Details

sample234.0ms

Algorithm

intervals

Results

102.0ms	398×	body	80	valid
97.0ms	629×	body	80	nan

simplify1.5s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

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)))

rewrite52.0ms

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:

12.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
12.0ms	(* n (* 2 PI))
25.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series515.0ms

Counts

3 → 9

Calls

3 calls:

290.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
48.0ms	(* n (* 2 PI))
177.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify1.2s

Counts

127 → 127

Iterations

Iter	Nodes
2	2014
1	644
0	267

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

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:

29.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
5.0ms	(/ 1 (sqrt k))
15.0ms	(* (* 2 PI) n)
37.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series633.0ms

Counts

4 → 12

Calls

4 calls:

342.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
29.0ms	(/ 1 (sqrt k))
67.0ms	(* (* 2 PI) n)
194.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

simplify1.5s

Counts

188 → 188

Iterations

Iter	Nodes
2	2648
1	922
0	345

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

26×	`pow1` `add-exp-log`
18×	`add-sqr-sqrt`
14×	`add-cbrt-cube`
12×	`pow-unpow` `*-un-lft-identity` `pow-prod-down` `prod-exp`
8×	`add-cube-cbrt`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod`
4×	`unpow-prod-up` `insert-posit16` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `sub-neg` `unpow-prod-down` `times-frac` `associate-r` `*-commutative` `distribute-lft-out--` `pow-sub` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

26.0ms	(* n (* 2 PI))
27.0ms	(* n (* 2 PI))
26.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
32.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series493.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* n (* 2 PI))
42.0ms	(* n (* 2 PI))
198.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
191.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify2.1s

Counts

102 → 102

Iterations

Iter	Nodes
3	3953
2	1097
1	338
0	123

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* n (* 2 PI))
0.5b	(pow (* 2 PI) (- 1/2 (/ k 2)))
0.7b	(pow n (- 1/2 (/ k 2)))
0.7b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`pow1` `add-exp-log`
18×	`pow-unpow`
15×	`*-un-lft-identity`
9×	`add-cbrt-cube` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp`
6×	`unpow-prod-up` `pow-pow` `pow-exp` `difference-of-squares`
5×	`unpow-prod-down`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `sub-neg` `times-frac` `associate-l` `cbrt-unprod` `distribute-lft-out--` `pow-sub` `sqr-pow`
1×	`associate-r` `*-commutative`

Counts

4 → 93

Calls

4 calls:

25.0ms	(* n (* 2 PI))
17.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
11.0ms	(pow n (- 1/2 (/ k 2)))
19.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* n (* 2 PI))
85.0ms	(pow (* 2 PI) (- 1/2 (/ k 2)))
99.0ms	(pow n (- 1/2 (/ k 2)))
212.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

simplify6.4s

Counts

105 → 105

Iterations

Iter	Nodes
3	6435
2	1816
1	545
0	192

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes298.0ms

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
2	16
1	16
0	13

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	21022×	body	80	nan
2.3s	11987×	body	80	valid
1.0ms	2×	body	160	nan