Details

sample244.0ms

Algorithm

intervals

Results

186.0ms	789×	body	80	nan
23.0ms	385×	body	80	valid

simplify36.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1044	8
5	5001	8
done	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

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

rewrite95.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

41.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
9.0ms	(/ 1.0 (sqrt k))
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series527.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
32.0ms	(* (* 2.0 PI) n)
41.0ms	(/ 1.0 (sqrt k))
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Counts

169 → 169

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383
done	5003	1383

prune496.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))
0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

200×	`sqrt-prod`
173×	`add-sqr-sqrt`
151×	`times-frac`
109×	`*-un-lft-identity`
103×	`add-cube-cbrt`
33×	`swap-sqr`
25×	`pow1` `associate-r` `associate-l`
19×	`pow-unpow`
16×	`add-exp-log` `unswap-sqr`
12×	`associate-/r*`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2`
7×	`div-inv`
6×	`pow-prod-down` `associate-/l*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-r/` `associate-l/` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 249

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt k))
6.0ms	(/ 1.0 (sqrt k))
51.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series313.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt k))
37.0ms	(/ 1.0 (sqrt k))
95.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
138.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Counts

261 → 261

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	769	1839
1	3492	1677
2	5001	1651
done	5001	1651

prune761.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (* 1.0 1.0) k))
0.2b	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
27×	`add-exp-log`
26×	`*-un-lft-identity`
24×	`times-frac`
20×	`add-cube-cbrt`
19×	`pow-unpow`
18×	`sqrt-prod`
16×	`pow1`
14×	`prod-exp`
11×	`associate-l` `add-cbrt-cube`
8×	`associate-r`
6×	`pow-prod-down` `pow-exp` `unswap-sqr`
5×	`sqr-pow`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `sqrt-div` `div-sub` `div-inv` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`

Counts

4 → 119

Calls

4 calls:

5.0ms	(sqrt (/ (* 1.0 1.0) k))
44.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series621.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(sqrt (/ (* 1.0 1.0) k))
388.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
32.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify92.0ms

Counts

131 → 131

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	912	1255
1	3716	1173
2	5002	1153
done	5002	1153

prune422.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
0.3b	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
0.8b	(pow n (/ (- 1.0 k) 2.0))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-exp-log`
48×	`add-sqr-sqrt`
44×	`prod-exp`
41×	`*-un-lft-identity`
38×	`pow-unpow`
33×	`times-frac`
29×	`add-cube-cbrt`
23×	`pow-exp`
16×	`pow-to-exp`
15×	`associate-l`
14×	`div-sub` `pow-sub`
11×	`add-cbrt-cube`
10×	`pow1` `unpow-prod-down`
9×	`sqr-pow`
8×	`associate-r`
7×	`sqrt-prod`
6×	`frac-times` `associate-*r/` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `sqrt-div` `associate-*l/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-prod-down` `div-inv`
2×	`*-commutative`

Counts

4 → 161

Calls

4 calls:

67.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
23.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
8.0ms	(pow n (/ (- 1.0 k) 2.0))

series1.1s

Counts

4 → 12

Calls

4 calls:

663.0ms	(* (sqrt (/ (* 1.0 1.0) k)) (* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0))))
284.0ms	(* (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)) (pow n (/ (- 1.0 k) 2.0)))
77.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
62.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify104.0ms

Counts

173 → 173

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	1034	1864
1	4155	1727
2	5001	1718
done	5001	1718

prune543.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes219.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	15
1	19	15
done	19	15

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	20965×	body	80	nan
719.0ms	11987×	body	80	valid
0.0ms	1×	body	160	nan