Details

sample83.0ms

Algorithm

intervals

Results

37.0ms	649×	body	80	nan
23.0ms	396×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	114	16
4	300	16
5	849	16
6	3228	16
done	5001	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt`
55×	`times-frac`
49×	`*-un-lft-identity`
46×	`add-exp-log`
43×	`add-cube-cbrt`
23×	`associate-l` `sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
16×	`add-cbrt-cube`
15×	`pow1`
9×	`pow-exp`
8×	`associate-r`
6×	`div-exp` `pow-prod-down` `associate-/r*` `unswap-sqr`
5×	`cbrt-unprod` `sqr-pow`
4×	`add-log-exp`
3×	`pow-to-exp` `pow-pow` `div-sub` `div-inv` `associate-/l*` `distribute-lft-out--` `pow-sub` `difference-of-squares`
2×	`cbrt-undiv` `unpow-prod-down` `*-commutative`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 149

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))

series520.0ms

Counts

4 → 12

Calls

4 calls:

311.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
33.0ms	(* (* 2.0 PI) n)
134.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
42.0ms	(/ 1.0 (sqrt k))

simplify988.0ms

Counts

161 → 161

Iterations

Useful iterations: done (980.0ms)

Iter	Nodes	Cost
0	361	2800
1	956	2643
2	3447	2475
done	5001	2463

prune440.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
24×	`sqrt-prod`
19×	`add-exp-log` `pow-unpow`
15×	`pow1`
13×	`add-cbrt-cube`
12×	`associate-/r*`
6×	`pow-prod-down` `prod-exp` `associate-/l*`
4×	`add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 132

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
3.0ms	(/ 1.0 (sqrt k))
3.0ms	(/ 1.0 (sqrt k))

series246.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
37.0ms	(/ 1.0 (sqrt k))
41.0ms	(/ 1.0 (sqrt k))

simplify605.0ms

Counts

144 → 144

Iterations

Useful iterations: done (602.0ms)

Iter	Nodes	Cost
0	234	1642
1	573	1523
2	1924	1409
done	5000	1399

prune471.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.4b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

594×	`sqrt-prod`
591×	`times-frac`
328×	`add-sqr-sqrt` `*-un-lft-identity`
322×	`add-cube-cbrt`
34×	`associate-/l*`
22×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
6×	`pow-prod-down` `prod-exp`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`pow-pow` `associate-r` `pow-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-to-exp` `unpow-prod-down` `div-sub` `associate-l` `*-commutative` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 439

Calls

4 calls:

6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt (sqrt k)))
16.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
166.0ms	(/ 1.0 (sqrt (sqrt k)))
38.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))

simplify1.3s

Counts

451 → 451

Iterations

Useful iterations: 2 (399.0ms)

Iter	Nodes	Cost
0	558	8953
1	1346	7944
2	4263	7227
done	5000	7227

prune884.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.3b	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
0.3b	(/ 1.0 (sqrt k))
0.3b	(/ 1.0 (sqrt k))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
51×	`times-frac`
47×	`add-cube-cbrt`
28×	`sqrt-prod`
25×	`pow1`
24×	`sqrt-div`
19×	`pow-unpow`
17×	`frac-times` `div-sub` `pow-sub`
16×	`add-exp-log`
12×	`associate-/r*`
11×	`associate-r/` `associate-l/`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2`
6×	`pow-prod-down` `associate-/l*`
5×	`pow-prod-up`
4×	`swap-sqr` `associate-r` `associate-l` `prod-exp` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `pow-to-exp` `unpow-prod-down` `pow-plus` `sqrt-unprod` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 167

Calls

4 calls:

9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
57.0ms	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
3.0ms	(/ 1.0 (sqrt k))
3.0ms	(/ 1.0 (sqrt k))

series677.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
454.0ms	(* (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))) (sqrt (* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
38.0ms	(/ 1.0 (sqrt k))
43.0ms	(/ 1.0 (sqrt k))

simplify85.0ms

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	368	3823