Details

sample254.0ms

Algorithm

intervals

Results

148.0ms	786×	body	80	nan
72.0ms	399×	body	80	valid

simplify271.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

271.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.2b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite67.0ms

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

24.0ms	(* n (* 2 PI))
21.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
18.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series559.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

316.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
198.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
44.0ms	(* n (* 2 PI))

simplify26.5s

Counts

124 → 133

Calls

124 calls:

Slowest

722.0ms	(/ (sqrt (pow (* n (* 2 PI)) (/ (- 1 k) 2))) (sqrt 1))
647.0ms	(/ (* (* (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)))
552.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
507.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
499.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt (cbrt k)))

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite69.0ms

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`

Counts

4 → 222

Calls

4 calls:

Slowest

16.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
16.0ms	(* n (* 2 PI))
15.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
13.0ms	(* n (* 2 PI))

series452.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
160.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
52.0ms	(* n (* 2 PI))
49.0ms	(* n (* 2 PI))

simplify13.5s

Counts

184 → 234

Calls

184 calls:

Slowest

460.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
446.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
399.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
385.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
380.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.5b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite107.0ms

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

Counts

4 → 126

Calls

4 calls:

Slowest

28.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
27.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
25.0ms	(* n (* 2 PI))
25.0ms	(* n (* 2 PI))

series491.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

212.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
191.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
50.0ms	(* n (* 2 PI))
38.0ms	(* n (* 2 PI))

simplify6.6s

Counts

88 → 138

Calls

88 calls:

Slowest

497.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
492.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
441.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
435.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
388.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))

prune2.0s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.4b	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
0.3b	(* n (* 2 PI))
0.3b	(* n (* 2 PI))

rewrite84.0ms

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`

Counts

4 → 222

Calls

4 calls:

Slowest

26.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
18.0ms	(* n (* 2 PI))
17.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
14.0ms	(* n (* 2 PI))

series456.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

186.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
183.0ms	(pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2))
48.0ms	(* n (* 2 PI))
39.0ms	(* n (* 2 PI))

simplify13.8s

Counts

184 → 234

Calls

184 calls:

Slowest

485.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
452.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* -2 PI)) (log (/ -1 n))))))
410.0ms	(exp (* 1/4 (* (- 1 k) (- (log (* 2 PI)) (log (/ 1 n))))))
389.0ms	(* (* (* n n) n) (* (* (* 2 PI) (* 2 PI)) (* 2 PI)))
379.0ms	(pow n (/ (/ (- 1 k) 2) 2))

prune3.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes117.0ms

Accuracy

0% (0.4b remaining)

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

bsearch2.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.5s	20909×	body	80	nan
2.4s	11896×	body	80	valid
1.0ms	2×	body	160	nan