Details

sample211.0ms

Algorithm

intervals

Results

84.0ms	371×	body	80	valid
73.0ms	605×	body	80	nan

simplify4.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5002
6	2725
5	819
4	285
3	114
2	58
1	29
0	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize48.0ms

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

rewrite199.0ms

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:

85.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
13.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (* 2.0 PI) n)
54.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

632.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
69.0ms	(/ 1.0 (sqrt k))
57.0ms	(* (* 2.0 PI) n)
298.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify5.1s

Counts

169 → 169

Iterations

Iter	Nodes
done	5001
2	3472
1	1028
0	369

prune1.4s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 3 expressions with local error:

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

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 92

Calls

3 calls:

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

series936.0ms

Counts

3 → 9

Calls

3 calls:

597.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
73.0ms	(* (* 2.0 PI) n)
266.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.7s

Counts

101 → 101

Iterations

Iter	Nodes
done	5000
2	2571
1	765
0	270

prune974.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
1.0b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
46×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `sqr-pow`
19×	`pow-unpow`
16×	`div-exp` `add-cbrt-cube`
15×	`pow1`
12×	`prod-exp`
9×	`pow-exp` `associate-/l*`
7×	`div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `*-commutative`

Counts

4 → 282

Calls

4 calls:

52.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
27.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
35.0ms	(* (* 2.0 PI) n)
45.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

658.0ms	(/ 1.0 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
817.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
67.0ms	(* (* 2.0 PI) n)
286.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.9s

Counts

294 → 294

Iterations

Iter	Nodes
done	5000
1	1732
0	610

prune2.9s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

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:

11.0ms	(/ 1.0 (sqrt (sqrt k)))
36.0ms	(* (* 2.0 PI) n)
54.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
53.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series751.0ms

Counts

4 → 12

Calls

4 calls:

367.0ms	(/ 1.0 (sqrt (sqrt k)))
61.0ms	(* (* 2.0 PI) n)
53.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
269.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify4.4s

Counts

459 → 459

Iterations

Iter	Nodes
done	5023
2	3578
1	1372
0	566

prune2.6s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes449.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	20344×	body	80	nan
2.4s	11889×	body	80	valid
0.0ms	1×	body	160	nan