Details

sample136.0ms

Algorithm

intervals

Results

45.0ms	752×	body	80	nan
21.0ms	62×	body	1280	nan
20.0ms	329×	body	80	valid
15.0ms	60×	body	640	nan
6.0ms	32×	body	320	nan
1.0ms	12×	body	160	nan

simplify37.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 1

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

rewrite40.0ms

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

series533.0ms

Counts

4 → 12

Calls

4 calls:

322.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
30.0ms	(* (* 2.0 PI) n)
142.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
38.0ms	(/ 1.0 (sqrt k))

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	981	1502
1	4021	1398
2	5001	1383

prune437.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	13	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Merged error: 0.0b

Counts

170 → 13

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)

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))
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:

260.0ms	(pow (* (* 2.0 PI) n) (/ 1.0 2.0))
879.0ms	(/ (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
30.0ms	(* (* 2.0 PI) n)
36.0ms	(* (* 2.0 PI) n)

simplify103.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (88.0ms)

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

prune274.0ms

Filtered

138 candidates to 67 candidates (48.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Merged error: 0b

Counts

151 → 12

localize19.0ms

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)
6.0ms	(* (* 2.0 PI) n)

series1.1s

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0))))
886.0ms	(* (* 1.0 (pow (* (* 2.0 PI) n) (/ 1.0 2.0))) (/ 1 (* (sqrt k) (pow (* (* 2.0 PI) n) (/ k 2.0)))))
31.0ms	(* (* 2.0 PI) n)
31.0ms	(* (* 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

prune288.0ms

Filtered

234 candidates to 70 candidates (29.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	234	12	246

Merged error: 0b

Counts

246 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
45×	`add-exp-log`
40×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-l`
23×	`sqrt-prod`
22×	`prod-exp`
21×	`add-cbrt-cube`
14×	`pow1`
11×	`associate-r`
8×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `pow-exp` `associate-/r*` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow-to-exp` `div-inv`
1×	`unpow-prod-down` `frac-2neg` `associate-*l/` `clear-num`

Counts

4 → 137

Calls

4 calls:

5.0ms	(* (* 2.0 PI) n)
5.0ms	(* (* 2.0 PI) n)
4.0ms	(/ 1.0 (sqrt k))
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

series727.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 2.0 PI) n)
30.0ms	(* (* 2.0 PI) n)
43.0ms	(/ 1.0 (sqrt k))
617.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ 1.0 2.0)))

simplify72.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	608	1054
1	2498	949
2	5001	932

prune331.0ms

Filtered

149 candidates to 101 candidates (67.8%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	149	12	161

Merged error: 0b

Counts

161 → 12

regimes187.0ms

Accuracy

0% (0.4b 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	19	12
1	19	12

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	26647×	body	80	nan
666.0ms	1935×	body	1280	nan
646.0ms	10653×	body	80	valid
434.0ms	1636×	body	640	nan
143.0ms	773×	body	320	nan
52.0ms	429×	body	160	nan