Details

sample214.0ms

Algorithm

intervals

Results

117.0ms	607×	body	80	nan
69.0ms	382×	body	80	valid

simplify372.0ms

Calls

1 calls:

Slowest

372.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite61.0ms

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/`

Calls

3 calls:

Slowest

23.0ms	(* n (* 2 PI))
22.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
14.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series524.0ms

Calls

3 calls:

Slowest

271.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
196.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
58.0ms	(* n (* 2 PI))

simplify27.3s

Calls

124 calls:

Slowest

683.0ms	(/ (* (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))) (sqrt (sqrt k)))
643.0ms	(/ (* (* (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)))
535.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
525.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
516.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.9b	(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))))

rewrite78.0ms

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`

Calls

4 calls:

Slowest

33.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
14.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
13.0ms	(* n (* 2 PI))
9.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))

series941.0ms

Calls

4 calls:

Slowest

381.0ms	(/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2)))
352.0ms	(/ 1 (/ (sqrt k) (pow (* n (* 2 PI)) (/ (- 1 k) 2))))
162.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
46.0ms	(* n (* 2 PI))

simplify1.8m

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)))))
1.0s	(/ 1 (/ 1 (pow n (/ (- 1 k) 2))))
794.0ms	(/ (sqrt 1) (/ (sqrt k) (cbrt (pow (* n (* 2 PI)) (/ (- 1 k) 2)))))
772.0ms	(/ (* (cbrt 1) (cbrt 1)) (/ (sqrt (* (cbrt k) (cbrt k))) (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))))
678.0ms	(/ (sqrt 1) (/ (* (cbrt (sqrt k)) (cbrt (sqrt k))) (pow n (/ (- 1 k) 2))))

prune3.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

30.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
29.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
19.0ms	(* n (* 2 PI))
12.0ms	(* n (* 2 PI))

series471.0ms

Calls

4 calls:

Slowest

201.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
192.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
45.0ms	(* n (* 2 PI))
33.0ms	(* n (* 2 PI))

simplify14.8s

Calls

184 calls:

Slowest

807.0ms	(* (* (* n n) n) (* (* (* 2 2) 2) (* (* PI PI) PI)))
483.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
463.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
452.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
417.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))

prune3.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

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

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

1260×	`times-frac`
707×	`add-sqr-sqrt` `*-un-lft-identity`
518×	`add-cube-cbrt`
498×	`pow-unpow`
126×	`difference-of-squares`
63×	`distribute-lft-out--`
30×	`div-inv`
27×	`pow1` `add-exp-log`
12×	`pow-prod-down` `prod-exp`
9×	`pow-pow` `add-cbrt-cube` `pow-exp`
8×	`div-sub`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `unpow-prod-down` `associate-l` `cbrt-unprod` `pow-sub` `sqr-pow`
1×	`associate-r` `*-commutative`

Calls

4 calls:

Slowest

36.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
20.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
17.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
16.0ms	(* n (* 2 PI))

series565.0ms

Calls

4 calls:

Slowest

178.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
172.0ms	(pow (* n (* 2 PI)) (/ (/ (/ (- 1 k) 2) 2) 2))
166.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
49.0ms	(* n (* 2 PI))

simplify55.1s

Calls

542 calls:

Slowest

512.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
496.0ms	(/ (/ (/ (- 1 (sqrt k)) (cbrt 2)) 2) 2)
494.0ms	(pow n (/ (/ (/ (- 1 k) 2) 2) 2))
459.0ms	(exp (* 1/8 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
445.0ms	(pow n (/ (/ (/ (- 1 k) 2) 2) 2))

prune10.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes185.0ms

Accuracy

0% (0.4b remaining)

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

bsearch3.0ms

end0.0ms

sample7.2s

Algorithm

intervals

Results

4.4s	20279×	body	80	nan
2.3s	11735×	body	80	valid
1.0ms	2×	body	160	nan