Details

sample93.0ms

Algorithm

intervals

Results

37.0ms	715×	body	80	nan
23.0ms	387×	body	80	valid

simplify2.3s

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: 0.4b

localize17.0ms

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)
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite90.0ms

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:

40.0ms	(* (/ 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)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series544.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
33.0ms	(* (* 2.0 PI) n)
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.5s

Counts

169 → 169

Iterations

Useful iterations: done (1.5s)

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

prune496.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (sqrt k)))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite103.0ms

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:

8.0ms	(/ 1.0 (sqrt (sqrt k)))
19.0ms	(* (* 2.0 PI) n)
25.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series398.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ 1.0 (sqrt (sqrt k)))
39.0ms	(* (* 2.0 PI) n)
39.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
148.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

459 → 459

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	566	9021
1	1341	7684
2	3110	7109
done	5000	6936

prune841.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

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)
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite57.0ms

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:

8.0ms	(/ 1.0 (sqrt k))
6.0ms	(/ 1.0 (sqrt k))
17.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series253.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt k))
38.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify864.0ms

Counts

152 → 152

Iterations

Useful iterations: done (860.0ms)

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

prune516.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize17.0ms

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))
1.3b	(pow n (/ (- 1.0 k) 2.0))

rewrite63.0ms

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:

6.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series478.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
299.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
74.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
67.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify1.1s

Counts

181 → 181

Iterations

Useful iterations: done (1.1s)

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

prune558.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.1s	21119×	body	80	nan
734.0ms	11933×	body	80	valid
0.0ms	1×	body	160	nan