Details

sample224.0ms

Algorithm

intervals

Results

106.0ms	648×	body	80	nan
54.0ms	387×	body	80	valid

simplify1.4s

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	1555	16
done	5001	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize33.0ms

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))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite178.0ms

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:

66.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(* (* 2.0 PI) n)
14.0ms	(/ 1.0 (sqrt k))
47.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series755.0ms

Counts

4 → 12

Calls

4 calls:

475.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
41.0ms	(* (* 2.0 PI) n)
68.0ms	(/ 1.0 (sqrt k))
171.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.8s

Counts

169 → 169

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	369	2880
1	1037	2720
2	4934	2550
done	5000	2548

prune682.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.7b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
150×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
114×	`add-cube-cbrt`
23×	`add-exp-log`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `div-inv`
6×	`pow-pow` `pow-exp` `associate-/r*`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 221

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
13.0ms	(/ 1.0 (sqrt k))
31.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
63.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series478.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* 2.0 PI) n)
43.0ms	(/ 1.0 (sqrt k))
188.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
200.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify2.7s

Counts

233 → 233

Iterations

Useful iterations: done (2.7s)

Iter	Nodes	Cost
0	332	3588
1	979	3316
2	4191	3202
done	5000	3197

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

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))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite104.0ms

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:

24.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt k))
12.0ms	(/ 1.0 (sqrt k))
51.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series438.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* 2.0 PI) n)
70.0ms	(/ 1.0 (sqrt k))
64.0ms	(/ 1.0 (sqrt k))
242.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify2.1s

Counts

152 → 152

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	240	1698
1	616	1560
2	2748	1456
done	5000	1451

prune819.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
0.7b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite154.0ms

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:

27.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt (sqrt k)))
43.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
37.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series568.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* 2.0 PI) n)
271.0ms	(/ 1.0 (sqrt (sqrt k)))
45.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
192.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify790.0ms

Counts

459 → 459

Iterations

Useful iterations: done (757.0ms)

Iter	Nodes	Cost
0	566	9021
1	1407	7684
done	5001	7188

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes216.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	32
1	20	32
done	20	32

end0.0ms

sample6.5s

Algorithm

intervals

Results

3.7s	20461×	body	80	nan
1.5s	11878×	body	80	valid
0.0ms	1×	body	160	nan