Details

sample175.0ms

Algorithm

intervals

Results

91.0ms	694×	body	80	nan
36.0ms	397×	body	80	valid

simplify4.1s

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 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)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite140.0ms

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:

49.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
14.0ms	(/ 1.0 (sqrt k))
25.0ms	(* (* 2.0 PI) n)
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series802.0ms

Counts

4 → 12

Calls

4 calls:

467.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
51.0ms	(/ 1.0 (sqrt k))
59.0ms	(* (* 2.0 PI) n)
226.0ms	(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

prune785.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.3b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 200

Calls

4 calls:

35.0ms	(* (* 2.0 PI) n)
34.0ms	(* (* 2.0 PI) n)
27.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
41.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series517.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (* 2.0 PI) n)
43.0ms	(* (* 2.0 PI) n)
218.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
207.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify1.6s

Counts

212 → 212

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	245	3332
1	682	3090
2	2126	2974
done	5000	2930

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`add-exp-log` `pow-unpow`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`associate-/r*`
6×	`pow-prod-down` `prod-exp` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 140

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
6.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* 2.0 PI) n)
36.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series335.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (sqrt k))
52.0ms	(/ 1.0 (sqrt k))
41.0ms	(* (* 2.0 PI) n)
191.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.3s

Counts

152 → 152

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	240	1698
1	571	1560
2	1753	1456
done	5000	1434

prune798.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 447

Calls

4 calls:

34.0ms	(* (* 2.0 PI) n)
11.0ms	(/ 1.0 (sqrt (sqrt k)))
34.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
28.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series578.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* 2.0 PI) n)
290.0ms	(/ 1.0 (sqrt (sqrt k)))
49.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
196.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.3s

Counts

459 → 459

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	566	9021
1	1341	7684
2	3109	7109
done	5000	6936

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

regimes163.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	28
1	23	28
done	23	28

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.5s	21085×	body	80	nan
1.7s	11934×	body	80	valid
0.0ms	2×	body	160	nan