Details

sample140.0ms

Algorithm

intervals

Results

50.0ms	839×	body	80	nan
21.0ms	331×	body	80	valid
21.0ms	60×	body	1280	nan
10.0ms	37×	body	640	nan
5.0ms	27×	body	320	nan
2.0ms	14×	body	160	nan

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

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

localize20.0ms

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

12.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
9.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
5.0ms	(* (* 2.0 PI) n)

series557.0ms

Counts

4 → 12

Calls

4 calls:

337.0ms	(* (/ 1.0 (sqrt k)) (pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0)))
141.0ms	(pow (* (* 2.0 PI) n) (/ (- 1.0 k) 2.0))
45.0ms	(/ 1.0 (sqrt k))
33.0ms	(* (* 2.0 PI) n)

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	981	1502
1	4022	1398
2	5002	1383

prune660.0ms

Filtered

169 candidates to 119 candidates (70.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	160	9	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	161	9	170

Merged error: 0.0b

Counts

170 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
0.3b	(/ 1.0 (sqrt k))
0.3b	(* (* 2.0 PI) (sqrt n))
0.4b	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`times-frac`
32×	`add-cube-cbrt`
30×	`add-exp-log`
28×	`pow1`
20×	`add-cbrt-cube`
19×	`pow-unpow`
18×	`sqrt-prod`
15×	`pow-prod-down` `prod-exp`
12×	`associate-r`
9×	`cbrt-unprod`
6×	`associate-/r*`
4×	`expm1-log1p-u` `pow-pow` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
2×	`associate-l` `*-commutative` `div-inv`
1×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `frac-2neg` `div-sub` `div-exp` `clear-num` `pow-sub` `sqr-pow`

Counts

4 → 130

Calls

4 calls:

13.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) (sqrt n))
10.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

series364.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(pow (* (* (* 2.0 PI) (sqrt n)) (sqrt n)) (/ (- 1.0 k) 2.0))
43.0ms	(/ 1.0 (sqrt k))
72.0ms	(* (* 2.0 PI) (sqrt n))
50.0ms	(* (* (* 2.0 PI) (sqrt n)) (sqrt n))

simplify82.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	755	1027
1	3088	876
2	5001	848

prune385.0ms

Filtered

142 candidates to 92 candidates (64.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	142	9	151

Merged error: 0.0b

Counts

151 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

154×	`add-exp-log`
107×	`prod-exp`
48×	`add-sqr-sqrt`
42×	`pow-exp`
38×	`add-cube-cbrt` `*-un-lft-identity`
36×	`times-frac`
29×	`sqrt-prod`
28×	`associate-l`
25×	`add-cbrt-cube`
24×	`pow-to-exp`
17×	`div-exp` `associate-r`
12×	`div-sub` `pow-sub`
11×	`pow1` `unpow-prod-down`
10×	`cbrt-unprod`
8×	`unswap-sqr` `sqr-pow`
6×	`frac-times` `associate-r/` `associate-/r`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `clear-num`

Counts

4 → 194

Calls

4 calls:

18.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0))))
10.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)))
4.0ms	(/ 1.0 (sqrt k))
6.0ms	(* (* 2.0 PI) (sqrt n))

series1.5s

Counts

4 → 12

Calls

4 calls:

736.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0))))
612.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ (- 1.0 k) 2.0)) (pow (sqrt n) (/ (- 1.0 k) 2.0)))
39.0ms	(/ 1.0 (sqrt k))
80.0ms	(* (* 2.0 PI) (sqrt n))

simplify62.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1315	2870
1	5001	2559

prune575.0ms

Filtered

206 candidates to 118 candidates (57.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	206	9	215

Merged error: 0.0b

Counts

215 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 2.0 PI) (sqrt n))
0.3b	(* (* 2.0 PI) (sqrt n))
0.4b	(* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0)))
0.4b	(* (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

157×	`add-exp-log`
110×	`prod-exp`
42×	`pow-exp`
35×	`add-sqr-sqrt`
29×	`associate-l`
28×	`add-cbrt-cube`
25×	`add-cube-cbrt` `*-un-lft-identity`
24×	`pow-to-exp`
23×	`associate-r`
20×	`sqrt-prod`
18×	`times-frac`
16×	`pow1` `div-exp`
13×	`cbrt-unprod`
11×	`unpow-prod-down`
8×	`pow-prod-down` `unswap-sqr` `sqr-pow`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv`
1×	`associate-*l/` `div-inv`

Counts

4 → 167

Calls

4 calls:

6.0ms	(* (* 2.0 PI) (sqrt n))
7.0ms	(* (* 2.0 PI) (sqrt n))
9.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0)))
18.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0))))

series1.5s

Counts

4 → 12

Calls

4 calls:

82.0ms	(* (* 2.0 PI) (sqrt n))
74.0ms	(* (* 2.0 PI) (sqrt n))
746.0ms	(* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0)))
609.0ms	(* (/ 1.0 (sqrt k)) (* (pow (* (* 2.0 PI) (sqrt n)) (/ 1.0 2.0)) (pow (sqrt n) (/ 1.0 2.0))))

simplify106.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	839	2023
1	3359	1774
2	5001	1761

prune520.0ms

Filtered

179 candidates to 94 candidates (52.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	180	8	188

Merged error: 0b

Counts

188 → 8

regimes186.0ms

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	25	22
1	25	22

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.6s	27711×	body	80	nan
714.0ms	1985×	body	1280	nan
664.0ms	10671×	body	80	valid
442.0ms	1657×	body	640	nan
174.0ms	909×	body	320	nan
50.0ms	441×	body	160	nan