Details

sample240.0ms

Algorithm

intervals

Results

127.0ms	680×	body	80	nan
73.0ms	388×	body	80	valid

simplify1.4s

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 3 expressions with local error:

0.9b	(pow (* n (* 2 PI)) (* (- 1 k) 1/2))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
26×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp` `associate-/l*`
3×	`pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp`
1×	`cbrt-undiv` `pow-unpow` `clear-num` `frac-2neg` `associate-r` `*-commutative` `div-inv`

Counts

3 → 95

Calls

3 calls:

Slowest

25.0ms	(pow (* n (* 2 PI)) (* (- 1 k) 1/2))
25.0ms	(* n (* 2 PI))
24.0ms	(/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))

series600.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

332.0ms	(/ (pow (* n (* 2 PI)) (* (- 1 k) 1/2)) (sqrt k))
207.0ms	(pow (* n (* 2 PI)) (* (- 1 k) 1/2))
60.0ms	(* n (* 2 PI))

simplify1.3s

Counts: 104 → 104

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize26.0ms

Local error

Found 3 expressions with local error:

0.9b	(pow (* 2 (* n PI)) (* (- 1 k) 1/2))
0.3b	(* n PI)
0.2b	(/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

30×	`times-frac`
26×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-exp-log`
18×	`sqrt-prod`
11×	`pow1`
8×	`unpow-prod-down` `sqr-pow`
7×	`add-cbrt-cube` `prod-exp`
6×	`associate-/r*` `pow-exp`
5×	`div-exp` `associate-/l*`
4×	`pow-prod-down`
3×	`pow-pow` `associate-r` `associate-l` `insert-posit16` `add-log-exp`
2×	`pow-to-exp`
1×	`cbrt-undiv` `pow-unpow` `clear-num` `frac-2neg` `*-commutative` `cbrt-unprod` `div-inv` `unswap-sqr`

Counts

3 → 95

Calls

3 calls:

Slowest

12.0ms	(/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))
12.0ms	(pow (* 2 (* n PI)) (* (- 1 k) 1/2))
5.0ms	(* n PI)

series629.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

395.0ms	(/ (pow (* 2 (* n PI)) (* (- 1 k) 1/2)) (sqrt k))
212.0ms	(pow (* 2 (* n PI)) (* (- 1 k) 1/2))
22.0ms	(* n PI)

simplify1.1s

Counts: 104 → 104

prune1.7s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* n (* PI 2)) (/ (- 1 k) 2))
0.3b	(* n (* PI 2))
0.2b	(/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
0.2b	(/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
147×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub` `difference-of-squares`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 295

Calls

4 calls:

Slowest

33.0ms	(/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
27.0ms	(* n (* PI 2))
19.0ms	(/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
13.0ms	(pow (* n (* PI 2)) (/ (- 1 k) 2))

series854.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

337.0ms	(/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2)))
305.0ms	(/ 1 (/ (sqrt k) (pow (* n (* PI 2)) (/ (- 1 k) 2))))
178.0ms	(pow (* n (* PI 2)) (/ (- 1 k) 2))
35.0ms	(* n (* PI 2))

simplify1.3s

Counts: 307 → 307

prune3.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* n (* PI 2)) (/ (- 1 k) 2))
0.3b	(/ 1 (sqrt k))
0.3b	(* n (* PI 2))
0.2b	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

1199×	`times-frac`
519×	`add-sqr-sqrt` `*-un-lft-identity`
510×	`add-cube-cbrt`
207×	`add-exp-log`
201×	`sqrt-prod`
138×	`div-exp`
70×	`unpow-prod-down` `sqr-pow`
47×	`div-inv`
42×	`prod-exp`
39×	`pow-exp`
37×	`rec-exp` `1-exp`
26×	`associate-/r*`
25×	`associate-/l*`
24×	`div-sub` `associate-/r/` `pow-sub`
23×	`add-cbrt-cube`
22×	`pow-unpow`
17×	`pow1`
13×	`pow-to-exp`
9×	`cbrt-undiv`
6×	`pow-prod-down` `difference-of-squares`
4×	`insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `pow-flip` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `inv-pow` `associate-/l/`

Counts

4 → 668

Calls

4 calls:

Slowest

38.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))))
29.0ms	(* n (* PI 2))
15.0ms	(pow (* n (* PI 2)) (/ (- 1 k) 2))
7.0ms	(/ 1 (sqrt k))

series668.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

343.0ms	(/ (/ 1 (sqrt k)) (/ 1 (pow (* n (* PI 2)) (/ (- 1 k) 2))))
225.0ms	(pow (* n (* PI 2)) (/ (- 1 k) 2))
53.0ms	(* n (* PI 2))
47.0ms	(/ 1 (sqrt k))

simplify2.5s

Counts: 680 → 680

prune8.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes183.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.0s	20470×	body	80	nan
2.7s	11824×	body	80	valid
0.0ms	1×	body	160	nan