Details

sample146.0ms

Algorithm

intervals

Results

50.0ms	870×	body	80	nan
22.0ms	67×	body	1280	nan
21.0ms	353×	body	80	valid
15.0ms	60×	body	640	nan
5.0ms	28×	body	320	nan
1.0ms	9×	body	160	nan

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	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

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

rewrite39.0ms

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:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (* 2.0 PI) n)
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))

series545.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
39.0ms	(/ 1.0 (sqrt k))

simplify100.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5001	1383

prune457.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
105×	`prod-exp`
39×	`pow-exp`
36×	`div-exp`
26×	`add-cbrt-cube`
20×	`pow1`
13×	`add-sqr-sqrt` `pow-to-exp` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
10×	`times-frac` `cbrt-unprod`
9×	`pow-prod-down`
6×	`associate-r`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `clear-num` `associate-/r` `associate-/l` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

series1.2s

Counts

4 → 12

Calls

4 calls:

259.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
897.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))

simplify101.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	935	1406
1	4012	1247
2	5001	1237

prune303.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
21×	`add-cbrt-cube`
14×	`pow1`
11×	`associate-r`
8×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 137

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))
503.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify70.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	608	1054
1	2498	949
2	5001	932

prune426.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))))
0.2b	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

678×	`add-exp-log`
390×	`prod-exp`
218×	`div-exp`
144×	`pow-exp`
48×	`pow-to-exp`
44×	`add-cbrt-cube`
37×	`rec-exp` `1-exp`
20×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`pow1`
14×	`cbrt-unprod`
13×	`cbrt-undiv`
6×	`associate-r` `pow-prod-down` `associate-/r*` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 249

Calls

4 calls:

13.0ms	(/ 1 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))))
15.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.7s

Counts

4 → 12

Calls

4 calls:

800.0ms	(/ 1 (/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))))
844.0ms	(/ (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))) (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))))
40.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)

simplify62.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1406	3861
1	5002	3567

prune369.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes116.0ms

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	19	12
1	19	12

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	26413×	body	80	nan
823.0ms	1947×	body	1280	nan
650.0ms	10597×	body	80	valid
426.0ms	1636×	body	640	nan
153.0ms	829×	body	320	nan
46.0ms	411×	body	160	nan