Details

sample143.0ms

Algorithm

intervals

Results

45.0ms	809×	body	80	nan
23.0ms	64×	body	1280	nan
20.0ms	325×	body	80	valid
16.0ms	59×	body	640	nan
8.0ms	24×	body	320	nan
2.0ms	17×	body	160	nan

simplify38.0ms

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

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: 0.4b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt k))
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)

rewrite37.0ms

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:

4.0ms	(/ 1.0 (sqrt k))
12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
10.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(* (* 2.0 PI) n)

series549.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
334.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
145.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
32.0ms	(* (* 2.0 PI) n)

simplify107.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5001	1383

prune510.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Merged error: 0.0b

Counts

170 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

110×	`add-exp-log`
68×	`prod-exp`
63×	`add-sqr-sqrt`
55×	`times-frac`
50×	`*-un-lft-identity`
44×	`add-cube-cbrt`
27×	`pow-exp`
23×	`associate-l` `sqrt-prod`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`pow-to-exp`
17×	`div-exp`
12×	`associate-r`
11×	`div-sub` `pow-sub`
7×	`pow1` `cbrt-unprod`
6×	`frac-times` `associate-l/` `associate-/r` `unswap-sqr` `sqr-pow`
5×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`pow-pow` `*-commutative`
1×	`frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 188

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
12.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
11.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
8.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

series988.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
576.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
295.0ms	(* (/ 1.0 (sqrt k)) (pow (* 2.0 PI) (/ (- 1.0 k) 2.0)))
79.0ms	(pow (* 2.0 PI) (/ (- 1.0 k) 2.0))

simplify139.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (111.0ms)

Iter	Nodes	Cost
0	1162	2113
1	4931	1915
2	5001	1887

prune773.0ms

Filtered

200 candidates to 127 candidates (63.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	202	8	210

Merged error: 0b

Counts

210 → 8

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

276×	`add-exp-log`
215×	`prod-exp`
70×	`pow-to-exp` `pow-exp`
51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
41×	`div-exp`
36×	`add-cbrt-cube`
33×	`div-sub` `pow-sub`
23×	`associate-l`
22×	`frac-times`
21×	`sqrt-prod`
19×	`pow-unpow`
17×	`cbrt-unprod`
16×	`associate-r/` `associate-l/`
8×	`associate-r`
7×	`pow1`
6×	`unpow-prod-down` `associate-/r*`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `pow-prod-down` `clear-num`

Counts

4 → 243

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
18.0ms	(* (* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
13.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt k))
858.0ms	(* (* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0)))) (pow n (/ (- 1.0 k) 2.0)))
554.0ms	(* (/ 1.0 (sqrt k)) (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))))
46.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify70.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1533	3387
1	5001	2977

prune691.0ms

Filtered

255 candidates to 138 candidates (54.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	255	8	263

Merged error: 0b

Counts

263 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

279×	`add-exp-log`
233×	`prod-exp`
85×	`pow-to-exp` `pow-exp`
51×	`times-frac`
50×	`add-sqr-sqrt` `*-un-lft-identity`
44×	`add-cube-cbrt`
37×	`div-sub` `pow-sub`
32×	`div-exp` `add-cbrt-cube`
23×	`associate-l`
22×	`frac-times`
21×	`sqrt-prod`
19×	`pow-unpow`
16×	`associate-r/` `associate-l/`
15×	`cbrt-unprod`
8×	`associate-r`
7×	`pow1`
6×	`unpow-prod-down` `associate-/r*`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `div-inv` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`*-commutative` `sqr-pow`
1×	`pow-pow` `frac-2neg` `clear-num`

Counts

4 → 252

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt k))
19.0ms	(* (/ 1.0 (sqrt k)) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))))
11.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
6.0ms	(pow PI (/ (- 1.0 k) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ 1.0 (sqrt k))
861.0ms	(* (/ 1.0 (sqrt k)) (* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0))))
411.0ms	(* (* (pow 2.0 (/ (- 1.0 k) 2.0)) (pow PI (/ (- 1.0 k) 2.0))) (pow n (/ (- 1.0 k) 2.0)))
47.0ms	(pow PI (/ (- 1.0 k) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1462	3555
1	5001	3061

prune710.0ms

Filtered

264 candidates to 138 candidates (52.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	263	1	264
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	264	8	272

Merged error: 0b

Counts

272 → 8

regimes135.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	14
1	18	14

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	27202×	body	80	nan
750.0ms	2044×	body	1280	nan
694.0ms	10624×	body	80	valid
474.0ms	1711×	body	640	nan
165.0ms	839×	body	320	nan
51.0ms	427×	body	160	nan