Details

sample251.0ms

Algorithm

intervals

Results

120.0ms	667×	body	80	nan
92.0ms	373×	body	80	valid

simplify287.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

286.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

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

31.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
14.0ms	(* n (* 2 PI))
11.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series588.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

333.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
192.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
62.0ms	(* n (* 2 PI))

simplify26.4s

Counts

124 → 133

Calls

124 calls:

Slowest

768.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
601.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
565.0ms	(/ (pow n (/ (- 1 k) 2)) 1)
563.0ms	(/ (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (sqrt k) (sqrt k)) (sqrt k)))
551.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

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

39.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
39.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
27.0ms	(* (* 2 PI) n)
10.0ms	(/ 1 (sqrt k))

series592.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

321.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
192.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
40.0ms	(/ 1 (sqrt k))
39.0ms	(* (* 2 PI) n)

simplify20.0s

Counts

171 → 196

Calls

171 calls:

Slowest

820.0ms	(* (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))) (* (* (pow (* (* 2 PI) n) (/ (- 1 k) 2)) (pow (* (* 2 PI) n) (/ (- 1 k) 2))) (pow (* (* 2 PI) n) (/ (- 1 k) 2))))
721.0ms	(sqrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
593.0ms	(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
519.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
478.0ms	(+ (- 0 (log (sqrt k))) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 3 expressions with local error:

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

rewrite118.0ms

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

52.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
34.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
29.0ms	(* (* 2 PI) n)

series576.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

347.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
191.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
38.0ms	(* (* 2 PI) n)

simplify11.5s

Counts

87 → 118

Calls

87 calls:

Slowest

552.0ms	(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
489.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
392.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
383.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
362.0ms	(cbrt (pow (* (* 2 PI) n) (/ (- 1 k) 2)))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

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

31.0ms	(* n (* 2 PI))
29.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
22.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
19.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series973.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

356.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
353.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
203.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
61.0ms	(* n (* 2 PI))

simplify1.8m

Counts

390 → 315

Calls

390 calls:

Slowest

1.0s	(/ (* (* 1 1) 1) (* (* (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
820.0ms	(/ (sqrt (sqrt k)) (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
760.0ms	(/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
712.0ms	(/ (cbrt 1) (/ (sqrt (sqrt k)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
708.0ms	(/ (sqrt 1) (/ (sqrt (sqrt k)) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))

prune3.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

regimes321.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.4s	20569×	body	80	nan
2.3s	11837×	body	80	valid
2.0ms	7×	body	160	nan