Details

sample75.0ms

Algorithm

intervals

Results

29.0ms	593×	body	80	nan
22.0ms	358×	body	80	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	29	16
2	57	16
3	113	16
4	291	16
5	803	16
6	3027	16
done	5000	16

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite42.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 157

Calls

4 calls:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
6.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series527.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.2s

Counts

169 → 169

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	369	2880
1	974	2712
2	3328	2538
done	5000	2523

prune446.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-exp-log`
23×	`add-sqr-sqrt` `*-un-lft-identity`
21×	`times-frac`
19×	`pow-unpow`
17×	`add-cube-cbrt`
14×	`pow1` `prod-exp`
13×	`add-cbrt-cube`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `sqrt-prod`
4×	`cbrt-unprod`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`cbrt-undiv` `pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `associate-l` `clear-num` `-commutative` `associate-/l/` `associate-/l*` `sqr-pow`

Counts

3 → 92

Calls

3 calls:

7.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
7.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series465.0ms

Counts

3 → 9

Calls

3 calls:

290.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
31.0ms	(* (* 2.0 PI) n)
143.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify929.0ms

Counts

101 → 101

Iterations

Useful iterations: done (926.0ms)

Iter	Nodes	Cost
0	270	1898
1	733	1762
2	2540	1596
done	5000	1586

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
0.2b	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-exp-log`
78×	`times-frac`
48×	`add-sqr-sqrt` `*-un-lft-identity`
42×	`add-cube-cbrt`
38×	`div-exp` `prod-exp`
23×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`sqrt-prod`
16×	`pow1`
15×	`pow-exp`
12×	`associate-/r*`
9×	`associate-/l*`
7×	`cbrt-undiv` `rec-exp` `1-exp` `div-inv`
6×	`div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp` `associate-*r/` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`unpow-prod-down` `pow-flip` `associate-l` `*-commutative` `inv-pow` `sqr-pow`

Counts

4 → 178

Calls

4 calls:

14.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
7.0ms	(/ (sqrt k) (* 1.0 (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))

series918.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
420.0ms	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
31.0ms	(* (* 2.0 PI) n)
143.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify1.7s

Counts

190 → 190

Iterations

Useful iterations: 2 (740.0ms)

Iter	Nodes	Cost
0	474	4443
1	1290	4049
2	4275	3673
done	5000	3673

prune385.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(/ 1.0 (sqrt (sqrt k)))
0.2b	(* (* 2.0 PI) n)
0.9b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

4409×	`times-frac`
2853×	`sqrt-prod`
1811×	`add-sqr-sqrt` `*-un-lft-identity`
1805×	`add-cube-cbrt`
289×	`unpow-prod-down` `sqr-pow`
86×	`div-inv`
61×	`add-exp-log`
59×	`associate-/r*`
34×	`associate-/l*`
33×	`div-sub` `associate-/r/` `pow-sub`
29×	`div-exp`
23×	`add-cbrt-cube`
19×	`pow-unpow`
15×	`pow1`
12×	`prod-exp`
9×	`cbrt-undiv` `pow-exp`
6×	`pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`associate-l` `*-commutative` `associate-/l/`

Counts

4 → 1772

Calls

4 calls:

54.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
4.0ms	(/ 1.0 (sqrt (sqrt k)))
6.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series647.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (/ (sqrt (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
156.0ms	(/ 1.0 (sqrt (sqrt k)))
31.0ms	(* (* 2.0 PI) n)
137.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify790.0ms

Counts

1784 → 1784

Iterations

Useful iterations: done (675.0ms)

Iter	Nodes	Cost
0	2004	80350
done	5000	80335

prune6.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes109.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	17	21
done	17	21

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.1s	20329×	body	80	nan
720.0ms	11817×	body	80	valid
0.0ms	2×	body	160	nan