Details

sample232.0ms

Algorithm

intervals

Results

124.0ms	559×	body	80	nan
72.0ms	362×	body	80	valid

simplify1.2s

Counts: 1 → 1

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 3 expressions with local error:

2.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
42×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`add-cube-cbrt`
26×	`add-exp-log`
22×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`associate-/r*` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`div-exp` `associate-/l*`
3×	`expm1-log1p-u` `pow-pow` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-r` `*-commutative` `associate-/l/`

Counts

3 → 124

Calls

3 calls:

Slowest

20.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
14.0ms	(* n (* 2 PI))
14.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series585.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

341.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
209.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
35.0ms	(* n (* 2 PI))

simplify760.0ms

Counts: 166 → 133

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

2.1b	(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)))

rewrite96.0ms

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

37.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
23.0ms	(* (* 2 PI) n)
22.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
9.0ms	(/ 1 (sqrt k))

series591.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

329.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
192.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
38.0ms	(* (* 2 PI) n)
32.0ms	(/ 1 (sqrt k))

simplify717.0ms

Counts: 226 → 196

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 3 expressions with local error:

2.1b	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
0.3b	(* (* 2 PI) n)
0.2b	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
33×	`add-sqr-sqrt`
30×	`prod-exp`
26×	`*-un-lft-identity`
22×	`pow-unpow`
18×	`times-frac`
17×	`pow-exp` `add-cube-cbrt`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`pow-to-exp`
8×	`associate-r` `associate-l` `sqr-pow`
7×	`unpow-prod-down`
6×	`pow-prod-down` `difference-of-squares` `unswap-sqr`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
2×	`div-sub` `*-commutative` `pow-sub`
1×	`associate-*r/` `div-inv`

Counts

3 → 109

Calls

3 calls:

Slowest

50.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
31.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
28.0ms	(* (* 2 PI) n)

series555.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

352.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
164.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
39.0ms	(* (* 2 PI) n)

simplify567.0ms

Counts: 125 → 118

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

2.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.2b	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
0.1b	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
147×	`add-sqr-sqrt` `*-un-lft-identity`
138×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
22×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub` `difference-of-squares`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-l` `cbrt-unprod` `distribute-lft-out--`
2×	`clear-num` `frac-2neg`
1×	`associate-r` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 303

Calls

4 calls:

Slowest

37.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
32.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
23.0ms	(* n (* 2 PI))
18.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series933.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

369.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
297.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
209.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
59.0ms	(* n (* 2 PI))

simplify1.6s

Counts: 453 → 315

prune4.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes209.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.0s	20456×	body	80	nan
2.3s	11762×	body	80	valid