Details

sample195.0ms

Algorithm

intervals

Results

91.0ms	648×	body	80	nan
46.0ms	378×	body	80	valid

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	59	16
3	120	16
4	330	16
5	1545	16
done	5000	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize16.0ms

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)
1.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite116.0ms

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:

64.0ms	(* (/ 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)
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series773.0ms

Counts

4 → 12

Calls

4 calls:

440.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
71.0ms	(/ 1.0 (sqrt k))
59.0ms	(* (* 2.0 PI) n)
203.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.8s

Counts

161 → 161

Iterations

Useful iterations: 2 (994.0ms)

Iter	Nodes	Cost
0	361	2800
1	1008	2643
2	4735	2473
done	5001	2473

prune740.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

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))
1.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite120.0ms

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:

13.0ms	(/ 1.0 (sqrt k))
57.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
24.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
16.0ms	(pow n (/ (- 1.0 k) 2.0))

series596.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ 1.0 (sqrt k))
351.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
79.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
112.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.5s

Counts

162 → 162

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	316	2486
1	851	2288
2	3379	2162
done	5001	2147

prune739.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow PI (/ (- 1.0 k) 2.0))
1.6b	(pow n (/ (- 1.0 k) 2.0))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-exp-log`
57×	`prod-exp`
53×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`pow-to-exp` `pow-exp`
14×	`div-sub` `pow-sub`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`unpow-prod-down`
7×	`associate-r`
6×	`pow1` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
5×	`frac-times` `associate-*l/`
4×	`add-log-exp`
3×	`associate-r/` `cbrt-unprod` `div-inv` `associate-/l` `sqr-pow`
2×	`pow-pow` `pow-prod-down`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 163

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
83.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
8.0ms	(pow PI (/ (- 1.0 k) 2.0))
9.0ms	(pow n (/ (- 1.0 k) 2.0))

series898.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/ 1.0 (sqrt k))
625.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
98.0ms	(pow PI (/ (- 1.0 k) 2.0))
110.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify2.7s

Counts

175 → 175

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	359	3070
1	1025	2728
2	4188	2376
done	5000	2360

prune792.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.3b	(* (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow PI (* 0.5 (- 1.0 k)))) (pow (/ 1 n) (* -0.5 (- 1.0 k))))
0.5b	(pow PI (* 0.5 (- 1.0 k)))
1.7b	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

150×	`add-exp-log`
114×	`prod-exp`
81×	`pow-exp`
48×	`pow-to-exp`
36×	`times-frac`
35×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
29×	`unpow-prod-down`
23×	`div-exp`
21×	`associate-r`
12×	`unpow-prod-up` `sqrt-prod`
11×	`rec-exp` `1-exp` `add-cbrt-cube`
7×	`pow1`
6×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-/r*`
4×	`pow-pow` `add-log-exp`
3×	`cbrt-unprod` `div-inv` `associate-/l*` `sqr-pow`
2×	`pow-unpow`
1×	`cbrt-undiv` `pow-flip` `frac-2neg` `associate-l` `clear-num` `*-commutative` `inv-pow`

Counts

4 → 184

Calls

4 calls:

8.0ms	(/ 1.0 (sqrt k))
116.0ms	(* (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow PI (* 0.5 (- 1.0 k)))) (pow (/ 1 n) (* -0.5 (- 1.0 k))))
9.0ms	(pow PI (* 0.5 (- 1.0 k)))
21.0ms	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

series831.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ 1.0 (sqrt k))
586.0ms	(* (* (pow 2.0 (* 0.5 (- 1.0 k))) (pow PI (* 0.5 (- 1.0 k)))) (pow (/ 1 n) (* -0.5 (- 1.0 k))))
81.0ms	(pow PI (* 0.5 (- 1.0 k)))
95.0ms	(pow (/ 1 n) (* -0.5 (- 1.0 k)))

simplify634.0ms

Counts

196 → 196

Iterations

Useful iterations: done (624.0ms)

Iter	Nodes	Cost
0	375	4249
1	1105	3789
done	5000	3438

prune858.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes162.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	30
1	27	30
done	27	30

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.3s	20845×	body	80	nan
1.6s	11893×	body	80	valid
1.0ms	3×	body	160	nan