Details

sample72.0ms

Algorithm

intervals

Results

29.0ms	605×	body	80	nan
20.0ms	346×	body	80	valid

simplify36.0ms

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: 0.4b

localize12.0ms

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

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×	`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:

11.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)
13.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series530.0ms

Counts

4 → 12

Calls

4 calls:

321.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
37.0ms	(/ 1.0 (sqrt k))
36.0ms	(* (* 2.0 PI) n)
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (81.0ms)

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

prune416.0ms

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	(* (* 2.0 PI) n)
0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.9b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

204×	`times-frac`
143×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
122×	`pow-unpow`
103×	`add-cube-cbrt`
91×	`add-exp-log`
64×	`prod-exp`
36×	`pow-exp`
21×	`pow1`
18×	`distribute-lft-out--` `difference-of-squares`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`pow-prod-down` `sqr-pow`
8×	`associate-r` `div-inv`
6×	`unpow-prod-down` `pow-pow` `associate-l` `pow-sub`
5×	`swap-sqr`
4×	`cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`*-commutative`
1×	`pow2` `frac-times` `associate-r/` `associate-l/` `pow-sqr` `pow-prod-up`

Counts

4 → 234

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
10.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
14.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
14.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series508.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* 2.0 PI) n)
193.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
144.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
141.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify105.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	875	2384
1	3640	2189
2	5002	2154

prune739.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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:

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

series256.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt k))
43.0ms	(/ 1.0 (sqrt k))
31.0ms	(* (* 2.0 PI) n)
144.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	563	883
1	2197	815
2	5001	791

prune428.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))))
0.6b	(cbrt k)
0.6b	(cbrt k)
2.0b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
53×	`add-sqr-sqrt`
48×	`times-frac`
42×	`*-un-lft-identity`
36×	`add-cube-cbrt`
35×	`prod-exp`
31×	`associate-r`
25×	`add-cbrt-cube`
22×	`div-exp`
20×	`sqrt-prod`
19×	`pow-unpow`
16×	`cbrt-prod`
12×	`pow1` `1-exp`
8×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-l`
6×	`rec-exp`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
3×	`pow-pow` `pow-exp` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`frac-times` `pow-to-exp` `unpow-prod-down` `div-sub` `associate-r/` `associate-l/` `*-commutative` `pow-sub` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

22.0ms	(* (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series775.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(* (/ 1 (* (fabs (cbrt k)) 1)) (/ 1.0 (sqrt (cbrt k))))
178.0ms	(cbrt k)
186.0ms	(cbrt k)
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	888	1243
1	3654	1065
2	5001	1044

prune697.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

regimes112.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	16
1	19	16

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.0s	20218×	body	80	nan
697.0ms	11772×	body	80	valid
0.0ms	5×	body	160	nan