Details

sample243.0ms

Algorithm

intervals

Results

140.0ms	643×	body	80	nan
69.0ms	383×	body	80	valid

simplify301.0ms

Calls

1 calls:

Slowest

300.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite148.0ms

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×	`expm1-log1p-u` `pow-pow` `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-/l/`

Calls

3 calls:

Slowest

77.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
35.0ms	(* n (* 2 PI))
30.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))

series544.0ms

Calls

3 calls:

Slowest

325.0ms	(/ (pow (* n (* 2 PI)) (/ (- 1 k) 2)) (sqrt k))
175.0ms	(pow (* n (* 2 PI)) (/ (- 1 k) 2))
44.0ms	(* n (* 2 PI))

simplify2.5m

Calls

431 calls:

Slowest

993.0ms	(/ (pow (* (cbrt (* n (* 2 PI))) (cbrt (* n (* 2 PI)))) (/ (- 1 k) 2)) 1)
890.0ms	(/ (pow (* (cbrt n) (* 2 PI)) (/ (- 1 k) 2)) (sqrt (sqrt k)))
882.0ms	(/ (pow (* n (* 2 PI)) (/ (/ (- 1 k) 2) 2)) (sqrt 1))
851.0ms	(/ (pow PI (/ (- 1 k) 2)) (cbrt (sqrt k)))
773.0ms	(/ (pow (* n (* (cbrt (* 2 PI)) (cbrt (* 2 PI)))) (/ (- 1 k) 2)) (sqrt (sqrt k)))

prune3.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow (* n (sqrt 2)) (/ (- 1 k) 2))
0.5b	(* n (sqrt 2))
0.2b	(/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k))
0.2b	(* (/ (pow (* n (sqrt 2)) (/ (- 1 k) 2)) 1) (/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k)))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

1355×	`add-sqr-sqrt`
1348×	`unpow-prod-down`
1201×	`associate-/l*`
810×	`frac-times`
652×	`*-un-lft-identity`
614×	`sqrt-prod`
587×	`add-cube-cbrt`
538×	`times-frac`
463×	`associate-r`
418×	`associate-l`
363×	`unswap-sqr`
267×	`associate-/r*`
163×	`add-exp-log`
120×	`sqr-pow`
80×	`div-exp`
78×	`*-commutative`
67×	`prod-exp`
61×	`clear-num` `div-sub` `pow-sub`
60×	`frac-2neg` `associate-/l/`
42×	`pow-exp`
30×	`associate-*r/`
27×	`associate-*l/`
22×	`pow-unpow`
21×	`pow-to-exp`
20×	`add-cbrt-cube` `1-exp`
11×	`pow1`
6×	`difference-of-squares`
5×	`cbrt-undiv` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`pow-pow` `un-div-inv`

Calls

4 calls:

Slowest

203.0ms	(* (/ (pow (* n (sqrt 2)) (/ (- 1 k) 2)) 1) (/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k)))
52.0ms	(/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k))
26.0ms	(pow (* n (sqrt 2)) (/ (- 1 k) 2))
14.0ms	(* n (sqrt 2))

series1.5s

Calls

4 calls:

Slowest

931.0ms	(* (/ (pow (* n (sqrt 2)) (/ (- 1 k) 2)) 1) (/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k)))
293.0ms	(/ (pow (* (sqrt 2) PI) (/ (- 1 k) 2)) (sqrt k))
219.0ms	(pow (* n (sqrt 2)) (/ (- 1 k) 2))
42.0ms	(* n (sqrt 2))