Details

sample268.0ms

Algorithm

intervals

Results

125.0ms	681×	body	80	nan
72.0ms	389×	body	80	valid

simplify1.5s

Counts: 1 → 1

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 3 expressions with local error:

1.2b	(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))

rewrite117.0ms

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

37.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
31.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
25.0ms	(* n (* 2 PI))

series934.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

555.0ms	(pow (* n (* 2 PI)) (- 1/2 (/ k 2)))
321.0ms	(/ (pow (* n (* 2 PI)) (- 1/2 (/ k 2))) (sqrt k))
58.0ms	(* n (* 2 PI))

simplify1.8s

Counts: 445 → 445

prune7.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b	(* (* 2 PI) n)
0.2b	(/ 1 (sqrt k))
0.2b	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite138.0ms

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

60.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
30.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
27.0ms	(* (* 2 PI) n)
15.0ms	(/ 1 (sqrt k))

series678.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

362.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
207.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
60.0ms	(* (* 2 PI) n)
49.0ms	(/ 1 (sqrt k))

simplify1.7s

Counts: 196 → 196

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
1.1b	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
0.3b	(* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
0.3b	(* (* 2 PI) n)

rewrite157.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
173×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
140×	`pow-unpow`
115×	`add-cube-cbrt`
91×	`add-exp-log`
64×	`prod-exp`
36×	`pow-exp` `difference-of-squares`
21×	`pow1`
18×	`distribute-lft-out--`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r` `div-inv`
6×	`unpow-prod-down` `pow-pow` `associate-l` `pow-sub`
5×	`swap-sqr`
4×	`expm1-log1p-u` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`pow2` `frac-times` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`

Counts

4 → 264

Calls

4 calls:

Slowest

71.0ms	(* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
33.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
33.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
13.0ms	(* (* 2 PI) n)

series709.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

278.0ms	(* (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)) (pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2)))
202.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
188.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
40.0ms	(* (* 2 PI) n)

simplify1.8s

Counts: 276 → 276

prune3.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
1.2b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b	(* (* 2 PI) n)
0.3b	(* (* 2 PI) n)

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt` `pow-unpow` `*-un-lft-identity`
36×	`times-frac`
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-r` `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-l` `*-commutative` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

Slowest

37.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
31.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
28.0ms	(* (* 2 PI) n)
21.0ms	(* (* 2 PI) n)

series512.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

231.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
189.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
51.0ms	(* (* 2 PI) n)
40.0ms	(* (* 2 PI) n)

simplify759.0ms

Counts: 138 → 138

prune2.0s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes287.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch4.0ms

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.1s	20763×	body	80	nan
2.6s	12036×	body	80	valid
1.0ms	2×	body	160	nan