt-unprod` `associate-/l*` `pow-sub`
4×	`add-log-exp`
3×	`pow-pow` `associate-*r/` `div-inv`
2×	`cbrt-undiv`
1×	`frac-times` `frac-2neg` `associate-l` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l/`

Counts

4 → 165

Calls

4 calls:

482.0ms	(* (* 1.0 (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
20.0ms	(/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt k))
12.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

794.0ms	(* (* 1.0 (/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt k))) (pow n (/ (- 1.0 k) 2.0)))
329.0ms	(/ (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (sqrt k))
118.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
98.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

177 → 177

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	400	3912
1	1026	3662
2	3389	3446
done	5000	3411

prune659.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes150.0ms

Accuracy

0% (0.4b 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	15	28
1	18	28
done	18	28

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.0s	20954×	body	80	nan
1.7s	11924×	body	80	valid
0.0ms	1×	body	160	nan