Details

sample145.0ms

Algorithm

intervals

Results

48.0ms	847×	body	80	nan
21.0ms	354×	body	80	valid
19.0ms	58×	body	640	nan
19.0ms	54×	body	1280	nan
4.0ms	22×	body	320	nan
2.0ms	21×	body	160	nan

simplify44.0ms

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: 0.4b

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))

rewrite36.0ms

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:

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))

series572.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
152.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
33.0ms	(* (* 2.0 PI) n)
47.0ms	(/ 1.0 (sqrt k))

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5002	1383

prune492.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(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)

rewrite34.0ms

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` `expm1-log1p-u` `log1p-expm1-u` `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 → 126

Calls

4 calls:

7.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
11.0ms	(/ (* 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)

series1.3s

Counts

4 → 12

Calls

4 calls:

273.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
938.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
33.0ms	(* (* 2.0 PI) n)
39.0ms	(* (* 2.0 PI) n)

simplify106.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	935	1406
1	4012	1247
2	5001	1237

prune331.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
0.2b	(* (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
0.3b	(* (* 2.0 PI) n)
0.3b	(* (* 2.0 PI) n)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

582×	`add-exp-log`
440×	`prod-exp`
120×	`pow-exp`
84×	`div-exp`
42×	`rec-exp` `1-exp`
40×	`pow-to-exp` `add-cbrt-cube`
18×	`cbrt-unprod`
17×	`pow1`
13×	`associate-r`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow-prod-down`
6×	`cbrt-undiv` `times-frac`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `-commutative` `associate-/l`
2×	`div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `clear-num` `associate-/r` `un-div-inv` `inv-pow`

Counts

4 → 222

Calls

4 calls:

8.0ms	(/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
15.0ms	(* (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)

series1.4s

Counts

4 → 12

Calls

4 calls:

199.0ms	(/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
1.1s	(* (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
34.0ms	(* (* 2.0 PI) n)
35.0ms	(* (* 2.0 PI) n)

simplify127.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1323	2960
1	4908	2698
2	5001	2698

prune339.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
38×	`add-sqr-sqrt` `*-un-lft-identity`
32×	`add-cube-cbrt`
26×	`add-exp-log`
19×	`pow-unpow`
18×	`sqrt-prod`
14×	`pow1`
10×	`add-cbrt-cube`
9×	`prod-exp`
8×	`unpow-prod-down` `sqr-pow`
6×	`pow-prod-down` `pow-exp` `associate-/r*`
5×	`div-exp` `associate-/l*`
3×	`expm1-log1p-u` `pow-pow` `associate-r` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
2×	`pow-to-exp` `div-sub` `div-inv` `pow-sub`
1×	`cbrt-undiv` `frac-2neg` `associate-l` `clear-num` `*-commutative` `associate-/l/`

Counts

3 → 118

Calls

3 calls:

7.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) n)

series434.0ms

Counts

3 → 9

Calls

3 calls:

254.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
147.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
33.0ms	(* (* 2.0 PI) n)

simplify77.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	718	1382
1	2834	1296
2	5002	1248

prune329.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes107.0ms

Accuracy

0% (0.4b 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	19	12
1	19	12

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.5s	26784×	body	80	nan
704.0ms	2025×	body	1280	nan
661.0ms	10556×	body	80	valid
446.0ms	1696×	body	640	nan
145.0ms	781×	body	320	nan
55.0ms	420×	body	160	nan