Details

sample166.0ms

Algorithm

intervals

Results

87.0ms	694×	body	80	nan
33.0ms	397×	body	80	valid

simplify118.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

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	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite132.0ms

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:

53.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(/ 1.0 (sqrt k))
19.0ms	(* (* 2.0 PI) n)
34.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series757.0ms

Counts

4 → 12

Calls

4 calls:

466.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
43.0ms	(/ 1.0 (sqrt k))
55.0ms	(* (* 2.0 PI) n)
193.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify127.0ms

Counts: 161 → 161

prune700.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite161.0ms

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:

33.0ms	(* (* 2.0 PI) n)
34.0ms	(* (* 2.0 PI) n)
46.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
35.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series544.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* 2.0 PI) n)
38.0ms	(* (* 2.0 PI) n)
218.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
226.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify98.0ms

Counts: 204 → 204

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite115.0ms

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×	`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 → 132

Calls

4 calls:

12.0ms	(/ 1.0 (sqrt k))
13.0ms	(/ 1.0 (sqrt k))
45.0ms	(* (* 2.0 PI) n)
35.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series387.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1.0 (sqrt k))
50.0ms	(/ 1.0 (sqrt k))
54.0ms	(* (* 2.0 PI) n)
226.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify78.0ms

Counts: 144 → 144

prune797.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.4b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite330.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
38×	`pow-unpow`
36×	`pow1`
30×	`times-frac`
27×	`add-cube-cbrt`
24×	`sqrt-div`
23×	`add-exp-log`
18×	`div-sub` `pow-sub`
17×	`frac-times`
12×	`pow-prod-down`
11×	`associate-r/` `associate-l/` `add-cbrt-cube`
10×	`prod-exp`
8×	`sqrt-pow1` `pow1/2`
7×	`associate-r`
6×	`pow-pow` `pow-exp` `distribute-lft-out--` `difference-of-squares`
5×	`associate-l` `pow-prod-up`
4×	`swap-sqr` `sqrt-prod` `cbrt-unprod` `add-log-exp`
3×	`pow-sqr`
2×	`pow-to-exp` `unpow-prod-down` `*-commutative` `div-inv` `sqr-pow`
1×	`pow2` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `unswap-sqr`

Counts

4 → 143

Calls

4 calls:

19.0ms	(* (* 2.0 PI) n)
245.0ms	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
27.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
32.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series1.2s

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* 2.0 PI) n)
705.0ms	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
246.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
209.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify114.0ms

Counts: 155 → 155

prune681.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes217.0ms

Accuracy

22.3% (0.3b remaining)

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

bsearch0.0ms

simplify114.0ms

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.3s	21085×	body	80	nan
1.6s	11934×	body	80	valid
0.0ms	2×	body	160	nan