Details

sample90.0ms

Algorithm

intervals

Results

39.0ms	726×	body	80	nan
25.0ms	411×	body	80	valid

simplify37.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	8
1	59	8
2	119	8
3	325	8
4	1034	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

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))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite88.0ms

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:

40.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
17.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series481.0ms

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
29.0ms	(* (* 2.0 PI) n)
34.0ms	(/ 1.0 (sqrt k))
127.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify98.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	950	1461
1	3924	1358
2	5002	1344

prune593.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite63.0ms

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×	`pow-pow` `associate-r` `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 → 86

Calls

3 calls:

23.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
16.0ms	(* (* 2.0 PI) n)
21.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series425.0ms

Counts

3 → 9

Calls

3 calls:

266.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))) (sqrt k))
29.0ms	(* (* 2.0 PI) n)
130.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify83.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	709	938
1	2966	838
2	5002	830

prune367.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize14.0ms

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)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite102.0ms

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×	`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 → 170

Calls

4 calls:

35.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
18.0ms	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
19.0ms	(* (* 2.0 PI) n)
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series857.0ms

Counts

4 → 12

Calls

4 calls:

298.0ms	(/ 1 (/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))))
397.0ms	(/ (sqrt k) (* 1.0 (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
30.0ms	(* (* 2.0 PI) n)
132.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify48.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1268	2210
1	5002	1999

prune669.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite101.0ms

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:

17.0ms	(* (* 2.0 PI) n)
10.0ms	(/ 1.0 (sqrt (sqrt k)))
23.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series358.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (* 2.0 PI) n)
158.0ms	(/ 1.0 (sqrt (sqrt k)))
33.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
132.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

451 → 451

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1334	5795
1	5001	5011

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes105.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.3s	20692×	body	80	nan
760.0ms	11916×	body	80	valid
0.0ms	3×	body	160	nan