Details

sample200.0ms

Algorithm

intervals

Results

106.0ms	640×	body	80	nan
63.0ms	373×	body	80	valid

simplify346.0ms

Calls

1 calls:

Slowest

346.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize20.0ms

Local error

Found 3 expressions with local error:

1.2b	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
0.3b	(* n (* 2 PI))
0.1b	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

190×	`add-sqr-sqrt`
176×	`unpow-prod-down`
174×	`times-frac`
135×	`associate-r`
127×	`*-un-lft-identity`
118×	`add-cube-cbrt`
81×	`sqrt-prod`
54×	`associate-l`
36×	`unswap-sqr`
26×	`add-exp-log` `associate-/l*`
22×	`pow-unpow`
18×	`*-commutative`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`sqr-pow`
6×	`associate-/r*` `pow-prod-down` `pow-exp` `difference-of-squares`
5×	`div-exp`
3×	`pow-pow` `cbrt-unprod` `insert-posit16` `distribute-lft-out--` `add-log-exp`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `associate-/l/`

Calls

3 calls:

Slowest

91.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
42.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
38.0ms	(* n (* 2 PI))

series552.0ms

Calls

3 calls:

Slowest

322.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
197.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
33.0ms	(* n (* 2 PI))

simplify2.4m

Calls

431 calls:

Slowest

881.0ms	(/ (pow (* (cbrt n) (cbrt n)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
846.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (cbrt (sqrt k)))
786.0ms	(/ (pow PI (/ (- 1 k) 2)) (sqrt k))
752.0ms	(/ (* (* (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)))
714.0ms	(/ (pow (* n (sqrt (* 2 PI))) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* (* (sqrt PI) 2) n) (/ (- 1 k) 2))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
0.3b	(* (* (sqrt PI) 2) n)

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
44×	`associate-l`
36×	`*-un-lft-identity`
27×	`unpow-prod-down` `add-cube-cbrt`
22×	`pow-unpow`
18×	`times-frac`
17×	`pow1`
16×	`sqrt-prod`
15×	`add-exp-log`
14×	`unswap-sqr`
12×	`associate-r`
9×	`add-cbrt-cube`
6×	`pow-prod-down` `prod-exp` `difference-of-squares`
4×	`*-commutative` `insert-posit16` `add-log-exp`
3×	`pow-pow` `pow-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `div-sub` `div-inv` `pow-sub` `sqr-pow`

Calls

4 calls:

Slowest

39.0ms	(pow (* (* (sqrt PI) 2) n) (/ (- 1 k) 2))
29.0ms	(* (* (sqrt PI) 2) n)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series394.0ms

Calls

4 calls:

Slowest

291.0ms	(pow (* (* (sqrt PI) 2) n) (/ (- 1 k) 2))
103.0ms	(* (* (sqrt PI) 2) n)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify10.1s

Calls

99 calls:

Slowest

705.0ms	(- (+ (* 1/4 (* (log n) (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2))))) (+ (* 1/8 (* (pow (log n) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (+ (* 1/8 (* (pow (log (* 2 (sqrt PI))) 2) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (pow k 2)))) (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n))))))) (+ (* 1/2 (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) (* (log n) k))) (* 1/2 (* (log (* 2 (sqrt PI))) (* (exp (* 1/2 (+ (log (* 2 (sqrt PI))) (log n)))) k)))))
538.0ms	(* (log (* (* (sqrt PI) 2) n)) (/ (- 1 k) 2))
536.0ms	(* (+ (log (* (sqrt PI) 2)) (log n)) (/ (- 1 k) 2))
412.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* 2 (sqrt PI))) (log (/ 1 n))))))
402.0ms	(exp (* 1/2 (* (- 1 k) (- (log (* -2 (sqrt PI))) (log (/ -1 n))))))

prune2.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (* n PI) (/ (- 1 k) 2))
0.3b	(* n PI)
0.2b	(/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
0.1b	(/ (pow (* n PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

1526×	`times-frac`
918×	`unpow-prod-down`
813×	`add-sqr-sqrt`
713×	`*-un-lft-identity`
704×	`add-cube-cbrt`
384×	`sqrt-prod`
159×	`sqr-pow`
150×	`associate-r` `associate-l`
61×	`associate-/r*`
54×	`add-exp-log`
50×	`*-commutative` `unswap-sqr`
34×	`associate-/r/`
31×	`div-exp`
28×	`associate-/l*`
22×	`pow-unpow`
20×	`div-sub` `div-inv` `pow-sub`
15×	`pow-exp`
13×	`add-cbrt-cube`
10×	`pow-to-exp`
9×	`pow1`
6×	`prod-exp` `difference-of-squares`
4×	`cbrt-undiv` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `distribute-lft-out--`
2×	`pow-pow` `pow-prod-down`
1×	`cbrt-unprod` `associate-/l/`

Calls

4 calls:

Slowest

65.0ms	(/ (pow (* n PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))
15.0ms	(/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
10.0ms	(pow (* n PI) (/ (- 1 k) 2))
5.0ms	(* n PI)

series988.0ms

Calls

4 calls:

Slowest

517.0ms	(/ (pow (* n PI) (/ (- 1 k) 2)) (/ (sqrt k) (pow 2 (/ (- 1 k) 2))))
304.0ms	(/ (sqrt k) (pow 2 (/ (- 1 k) 2)))
133.0ms	(pow (* n PI) (/ (- 1 k) 2))
33.0ms	(* n PI)