Details

sample128.0ms

Algorithm

intervals

Results

57.0ms	689×	body	80	nan
37.0ms	394×	body	80	valid

simplify4.0s

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	853	16
6	3196	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

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))

rewrite166.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

61.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (* 2.0 PI) n)
44.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series789.0ms

Counts

4 → 12

Calls

4 calls:

442.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
66.0ms	(/ 1.0 (sqrt k))
65.0ms	(* (* 2.0 PI) n)
216.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

169 → 169

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3137	2550
done	5000	2540

prune779.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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))

rewrite73.0ms

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×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `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 → 169

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
38.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series651.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ 1.0 (sqrt k))
393.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
107.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
103.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.9s

Counts

181 → 181

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	333	2626
1	831	2468
2	2409	2362
done	5000	2337

prune843.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize33.0ms

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))

rewrite129.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 178

Calls

4 calls:

13.0ms	(/ 1.0 (sqrt k))
83.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
8.0ms	(pow PI (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (sqrt k))
829.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
57.0ms	(pow PI (/ (- 1.0 k) 2.0))
106.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

190 → 190

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	384	3225
1	1040	2900
2	3303	2698
done	5002	2678

prune964.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

423×	`add-exp-log`
279×	`prod-exp`
109×	`pow-exp`
100×	`div-exp`
68×	`pow-to-exp`
35×	`add-sqr-sqrt`
34×	`add-cbrt-cube`
32×	`pow-unpow`
30×	`*-un-lft-identity`
26×	`times-frac`
24×	`add-cube-cbrt`
13×	`cbrt-unprod`
8×	`pow1` `cbrt-undiv` `unpow-prod-down`
7×	`associate-r`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp` `sqr-pow`
3×	`pow-pow` `div-sub` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 220

Calls

4 calls:

106.0ms	(* (/ (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
47.0ms	(/ (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0))))
17.0ms	(pow n (/ (- 1.0 k) 2.0))
16.0ms	(pow (* 2.0 PI) (/ 1.0 2.0))

series2.7s

Counts

4 → 10

Calls

4 calls:

1.7s	(* (/ (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
940.0ms	(/ (* 1.0 (pow (* 2.0 PI) (/ 1.0 2.0))) (* (sqrt k) (pow (* 2.0 PI) (/ k 2.0))))
67.0ms	(pow n (/ (- 1.0 k) 2.0))
0.0ms	(pow (* 2.0 PI) (/ 1.0 2.0))

simplify2.8s

Counts

230 → 230

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	430	6612
1	1201	5980
2	4496	5531
done	5000	5522

prune864.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes152.0ms

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

3.2s	20954×	body	80	nan
1.9s	11924×	body	80	valid
0.0ms	1×	body	160	nan