Details

sample153.0ms

Algorithm

intervals

Results

46.0ms	770×	body	80	nan
27.0ms	345×	body	80	valid
23.0ms	61×	body	1280	nan
17.0ms	60×	body	640	nan
5.0ms	23×	body	320	nan
1.0ms	7×	body	160	nan

simplify42.0ms

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 (100.0%)

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

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

135×	`add-sqr-sqrt`
68×	`*-un-lft-identity`
67×	`associate-l`
62×	`add-cube-cbrt`
61×	`times-frac`
53×	`unpow-prod-down`
46×	`add-exp-log`
44×	`associate-r`
36×	`unswap-sqr`
32×	`sqrt-prod`
22×	`prod-exp`
19×	`pow-unpow`
18×	`associate-/r*`
17×	`pow1`
16×	`add-cbrt-cube`
14×	`div-sub` `pow-sub`
12×	`frac-times` `associate-*l/`
9×	`pow-exp` `associate-/l*`
7×	`pow-prod-down` `*-commutative`
6×	`div-exp`
5×	`cbrt-unprod` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `frac-2neg` `clear-num` `div-inv` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv`
1×	`associate-*r/`

Counts

4 → 244

Calls

4 calls:

17.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
5.0ms	(/ 1.0 (sqrt k))
8.0ms	(* (* 2.0 PI) n)
34.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

series609.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
48.0ms	(/ 1.0 (sqrt k))
34.0ms	(* (* 2.0 PI) n)
368.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1272	2375
1	5001	2269

prune564.0ms

Filtered

256 candidates to 178 candidates (30.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	246	10	256
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	247	10	257

Merged error: 0.0b

Counts

257 → 10

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

418×	`add-sqr-sqrt`
244×	`unswap-sqr`
134×	`unpow-prod-down`
126×	`add-exp-log`
103×	`sqrt-prod`
99×	`associate-l`
86×	`prod-exp`
78×	`times-frac`
52×	`div-sub` `associate-r` `pow-sub`
49×	`frac-times` `associate-*l/`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`sqr-pow`
34×	`pow-exp`
24×	`associate-/r*`
17×	`pow-to-exp`
16×	`div-exp`
15×	`add-cbrt-cube`
13×	`pow1`
12×	`associate-/l*`
6×	`cbrt-unprod`
5×	`*-commutative`
4×	`expm1-log1p-u` `frac-2neg` `pow-prod-down` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`associate-*r/`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `div-inv`

Counts

4 → 318

Calls

4 calls:

73.0ms	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (sqrt PI)) (/ (- 1.0 k) 2.0))) (pow (* (sqrt PI) n) (/ (- 1.0 k) 2.0)))
5.0ms	(* (sqrt PI) n)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series1.1s

Counts

4 → 8

Calls

4 calls:

1.0s	(* (* (/ 1.0 (sqrt k)) (pow (* 2.0 (sqrt PI)) (/ (- 1.0 k) 2.0))) (pow (* (sqrt PI) n) (/ (- 1.0 k) 2.0)))
61.0ms	(* (sqrt PI) n)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify85.0ms

Algorithm

egg-herbie

Counts

326 → 326

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1491	6334
1	5002	6218

prune947.0ms

Filtered

326 candidates to 188 candidates (42.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	320	6	326
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	327	9	336

Merged error: 0b

Counts

336 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

322×	`add-sqr-sqrt`
207×	`unpow-prod-down`
178×	`associate-r`
170×	`times-frac`
158×	`sqrt-prod`
117×	`unswap-sqr`
100×	`*-un-lft-identity`
99×	`add-cube-cbrt`
62×	`add-exp-log`
56×	`associate-l`
41×	`associate-/l*`
33×	`div-sub` `pow-sub`
30×	`frac-times` `associate-*r/` `prod-exp` `sqr-pow`
18×	`pow-exp`
16×	`div-exp`
12×	`associate-/r*`
11×	`*-commutative` `add-cbrt-cube`
10×	`pow1`
9×	`pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `cbrt-unprod`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `un-div-inv` `associate-/l/`
1×	`cbrt-undiv` `associate-*l/` `div-inv`

Counts

4 → 349

Calls

4 calls:

92.0ms	(* (pow (* (sqrt PI) n) (/ (- 1.0 k) 2.0)) (/ (pow (* 2.0 (sqrt PI)) (/ (- 1.0 k) 2.0)) (sqrt k)))
5.0ms	(* (sqrt PI) n)
3.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series924.0ms

Counts

4 → 8

Calls

4 calls:

863.0ms	(* (pow (* (sqrt PI) n) (/ (- 1.0 k) 2.0)) (/ (pow (* 2.0 (sqrt PI)) (/ (- 1.0 k) 2.0)) (sqrt k)))
61.0ms	(* (sqrt PI) n)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify101.0ms

Algorithm

egg-herbie

Counts

357 → 357

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1621	5977
1	5002	5822

prune787.0ms

Filtered

357 candidates to 191 candidates (46.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	353	4	357
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	359	7	366

Merged error: 0b

Counts

366 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) n)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
6×	`add-exp-log` `associate-l` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r`
2×	`unswap-sqr`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 69

Calls

4 calls:

5.0ms	(* (sqrt PI) n)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)

series56.0ms

Counts

4 → 6

Calls

4 calls:

56.0ms	(* (sqrt PI) n)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify57.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	101	219
1	302	215
2	726	212
3	1724	212
4	5002	212

prune220.0ms

Filtered

75 candidates to 53 candidates (29.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Merged error: 0b

Counts

82 → 7

regimes112.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	18
1	24	18

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	26200×	body	80	nan
729.0ms	1958×	body	1280	nan
703.0ms	10649×	body	80	valid
471.0ms	1663×	body	640	nan
163.0ms	823×	body	320	nan
55.0ms	422×	body	160	nan