Details

sample89.0ms

Algorithm

intervals

Results

35.0ms	744×	body	80	nan
22.0ms	383×	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	1044	8
5	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 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))
1.2b	(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×	`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:

38.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
16.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series513.0ms

Counts

4 → 12

Calls

4 calls:

310.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
38.0ms	(/ 1.0 (sqrt k))
133.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify97.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (83.0ms)

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

prune447.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
0.3b	(/ 1.0 (sqrt k))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
1.1b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

222×	`times-frac`
157×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
122×	`pow-unpow`
117×	`add-cube-cbrt`
88×	`add-exp-log`
61×	`prod-exp`
36×	`pow-exp`
18×	`distribute-lft-out--` `difference-of-squares`
16×	`pow1`
12×	`pow-to-exp` `div-sub` `sqrt-prod`
10×	`sqr-pow`
9×	`div-inv`
8×	`add-cbrt-cube`
7×	`pow-prod-down`
6×	`unpow-prod-down` `pow-pow` `associate-/r*` `pow-sub`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-/l*`
1×	`cbrt-undiv` `pow2` `frac-times` `frac-2neg` `associate-r/` `div-exp` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 263

Calls

4 calls:

42.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
6.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
26.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series497.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
39.0ms	(/ 1.0 (sqrt k))
133.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
140.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify101.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	1001	2614
1	3960	2403
2	5002	2356

prune821.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.2b	(/ 1.0 (sqrt (sqrt k)))
0.4b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
1.2b	(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` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `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 → 447

Calls

4 calls:

16.0ms	(* (* 2.0 PI) n)
7.0ms	(/ 1.0 (sqrt (sqrt k)))
26.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series377.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (* 2.0 PI) n)
165.0ms	(/ 1.0 (sqrt (sqrt k)))
41.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1355	5833
1	5001	5050

prune777.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
0.3b	(/ 1.0 (sqrt k))
0.5b	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
1.1b	(pow n (/ (- 1.0 k) 2.0))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-sqr-sqrt`
70×	`times-frac`
64×	`*-un-lft-identity`
52×	`add-cube-cbrt`
38×	`pow-unpow`
30×	`add-exp-log`
23×	`sqrt-prod`
22×	`associate-l`
11×	`prod-exp` `add-cbrt-cube`
8×	`pow1`
7×	`pow-exp`
6×	`associate-/r*` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down` `div-exp` `associate-r`
4×	`expm1-log1p-u` `pow-to-exp` `div-sub` `log1p-expm1-u` `div-inv` `pow-sub` `add-log-exp`
3×	`pow-pow` `associate-/l*`
2×	`cbrt-undiv` `cbrt-unprod`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 169

Calls

4 calls:

31.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
6.0ms	(/ 1.0 (sqrt k))
10.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
7.0ms	(pow n (/ (- 1.0 k) 2.0))

series446.0ms

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
40.0ms	(/ 1.0 (sqrt k))
74.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))
62.0ms	(pow n (/ (- 1.0 k) 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	844	1367
1	3255	1284
2	5002	1267

prune521.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

regimes133.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	20959×	body	80	nan
685.0ms	11810×	body	80	valid
0.0ms	3×	body	160	nan