Details

sample89.0ms

Algorithm

intervals

Results

35.0ms	650×	body	80	nan
22.0ms	372×	body	80	valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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:

0.2b	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.3b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite87.0ms

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:

36.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
19.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series511.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
36.0ms	(* (* 2.0 PI) n)
35.0ms	(/ 1.0 (sqrt k))
134.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify104.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

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

prune472.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (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))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite116.0ms

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:

41.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
9.0ms	(/ 1.0 (sqrt k))
24.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
25.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series492.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
42.0ms	(/ 1.0 (sqrt k))
131.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
132.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify107.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (82.0ms)

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

prune845.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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 (/ (sqrt k) 1.0))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
0.6b	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

342×	`times-frac`
217×	`add-sqr-sqrt`
213×	`*-un-lft-identity`
177×	`add-cube-cbrt`
122×	`pow-unpow`
97×	`add-exp-log`
61×	`prod-exp`
36×	`pow-exp` `sqrt-prod`
22×	`associate-/r*`
18×	`distribute-lft-out--` `difference-of-squares`
17×	`pow1`
13×	`div-inv`
12×	`pow-to-exp` `div-sub`
11×	`add-cbrt-cube`
10×	`sqr-pow`
7×	`div-exp` `pow-prod-down`
6×	`unpow-prod-down` `pow-pow` `pow-sub`
5×	`swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`pow2` `frac-times` `pow-flip` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `inv-pow`

Counts

4 → 336

Calls

4 calls:

43.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
12.0ms	(/ 1 (/ (sqrt k) 1.0))
24.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
28.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

series496.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(* (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)) (pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2)))
41.0ms	(/ 1 (/ (sqrt k) 1.0))
129.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))
142.0ms	(pow (* (* 2.0 PI) n) (/ (/ (- 1.0 k) 2.0) 2))

simplify59.0ms

Algorithm

egg-herbie

Counts

348 → 348

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1287	3308
1	5001	2995

prune1.0s

Pruning

10 alts after pruning (10 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	(/ 1.0 (sqrt k))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
0.6b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`times-frac`
38×	`add-cube-cbrt` `pow-unpow`
23×	`add-exp-log`
21×	`pow1`
12×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`pow-prod-down` `prod-exp`
6×	`pow-pow` `pow-exp` `associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod` `div-inv` `associate-/l*`
2×	`pow-to-exp` `unpow-prod-down` `div-sub` `pow-sub` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `associate-l` `clear-num` `*-commutative`

Counts

4 → 137

Calls

4 calls:

16.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
20.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series338.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 2.0 PI) n)
42.0ms	(/ 1.0 (sqrt k))
130.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
136.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	579	1002
1	2248	936
2	5001	903

prune469.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes197.0ms

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	13
1	19	13

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.0s	20324×	body	80	nan
712.0ms	11719×	body	80	valid
0.0ms	1×	body	160	nan