Details

sample82.0ms

Algorithm

intervals

Results

34.0ms	621×	body	80	nan
25.0ms	344×	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	1044	8
5	5001	8

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

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

rewrite46.0ms

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:

21.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
7.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series544.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
44.0ms	(/ 1.0 (sqrt k))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5003	1383

prune462.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 140

Calls

4 calls:

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

series260.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
38.0ms	(/ 1.0 (sqrt k))
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	579	912
1	2248	843
2	5001	807

prune479.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
0.6b	(cbrt k)
0.6b	(cbrt k)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
133×	`add-sqr-sqrt` `*-un-lft-identity`
127×	`add-cube-cbrt`
84×	`sqrt-prod`
48×	`cbrt-prod`
19×	`pow-unpow`
15×	`add-exp-log`
13×	`associate-/l*`
12×	`div-inv`
10×	`pow1`
9×	`associate-/r*` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-pow` `div-exp` `pow-prod-down` `pow-exp` `prod-exp` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3`
1×	`pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `clear-num` `associate-/l/` `pow-sub` `sqr-pow`

Counts

4 → 220

Calls

4 calls:

9.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
0.0ms	(cbrt k)
0.0ms	(cbrt k)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series773.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(/ (/ 1.0 (fabs (cbrt k))) (sqrt (cbrt k)))
173.0ms	(cbrt k)
179.0ms	(cbrt k)
146.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify87.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	929	2689
1	3525	2585
2	5001	2527

prune962.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
0.2b	(/ 1.0 (sqrt k))
0.5b	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

200×	`sqrt-prod`
173×	`add-sqr-sqrt`
151×	`times-frac`
109×	`*-un-lft-identity`
103×	`add-cube-cbrt`
33×	`swap-sqr`
25×	`pow1` `associate-r` `associate-l`
19×	`pow-unpow`
16×	`add-exp-log` `unswap-sqr`
12×	`associate-/r*`
10×	`add-cbrt-cube`
8×	`sqrt-pow1` `pow1/2`
7×	`div-inv`
6×	`pow-prod-down` `associate-/l*`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `sqrt-div` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `pow-exp` `pow-sqr` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-to-exp` `unpow-prod-down` `pow-plus` `sqrt-unprod` `div-sub` `associate-r/` `associate-l/` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `pow-sub` `sqr-pow`

Counts

4 → 249

Calls

4 calls:

3.0ms	(/ 1.0 (sqrt k))
3.0ms	(/ 1.0 (sqrt k))
38.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series331.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ 1.0 (sqrt k))
46.0ms	(/ 1.0 (sqrt k))
99.0ms	(* (sqrt (/ 1.0 (sqrt k))) (sqrt (/ 1.0 (sqrt k))))
149.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify100.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	769	1839
1	3492	1677
2	5001	1651

prune680.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes158.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	9
1	18	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.2s	20976×	body	80	nan
781.0ms	11978×	body	80	valid