Details

sample165.0ms

Algorithm

intervals

Results

93.0ms	573×	body	80	nan
48.0ms	346×	body	80	valid

simplify323.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

323.0ms

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

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.9b	(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)))

rewrite118.0ms

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

41.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
39.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
24.0ms	(* (* 2 PI) n)
6.0ms	(/ 1 (sqrt k))

series684.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

371.0ms	(* (/ 1 (sqrt k)) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
206.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
59.0ms	(* (* 2 PI) n)
47.0ms	(/ 1 (sqrt k))

simplify19.4s

Counts

171 → 196

Calls

171 calls:

Slowest

901.0ms	(* (* (* (/ 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))))
647.0ms	(* (sqrt k) (pow (* (* 2 PI) n) (/ k 2)))
514.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
469.0ms	(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
466.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))

prune2.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 3 expressions with local error:

0.9b	(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)))

rewrite83.0ms

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

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

series542.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

321.0ms	(* (pow k -1/2) (pow (* (* 2 PI) n) (/ (- 1 k) 2)))
183.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
38.0ms	(* (* 2 PI) n)

simplify12.3s

Counts

87 → 118

Calls

87 calls:

Slowest

735.0ms	(+ (log (pow k -1/2)) (* (+ (+ (log 2) (log PI)) (log n)) (/ (- 1 k) 2)))
525.0ms	(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
442.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
437.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
432.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))

prune1.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

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

31.0ms	(* (* 2 PI) n)
22.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
20.0ms	(* (* 2 PI) n)
18.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))

series525.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

207.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
199.0ms	(pow (* (* 2 PI) n) (/ (- 1 k) 2))
60.0ms	(* (* 2 PI) n)
59.0ms	(* (* 2 PI) n)

simplify6.9s

Counts

88 → 138

Calls

88 calls:

Slowest

468.0ms	(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
454.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
444.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
433.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))
432.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))

prune2.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite148.0ms

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-r` `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-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 222

Calls

4 calls:

Slowest

43.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
36.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
30.0ms	(* (* 2 PI) n)
30.0ms	(* (* 2 PI) n)

series534.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

210.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
199.0ms	(pow (* (* 2 PI) n) (/ (/ (- 1 k) 2) 2))
66.0ms	(* (* 2 PI) n)
59.0ms	(* (* 2 PI) n)

simplify15.1s

Counts

184 → 234

Calls

184 calls:

Slowest

925.0ms	(* (* (* (* 2 PI) (* 2 PI)) (* 2 PI)) (* (* n n) n))
542.0ms	(pow (* 2 PI) (/ (/ (- 1 k) 2) 2))
501.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
484.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
475.0ms	(* (* (* (* 2 2) 2) (* (* PI PI) PI)) (* (* n n) n))

prune3.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes281.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample7.0s

Algorithm

intervals

Results

4.0s	20378×	body	80	nan
2.3s	11700×	body	80	valid
0.0ms	1×	body	160	nan