Details

sample210.0ms

Algorithm

intervals

Results

120.0ms	710×	body	80	nan
58.0ms	371×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
6	2083
5	817
4	322
3	123
2	60
1	29
0	13

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
0.3b	(* n (* 2 PI))
0.7b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`add-exp-log`
24×	`sqrt-prod`
16×	`unpow-prod-up`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
7×	`associate-/l*`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `div-inv` `distribute-lft-out--` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

23.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms	(* n (* 2 PI))
21.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series577.0ms

Counts

3 → 9

Calls

3 calls:

346.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
55.0ms	(* n (* 2 PI))
176.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
2	2014
1	644
0	267

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
0.2b	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
0.3b	(* n (* 2 PI))
0.7b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
166×	`add-sqr-sqrt`
163×	`*-un-lft-identity`
161×	`add-cube-cbrt`
108×	`sqrt-prod`
72×	`add-exp-log`
64×	`unpow-prod-up`
54×	`associate-/r*`
32×	`sub-neg` `unpow-prod-down` `div-exp` `sqr-pow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
6×	`rec-exp` `pow-unpow` `1-exp` `pow-prod-down` `associate-/r/` `div-inv` `pow-sub`
5×	`pow-to-exp`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `difference-of-squares`
1×	`associate-r` `*-commutative` `pow-flip` `distribute-lft-out--` `inv-pow`

Counts

4 → 343

Calls

4 calls:

35.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
10.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
15.0ms	(* n (* 2 PI))
23.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

363.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2)))))
378.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (- 1/2 (/ k 2))))
57.0ms	(* n (* 2 PI))
245.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify6.5s

Counts

355 → 355

Iterations

Iter	Nodes
2	3999
1	1424
0	532

prune2.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
0.2b	(/ 1 (sqrt k))
0.3b	(* (* 2 PI) n)
0.7b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt` `add-exp-log`
62×	`times-frac`
57×	`*-un-lft-identity`
44×	`add-cube-cbrt`
38×	`prod-exp`
25×	`sqrt-prod`
23×	`associate-l`
22×	`pow-unpow`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-r`
7×	`sqr-pow`
6×	`rec-exp` `associate-/r*` `1-exp` `pow-prod-down` `difference-of-squares`
5×	`pow-to-exp` `cbrt-unprod`
4×	`insert-posit16` `add-log-exp`
3×	`pow-pow` `div-sub` `div-inv` `pow-flip` `associate-/l*` `distribute-lft-out--` `pow-sub`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l/` `associate-r/` `inv-pow`

Counts

4 → 176

Calls

4 calls:

43.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
15.0ms	(/ 1 (sqrt k))
28.0ms	(* (* 2 PI) n)
31.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series632.0ms

Counts

4 → 12

Calls

4 calls:

375.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
39.0ms	(/ 1 (sqrt k))
48.0ms	(* (* 2 PI) n)
169.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.6s

Counts

188 → 188

Iterations

Iter	Nodes
2	2648
1	922
0	345

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (* 2 PI))
0.3b	(* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
0.6b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.6b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
64×	`prod-exp`
63×	`add-sqr-sqrt`
44×	`pow-unpow`
42×	`times-frac`
41×	`*-un-lft-identity`
36×	`pow-exp`
29×	`add-cube-cbrt`
21×	`pow1`
12×	`pow-to-exp` `difference-of-squares`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-l`
6×	`unpow-prod-down` `pow-pow` `div-sub` `associate-r` `distribute-lft-out--` `pow-sub`
5×	`swap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`pow2` `frac-times` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`

Counts

4 → 160

Calls

4 calls:

27.0ms	(* n (* 2 PI))
76.0ms	(* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
30.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
30.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

series805.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* n (* 2 PI))
319.0ms	(* (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)))
229.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
199.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))

simplify1.8s

Counts

172 → 172

Iterations

Iter	Nodes
2	2056
1	653
0	232

prune1.6s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes320.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	16
1	16
0	13

end0.0ms

sample8.4s

Algorithm

intervals

Results

5.1s	21323×	body	80	nan
2.5s	11964×	body	80	valid
1.0ms	2×	body	160	nan