Details

sample79.0ms

Algorithm

intervals

Results

32.0ms	669×	body	80	nan
23.0ms	393×	body	80	valid

simplify37.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

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))

rewrite46.0ms

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:

18.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(* (* 2.0 PI) n)
3.0ms	(/ 1.0 (sqrt k))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series529.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
31.0ms	(* (* 2.0 PI) n)
37.0ms	(/ 1.0 (sqrt k))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify101.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (86.0ms)

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

prune448.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

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

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:

5.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
7.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series421.0ms

Counts

3 → 9

Calls

3 calls:

247.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt k))
31.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify78.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (64.0ms)

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

prune325.0ms

Filtered

127 candidates to 84 candidates (66.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

954×	`sqrt-prod`
951×	`times-frac`
448×	`add-sqr-sqrt` `*-un-lft-identity`
442×	`add-cube-cbrt`
101×	`unpow-prod-down` `sqr-pow`
54×	`associate-/l*`
46×	`add-exp-log`
19×	`pow-unpow`
18×	`associate-/r*`
16×	`div-exp` `add-cbrt-cube`
15×	`pow1`
13×	`div-inv`
12×	`prod-exp`
9×	`pow-exp`
6×	`pow-prod-down`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
2×	`frac-2neg` `div-sub` `clear-num` `associate-/l/` `pow-sub`
1×	`associate-l` `*-commutative`

Counts

4 → 656

Calls

4 calls:

7.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
24.0ms	(/ (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (sqrt (sqrt k)))
10.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series781.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k)))
242.0ms	(/ (/ (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)) (sqrt (sqrt k))) (sqrt (sqrt k)))
32.0ms	(* (* 2.0 PI) n)
286.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify148.0ms

Algorithm

egg-herbie

Counts

668 → 668

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1925	14121
1	5001	13025

prune1.0s

Filtered

668 candidates to 237 candidates (35.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize13.0ms

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

rewrite53.0ms

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:

17.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
5.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
7.0ms	(* (* 2.0 PI) n)
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

series897.0ms

Counts

4 → 12

Calls

4 calls:

314.0ms	(/ 1 (/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))))
407.0ms	(/ (sqrt k) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
36.0ms	(* (* 2.0 PI) n)
139.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1528	4369
1	5002	4116

prune689.0ms

Filtered

308 candidates to 172 candidates (55.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes112.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b 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

sample2.3s

Algorithm

intervals

Results

1.0s	20850×	body	80	nan
707.0ms	11994×	body	80	valid
0.0ms	4×	body	160	nan