Details

sample162.0ms

Algorithm

intervals

Results

68.0ms	789×	body	80	nan
36.0ms	385×	body	80	valid

simplify3.6s

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	853	16
6	3196	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite136.0ms

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:

56.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
36.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
31.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series844.0ms

Counts

4 → 12

Calls

4 calls:

514.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
66.0ms	(* (* 2.0 PI) n)
62.0ms	(/ 1.0 (sqrt k))
202.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

169 → 169

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	369	2880
1	961	2712
2	3131	2550
done	5000	2540

prune713.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.4b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite180.0ms

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:

19.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt (sqrt k)))
43.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
40.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series502.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (* 2.0 PI) n)
222.0ms	(/ 1.0 (sqrt (sqrt k)))
52.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
169.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.4s

Counts

459 → 459

Iterations

Useful iterations: done (2.4s)

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

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
0.5b	(cbrt k)
0.5b	(cbrt k)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

7227×	`times-frac`
6801×	`sqrt-prod`
3278×	`add-sqr-sqrt` `*-un-lft-identity`
3272×	`add-cube-cbrt`
666×	`cbrt-prod`
268×	`associate-/l*`
132×	`div-inv`
19×	`add-exp-log` `pow-unpow`
13×	`add-cbrt-cube`
10×	`pow1`
9×	`associate-/r*`
6×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `clear-num` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 2772

Calls

4 calls:

182.0ms	(/ (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
2.0ms	(cbrt k)
2.0ms	(cbrt k)
44.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ (/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k)))) (sqrt (sqrt k)))
238.0ms	(cbrt k)
240.0ms	(cbrt k)
216.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

2784 → 2784

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	2494	98869
done	5000	91452

prune15.7s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite116.0ms

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:

39.0ms	(* (* 2.0 PI) n)
12.0ms	(/ 1.0 (sqrt k))
12.0ms	(/ 1.0 (sqrt k))
44.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series374.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* 2.0 PI) n)
54.0ms	(/ 1.0 (sqrt k))
54.0ms	(/ 1.0 (sqrt k))
217.0ms	(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	1748	1456
done	5000	1434

prune649.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes211.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	27
1	24	27
done	24	27

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.6s	20965×	body	80	nan
1.1s	11987×	body	80	valid
0.0ms	1×	body	160	nan