Details

sample241.0ms

Algorithm

intervals

Results

120.0ms	734×	body	80	nan
68.0ms	400×	body	80	valid

simplify321.0ms

Calls

1 calls:

Slowest

321.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize42.0ms

Local error

Found 3 expressions with local error:

1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite74.0ms

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

28.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
25.0ms	(* n (* 2 PI))
20.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

series559.0ms

Calls

3 calls:

Slowest

322.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
192.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
44.0ms	(* n (* 2 PI))

simplify26.5s

Calls

124 calls:

Slowest

802.0ms	(/ (* (* (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)))
631.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (sqrt k)))
571.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
515.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
503.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(/ 1 (sqrt k))
0.2b	(* n (* 2 PI))
0.2b	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))

rewrite89.0ms

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-r`
22×	`pow-unpow`
17×	`pow1`
16×	`add-cbrt-cube`
15×	`pow-exp`
12×	`div-exp`
10×	`unswap-sqr`
8×	`associate-l`
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/` `un-div-inv` `inv-pow`

Calls

4 calls:

Slowest

47.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
16.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
5.0ms	(/ 1 (sqrt k))

series619.0ms

Calls

4 calls:

Slowest

364.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (/ 1 (sqrt k)))
187.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
35.0ms	(* n (* 2 PI))
33.0ms	(/ 1 (sqrt k))

simplify17.8s

Calls

173 calls:

Slowest

774.0ms	(* (* (* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (* (* (/ 1 (sqrt k)) (/ 1 (sqrt k))) (/ 1 (sqrt k))))
528.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
469.0ms	(* (pow (* n (* 2 PI)) (/ k 2)) (sqrt k))
450.0ms	(* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (/ 1 (sqrt (sqrt k))))
443.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 3 expressions with local error:

1.1b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.2b	(* n (* 2 PI))
0.2b	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))

rewrite95.0ms

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-*l/` `div-inv`

Calls

3 calls:

Slowest

46.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
26.0ms	(* n (* 2 PI))
17.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series652.0ms

Calls

3 calls:

Slowest

388.0ms	(* (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (pow k -1/2))
201.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
63.0ms	(* n (* 2 PI))

simplify11.5s

Calls

87 calls:

Slowest

656.0ms	(+ (* (+ (log n) (+ (log 2) (log PI))) (/ (- 1 k) 2)) (* (log k) -1/2))
400.0ms	(* (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt (pow k -1/2)))
391.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
382.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
370.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
1.0b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.2b	(* n (* 2 PI))
0.2b	(* n (* 2 PI))

rewrite101.0ms

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

33.0ms	(* n (* 2 PI))
26.0ms	(* n (* 2 PI))
19.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
15.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))

series461.0ms

Calls

4 calls:

Slowest

192.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
168.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
62.0ms	(* n (* 2 PI))
38.0ms	(* n (* 2 PI))

simplify14.2s

Calls

184 calls:

Slowest

507.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
452.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
412.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
406.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
402.0ms	(pow n (/ (/ (- 1 k) 2) 2))

prune3.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes124.0ms

Accuracy

0% (0.5b remaining)

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

bsearch5.0ms

end0.0ms

sample7.6s

Algorithm

intervals

Results

4.4s	21033×	body	80	nan
2.5s	12009×	body	80	valid
1.0ms	2×	body	160	nan