Details

sample144.0ms

Algorithm

intervals

Results

47.0ms	847×	body	80	nan
25.0ms	354×	body	80	valid
19.0ms	54×	body	1280	nan
16.0ms	58×	body	640	nan
4.0ms	22×	body	320	nan
2.0ms	21×	body	160	nan

simplify39.0ms

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	1034	8
5	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.4b

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

rewrite35.0ms

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

series553.0ms

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
148.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
32.0ms	(* (* 2.0 PI) n)
45.0ms	(/ 1.0 (sqrt k))

simplify98.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	950	1461
1	3925	1358
2	5003	1344

prune429.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite32.0ms

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` `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 → 118

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
10.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.2s

Counts

4 → 12

Calls

4 calls:

270.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
907.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
32.0ms	(* (* 2.0 PI) n)
37.0ms	(* (* 2.0 PI) n)

simplify99.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	916	1358
1	3952	1199
2	5002	1199

prune284.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

236×	`add-exp-log`
118×	`prod-exp`
85×	`add-sqr-sqrt`
83×	`times-frac`
77×	`div-exp`
60×	`pow-exp`
45×	`add-cube-cbrt` `*-un-lft-identity`
35×	`associate-r`
28×	`add-cbrt-cube`
26×	`sqrt-prod`
24×	`associate-l`
22×	`sqr-pow`
20×	`pow-to-exp`
16×	`pow1`
15×	`unswap-sqr`
10×	`unpow-prod-down` `cbrt-unprod`
7×	`pow-prod-down`
6×	`associate-/r*`
5×	`cbrt-undiv`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num`

Counts

4 → 209

Calls

4 calls:

22.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))

series898.0ms

Counts

4 → 12

Calls

4 calls:

784.0ms	(* (/ 1.0 (sqrt k)) (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0))))
38.0ms	(* (* 2.0 PI) n)
32.0ms	(* (* 2.0 PI) n)
44.0ms	(/ 1.0 (sqrt k))

simplify57.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1271	2638
1	5001	2478

prune565.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
0.2b	(/ (* 1.0 (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt k))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

145×	`add-exp-log`
65×	`prod-exp`
52×	`div-exp`
33×	`pow-exp`
23×	`add-cbrt-cube`
20×	`pow1`
17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
15×	`times-frac`
13×	`pow-unpow`
11×	`pow-to-exp`
9×	`pow-prod-down`
8×	`cbrt-unprod`
6×	`associate-r` `associate-/r*` `sqrt-prod`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-pow`
2×	`associate-l` `*-commutative` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-r/` `clear-num` `associate-/l/` `associate-/l` `sqr-pow`

Counts

4 → 119

Calls

4 calls:

6.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
12.0ms	(/ (* 1.0 (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt k))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.3s

Counts

4 → 12

Calls

4 calls:

274.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
931.0ms	(/ (* 1.0 (/ (pow (* (* 2.0 PI) n) (/ 1.0 2.0)) (pow (* (* 2.0 PI) n) (/ k 2.0)))) (sqrt k))
38.0ms	(* (* 2.0 PI) n)
33.0ms	(* (* 2.0 PI) n)

simplify97.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	973	1335
1	3981	1188
2	5001	1156

prune293.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes123.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.5s	26784×	body	80	nan
724.0ms	2025×	body	1280	nan
662.0ms	10556×	body	80	valid
447.0ms	1696×	body	640	nan
295.0ms	781×	body	320	nan
47.0ms	420×	body	160	nan