Details

sample231.0ms

Algorithm

intervals

Results

129.0ms	680×	body	80	nan
68.0ms	388×	body	80	valid

simplify1.6s

Counts: 1 → 1

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 3 expressions with local error:

0.9b	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

493×	`times-frac`
383×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
378×	`add-cube-cbrt`
328×	`unpow-prod-up`
312×	`prod-diff`
141×	`sqrt-prod`
46×	`associate-/l*`
26×	`add-exp-log`
25×	`div-inv`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sub-neg` `unpow-prod-down` `sqr-pow`
6×	`pow-unpow` `associate-/r*` `pow-prod-down` `pow-exp`
5×	`div-exp`
3×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `pow-sub` `difference-of-squares`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `distribute-lft-out--` `associate-/l/`

Counts

3 → 436

Calls

3 calls:

Slowest

30.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms	(* n (* 2 PI))
19.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))

series516.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

285.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
192.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
38.0ms	(* n (* 2 PI))

simplify2.4s

Counts: 445 → 445

prune6.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b	(/ 1 (sqrt k))
0.3b	(* (* 2 PI) n)
0.2b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite150.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 184

Calls

4 calls:

Slowest

65.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
34.0ms	(* (* 2 PI) n)
33.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
11.0ms	(/ 1 (sqrt k))

series688.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

348.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
226.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
65.0ms	(* (* 2 PI) n)
49.0ms	(/ 1 (sqrt k))

simplify1.5s

Counts: 196 → 196

prune2.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.9b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`pow-unpow`
42×	`times-frac`
38×	`*-un-lft-identity`
26×	`pow1` `add-exp-log` `add-cube-cbrt`
14×	`add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `difference-of-squares`
6×	`pow-pow` `associate-l` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-r` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

Slowest

42.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
26.0ms	(* n (* 2 PI))
18.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
14.0ms	(* n (* 2 PI))

series553.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
227.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
53.0ms	(* n (* 2 PI))
45.0ms	(* n (* 2 PI))

simplify2.8s

Counts: 138 → 138

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
0.8b	(pow n (/ (- 1/2 (/ k 2)) 2))
0.3b	(* n (* 2 PI))
0.2b	(* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

703×	`add-exp-log`
429×	`prod-exp`
291×	`div-exp`
205×	`pow-exp`
113×	`pow-to-exp`
87×	`add-sqr-sqrt`
79×	`times-frac`
78×	`1-exp`
57×	`*-un-lft-identity`
45×	`add-cube-cbrt`
44×	`pow-unpow`
35×	`associate-r`
30×	`add-cbrt-cube`
18×	`pow1`
17×	`sqrt-prod`
12×	`difference-of-squares`
11×	`cbrt-unprod`
10×	`unpow-prod-down` `associate-l` `sqr-pow`
7×	`cbrt-undiv` `pow-prod-down`
6×	`distribute-lft-out--`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 332

Calls

4 calls:

Slowest

48.0ms	(* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
34.0ms	(* n (* 2 PI))
17.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
12.0ms	(pow n (/ (- 1/2 (/ k 2)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

918.0ms	(* (/ (* (pow n (/ (- 1/2 (/ k 2)) 2)) (pow (* 2 PI) (/ (- 1/2 (/ k 2)) 2))) 1) (/ (pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2)) (sqrt k)))
203.0ms	(pow (* n (* 2 PI)) (/ (- 1/2 (/ k 2)) 2))
109.0ms	(pow n (/ (- 1/2 (/ k 2)) 2))
36.0ms	(* n (* 2 PI))

simplify2.0s

Counts: 344 → 344

prune5.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes326.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.2s	20470×	body	80	nan
2.6s	11824×	body	80	valid
0.0ms	1×	body	160	nan