Details

sample91.0ms

Algorithm

intervals

Results

39.0ms	726×	body	80	nan
25.0ms	411×	body	80	valid

simplify39.0ms

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: 0.2b

localize17.0ms

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

rewrite95.0ms

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:

43.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
6.0ms	(/ 1.0 (sqrt k))
22.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series505.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms	(* (* 2.0 PI) n)
35.0ms	(/ 1.0 (sqrt k))
132.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (89.0ms)

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

prune671.0ms

Pruning

11 alts after pruning (11 fresh and 0 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	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite62.0ms

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:

14.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
18.0ms	(* (* 2.0 PI) n)
25.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series399.0ms

Counts

3 → 9

Calls

3 calls:

233.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
30.0ms	(* (* 2.0 PI) n)
135.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify81.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	718	1382
1	2833	1296
2	5001	1248

prune517.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
0.2b	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
0.2b	(* (* 2.0 PI) n)
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
143×	`add-sqr-sqrt` `*-un-lft-identity`
137×	`add-cube-cbrt`
78×	`sqrt-prod`
72×	`add-exp-log`
40×	`associate-/r*`
32×	`unpow-prod-down` `div-exp` `sqr-pow`
19×	`pow-unpow`
18×	`prod-exp`
16×	`pow1` `add-cbrt-cube`
15×	`pow-exp`
9×	`associate-/l*`
7×	`div-inv`
6×	`rec-exp` `1-exp` `div-sub` `pow-prod-down` `associate-/r/` `pow-sub`
5×	`pow-to-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `clear-num`
1×	`pow-flip` `associate-l` `*-commutative` `inv-pow`

Counts

4 → 296

Calls

4 calls:

29.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
13.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
18.0ms	(* (* 2.0 PI) n)
23.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series848.0ms

Counts

4 → 12

Calls

4 calls:

292.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
384.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1528	4369
1	5002	4116

prune1.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2.0 PI) n)
0.3b	(/ 1.0 (sqrt (sqrt k)))
0.3b	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
1.1b	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

rewrite109.0ms

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:

20.0ms	(* (* 2.0 PI) n)
8.0ms	(/ 1.0 (sqrt (sqrt k)))
26.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
26.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series371.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* 2.0 PI) n)
165.0ms	(/ 1.0 (sqrt (sqrt k)))
35.0ms	(/ (/ 1.0 (sqrt (sqrt k))) (sqrt (sqrt k)))
140.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

459 → 459

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1355	5833
1	5001	5050

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes104.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	20692×	body	80	nan
748.0ms	11916×	body	80	valid
0.0ms	3×	body	160	nan