Details

sample134.0ms

Algorithm

intervals

Results

56.0ms	639×	body	80	nan
35.0ms	364×	body	80	valid

simplify4.2s

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: 0.4b

localize32.0ms

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

rewrite489.0ms

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:

57.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
19.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
401.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series807.0ms

Counts

4 → 12

Calls

4 calls:

483.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
45.0ms	(* (* 2.0 PI) n)
53.0ms	(/ 1.0 (sqrt k))
225.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.5s

Counts

169 → 169

Iterations

Useful iterations: done (2.5s)

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

prune685.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite143.0ms

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:

31.0ms	(* (* 2.0 PI) n)
32.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
8.0ms	(/ 1.0 (sqrt (sqrt k)))
31.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series631.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (* 2.0 PI) n)
52.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
308.0ms	(/ 1.0 (sqrt (sqrt k)))
228.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.2s

Counts

459 → 459

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	566	9021
1	1341	7684
2	3111	7109
done	5002	6936

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k))))
0.6b	(cbrt k)
0.6b	(cbrt k)
1.0b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

513×	`times-frac`
462×	`sqrt-prod`
282×	`add-sqr-sqrt` `*-un-lft-identity`
276×	`add-cube-cbrt`
75×	`cbrt-prod`
22×	`associate-/l*`
19×	`pow-unpow`
15×	`add-exp-log` `div-inv`
12×	`associate-/r*`
10×	`pow1`
9×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-exp` `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 → 379

Calls

4 calls:

30.0ms	(/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

496.0ms	(/ (/ 1.0 (sqrt (fabs (cbrt k)))) (sqrt (sqrt (cbrt k))))
358.0ms	(cbrt k)
312.0ms	(cbrt k)
181.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.0s

Counts

391 → 391

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	555	9033
1	1234	8064
2	2841	7922
done	5000	7913

prune2.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

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

rewrite93.0ms

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:

34.0ms	(* (* 2.0 PI) n)
12.0ms	(/ 1.0 (sqrt k))
11.0ms	(/ 1.0 (sqrt k))
30.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series416.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (* 2.0 PI) n)
76.0ms	(/ 1.0 (sqrt k))
68.0ms	(/ 1.0 (sqrt k))
206.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.4s

Counts

152 → 152

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	240	1698
1	571	1560
2	1748	1456
done	5000	1434

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes154.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	23
1	19	23
done	19	23

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.9s	20340×	body	80	nan
2.0s	11836×	body	80	valid
0.0ms	2×	body	160	nan