Details

sample125.0ms

Algorithm

intervals

Results

48.0ms	370×	body	80	valid
41.0ms	643×	body	80	nan

simplify142.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

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

rewrite159.0ms

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×	`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 → 149

Calls

4 calls:

80.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
11.0ms	(/ 1.0 (sqrt k))
32.0ms	(* (* 2.0 PI) n)
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series813.0ms

Counts

4 → 12

Calls

4 calls:

491.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
53.0ms	(/ 1.0 (sqrt k))
63.0ms	(* (* 2.0 PI) n)
206.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify116.0ms

Counts: 161 → 161

prune696.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
136×	`add-sqr-sqrt` `*-un-lft-identity`
122×	`pow-unpow`
100×	`add-cube-cbrt`
26×	`pow1` `add-exp-log`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp`
8×	`div-inv`
6×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod`
4×	`div-sub` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 192

Calls

4 calls:

19.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
59.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
40.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series546.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* 2.0 PI) n)
41.0ms	(* (* 2.0 PI) n)
214.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
247.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify80.0ms

Counts: 204 → 204

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
0.9b	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
1.0b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

1080×	`times-frac`
591×	`add-sqr-sqrt`
587×	`*-un-lft-identity`
461×	`add-cube-cbrt`
435×	`pow-unpow`
92×	`add-exp-log`
64×	`prod-exp`
63×	`distribute-lft-out--` `difference-of-squares`
39×	`pow-exp`
30×	`div-inv`
22×	`pow1`
20×	`div-sub`
13×	`pow-to-exp`
11×	`sqr-pow`
10×	`pow-prod-down`
9×	`pow-pow`
7×	`unpow-prod-down` `pow-sub`
6×	`add-cbrt-cube`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`add-log-exp` `unswap-sqr`
1×	`pow2` `frac-times` `associate-r/` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 546

Calls

4 calls:

68.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)))
54.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
59.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
36.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series953.0ms

Counts

4 → 12

Calls

4 calls:

283.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)) (pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2)))
238.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
209.0ms	(pow (* (* 2.0 PI) n) (/ (/ (/ (- 1.0 k) 2.0) 2) 2))
222.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify111.0ms

Counts: 558 → 558

prune3.6s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow n (/ (/ (- 1.0 k) 2.0) 2))
1.0b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 211

Calls

4 calls:

7.0ms	(/ 1.0 (sqrt k))
46.0ms	(* (* 2.0 PI) n)
16.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
33.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series398.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (sqrt k))
53.0ms	(* (* 2.0 PI) n)
73.0ms	(pow n (/ (/ (- 1.0 k) 2.0) 2))
216.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify84.0ms

Counts: 223 → 223

prune1.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes167.0ms

Accuracy

23.2% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify69.0ms

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.2s	20938×	body	80	nan
1.6s	11947×	body	80	valid
0.0ms	1×	body	160	nan