Details

sample80.0ms

Algorithm

intervals

Results

33.0ms	673×	body	80	nan
22.0ms	376×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	113	16
4	291	16
5	803	16
6	3027	16
done	5000	16

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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:

16.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series517.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
34.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

169 → 169

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	369	2880
1	974	2712
2	3328	2538
done	5000	2523

prune432.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.3b	(pow n (/ (- 1.0 k) 2.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
48×	`times-frac`
41×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
16×	`prod-exp`
13×	`pow-exp`
12×	`sqrt-prod`
10×	`unpow-prod-down`
9×	`pow-to-exp` `sqr-pow`
8×	`pow1` `add-cbrt-cube`
7×	`associate-r`
6×	`div-sub` `associate-/r*` `distribute-lft-out--` `pow-sub` `difference-of-squares` `unswap-sqr`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `associate-/l*`
2×	`pow-prod-down`
1×	`cbrt-undiv` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `*-commutative` `cbrt-unprod`

Counts

4 → 158

Calls

4 calls:

9.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
4.0ms	(pow n (/ (- 1.0 k) 2.0))

series457.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
63.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify817.0ms

Counts

170 → 170

Iterations

Useful iterations: done (812.0ms)

Iter	Nodes	Cost
0	324	2568
1	778	2337
2	2394	2228
done	5000	2223

prune494.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.3b	(pow n (/ (- 1.0 k) 2.0))

rewrite33.0ms

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:

15.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
3.0ms	(/ 1.0 (sqrt k))
5.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
4.0ms	(pow n (/ (- 1.0 k) 2.0))

series463.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
63.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify941.0ms

Counts

181 → 181

Iterations

Useful iterations: done (936.0ms)

Iter	Nodes	Cost
0	333	2626
1	838	2468
2	2543	2363
done	5000	2349

prune723.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.4b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
1.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite66.0ms

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:

6.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt (sqrt k)))
16.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
12.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series379.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
165.0ms	(/ 1.0 (sqrt (sqrt k)))
41.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.3s

Counts

459 → 459

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	566	9021
1	1357	7684
2	3385	7111
done	5000	7106

prune729.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes143.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	23
1	25	23
done	25	23

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20896×	body	80	nan
738.0ms	11974×	body	80	valid