Fix duplicate solutions, overflow in maxsols and improve symmetry reduction for H48.

This commit fixes two bugs: - A bug that caused duplicates solutions for symmetric scrambles. - An overflow in the maxsols parameter for the H48 solver, which caused it to find much fewer solutions than existed. Moreover, the H48 solvers has been improved by reducing by symmetry not only from the starting position, but also up to the first 4 moves.
author: Sebastiano Tronto <sebastiano@tronto.net> 2025-11-23 16:16:31 +0100
committer: Sebastiano Tronto <sebastiano@tronto.net> 2025-11-24 16:32:11 +0100
commit: 147b0c3c4615c32478a4923242909b8ae5a30d03 (patch)
tree: 5294d9b3655031535085a5163c2c5b5cbe7413b1 /benchmarks/benchmarks.md
parent: 78ec0d22d927bc4287aa090469d5ba5f84e8780b (diff)
download: nissy-core-147b0c3c4615c32478a4923242909b8ae5a30d03.tar.gz
nissy-core-147b0c3c4615c32478a4923242909b8ae5a30d03.zip
1 files changed, 32 insertions, 32 deletions
diff --git a/benchmarks/benchmarks.md b/benchmarks/benchmarks.md
index f84ddb3..33e8288 100644
--- a/benchmarks/benchmarks.md
+++ b/benchmarks/benchmarks.md
@@ -71,9 +71,9 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  0.23  |  1.15  |  5.08  | 31.30  | 278.47  |
+|H48 h11 k2|56.1GiB |  0.23  |  1.15  |  5.08  | 31.30  |  53.67  |
 |vcube 404 |31.8GiB |  0.30  |  1.25  |  6.87  | 57.49  | 291.31  |
-|H48 h10 k2|28.1GiB |  0.34  |  1.80  |  7.77  |        |         |
+|H48 h10 k2|28.1GiB |  0.34  |  1.80  |  7.77  |        |  81.89  |
 |vcube 308 |21.2GiB |  0.20  |  1.11  |  6.92  |        |         |
 |H48 h9 k2 |14.1GiB |  0.42  |  2.84  | 12.86  |        |         |
 |vcube 208 | 7.3GiB |  0.57  |  4.41  | 20.75  |        |         |
@@ -86,9 +86,9 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB | 12.90  | 64.51  | 284.99 |1755.93 |15622.17 |
+|H48 h11 k2|56.1GiB | 12.90  | 64.51  | 284.99 |1755.93 | 3010.89 |
 |vcube 404 |31.8GiB |  9.54  | 39.75  | 218.47 |1828.18 | 9263.66 |
-|H48 h10 k2|28.1GiB |  9.55  | 50.58  | 218.34 |        |         |
+|H48 h10 k2|28.1GiB |  9.55  | 50.58  | 218.34 |        | 2301.11 |
 |vcube 308 |21.2GiB |  4.24  | 23.53  | 146.70 |        |         |
 |H48 h9 k2 |14.1GiB |  5.92  | 40.04  | 181.33 |        |         |
 |vcube 208 | 7.3GiB |  4.16  | 32.19  | 151.48 |        |         |
@@ -110,11 +110,11 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  0.06  |  0.31  |  1.31  |  7.96  |  77.81  |
+|H48 h11 k2|56.1GiB |  0.06  |  0.31  |  1.31  |  7.96  |  14.01  |
 |vcube 404 |31.8GiB |  0.10  |  0.38  |  1.88  | 16.98  |   (a)   |
-|H48 h10 k2|28.1GiB |  0.10  |  0.47  |  2.00  | 13.54  | 114.35  |
+|H48 h10 k2|28.1GiB |  0.10  |  0.47  |  2.00  | 13.54  |  21.96  |
 |vcube 308 |21.2GiB |  0.06  |  0.42  |  1.95  | 17.73  |   (a)   |
-|H48 h9 k2 |14.1GiB |  0.14  |  0.83  |  3.82  | 25.98  | 162.72  |
+|H48 h9 k2 |14.1GiB |  0.14  |  0.83  |  3.82  | 25.98  |  31.68  |
 |vcube 208 | 7.3GiB |  0.17  |  1.49  |  5.88  |        |   (a)   |
 |H48 h8 k2 | 7.1GiB |  0.27  |  2.02  |  7.94  |        |         |
 |H48 h7 k2 | 3.6GiB |  0.35  |  2.59  | 12.41  |        |         |
@@ -125,11 +125,11 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  3.37  | 17.39  | 73.49  | 446.56 | 4365.92 |
+|H48 h11 k2|56.1GiB |  3.37  | 17.39  | 73.49  | 446.56 |  785.96 |
 |vcube 404 |31.8GiB |  3.80  | 12.08  | 59.78  | 539.96 |   (a)   |
-|H48 h10 k2|28.1GiB |  2.81  | 13.21  | 56.20  | 380.47 | 3213.24 |
+|H48 h10 k2|28.1GiB |  2.81  | 13.21  | 56.20  | 380.47 |  617.08 |
 |vcube 308 |21.2GiB |  1.27  |  8.90  | 41.34  | 375.88 |   (a)   |
-|H48 h9 k2 |14.1GiB |  1.97  | 11.70  | 53.86  | 366.32 | 2294.35 |
+|H48 h9 k2 |14.1GiB |  1.97  | 11.70  | 53.86  | 366.32 |  446.69 |
 |vcube 208 | 7.3GiB |  1.24  | 10.88  | 42.92  |        |   (a)   |
 |H48 h8 k2 | 7.1GiB |  1.92  | 14.34  | 56.37  |        |         |
 |H48 h7 k2 | 3.6GiB |  1.26  |  9.32  | 44.68  |        |         |
@@ -152,11 +152,11 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  0.02  |  0.10  |  0.43  |  2.48  |  26.29  |
+|H48 h11 k2|56.1GiB |  0.02  |  0.10  |  0.43  |  2.48  |   5.67  |
 |vcube 404 |31.8GiB |  0.03  |  0.16  |  0.67  |  6.36  |   (a)   |
-|H48 h10 k2|28.1GiB |  0.03  |  0.16  |  0.74  |  4.43  |         |
+|H48 h10 k2|28.1GiB |  0.03  |  0.16  |  0.74  |  4.43  |   8.81  |
 |vcube 308 |21.2GiB |  0.04  |  0.22  |  0.89  |  9.53  |   (a)   |
-|H48 h9 k2 |14.1GiB |  0.04  |  0.26  |  1.18  |  8.31  |         |
+|H48 h9 k2 |14.1GiB |  0.04  |  0.26  |  1.18  |  8.31  |  13.20  |
 |vcube 208 | 7.3GiB |  0.08  |  0.80  |  2.38  |        |   (a)   |
 |H48 h8 k2 | 7.1GiB |  0.08  |  0.60  |  2.48  |        |         |
 |H48 h7 k2 | 3.6GiB |  0.11  |  0.81  |  3.91  |        |         |
@@ -167,11 +167,11 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  1.12  |  5.61  | 24.12  | 139.13 | 1474.87 |
+|H48 h11 k2|56.1GiB |  1.12  |  5.61  | 24.12  | 139.13 | 318.09  |
 |vcube 404 |31.8GiB |  1.08  |  5.09  | 21.31  | 202.25 |   (a)   |
-|H48 h10 k2|28.1GiB |  0.84  |  4.50  | 20.79  | 124.48 |         |
+|H48 h10 k2|28.1GiB |  0.84  |  4.50  | 20.79  | 124.48 | 247.56  |
 |vcube 308 |21.2GiB |  0.85  |  4.66  | 18.87  | 202.04 |   (a)   |
-|H48 h9 k2 |14.1GiB |  0.56  |  3.67  | 16.64  | 117.17 |         |
+|H48 h9 k2 |14.1GiB |  0.56  |  3.67  | 16.64  | 117.17 | 186.12  |
 |vcube 208 | 7.3GiB |  0.58  |  5.84  | 17.37  |        |   (a)   |
 |H48 h8 k2 | 7.1GiB |  0.57  |  4.26  | 17.60  |        |         |
 |H48 h7 k2 | 3.6GiB |  0.40  |  2.92  | 14.07  |        |         |
@@ -196,25 +196,25 @@ Average time for finding all optimal solutions.
 Time per cube (in seconds, lower is better).
-|  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|
+|  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
-|:---------|:-------|-------:|-------:|-------:|-------:|
+|:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  0.05  |  0.50  |  4.24  | 19.75  |
+|H48 h11 k2|56.1GiB |  0.05  |  0.50  |  4.24  | 19.75  |  52.99  |
-|H48 h10 k2|28.1GiB |  0.08  |  0.88  |  6.94  |        |
+|H48 h10 k2|28.1GiB |  0.08  |  0.88  |  6.94  |        |         |
-|H48 h9 k2 |14.1GiB |  0.13  |  1.39  | 13.50  |        |
+|H48 h9 k2 |14.1GiB |  0.13  |  1.39  | 13.50  |        |         |
-|H48 h8 k2 | 7.1GiB |  0.25  |  2.85  |        |        |
+|H48 h8 k2 | 7.1GiB |  0.25  |  2.85  |        |        |         |
-|H48 h7 k2 | 3.6GiB |  0.36  |  4.24  |        |        |
+|H48 h7 k2 | 3.6GiB |  0.36  |  4.24  |        |        |         |
-|H48 h6 k2 | 1.8GiB |  0.69  |  8.20  |        |        |
+|H48 h6 k2 | 1.8GiB |  0.69  |  8.20  |        |        |         |
 Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
-|  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|
+|  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
-|:---------|:-------|-------:|-------:|-------:|-------:|
+|:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11 k2|56.1GiB |  2.81  | 28.05  | 237.86 |1107.98 |
+|H48 h11 k2|56.1GiB |  2.81  | 28.05  | 237.86 |1107.98 | 2972.74 |
-|H48 h10 k2|28.1GiB |  2.25  | 24.73  | 195.01 |        |
+|H48 h10 k2|28.1GiB |  2.25  | 24.73  | 195.01 |        |         |
-|H48 h9 k2 |14.1GiB |  1.83  | 19.60  | 190.35 |        |
+|H48 h9 k2 |14.1GiB |  1.83  | 19.60  | 190.35 |        |         |
-|H48 h8 k2 | 7.1GiB |  1.77  | 20.24  |        |        |
+|H48 h8 k2 | 7.1GiB |  1.77  | 20.24  |        |        |         |
-|H48 h7 k2 | 3.6GiB |  1.30  | 15.26  |        |        |
+|H48 h7 k2 | 3.6GiB |  1.30  | 15.26  |        |        |         |
-|H48 h6 k2 | 1.8GiB |  1.24  | 14.76  |        |        |
+|H48 h6 k2 | 1.8GiB |  1.24  | 14.76  |        |        |         |
 ## Comments on the results
author	Sebastiano Tronto <sebastiano@tronto.net>	2025-11-23 16:16:31 +0100
committer	Sebastiano Tronto <sebastiano@tronto.net>	2025-11-24 16:32:11 +0100
commit	147b0c3c4615c32478a4923242909b8ae5a30d03 (patch)
tree	5294d9b3655031535085a5163c2c5b5cbe7413b1 /benchmarks/benchmarks.md
parent	78ec0d22d927bc4287aa090469d5ba5f84e8780b (diff)
download	nissy-core-147b0c3c4615c32478a4923242909b8ae5a30d03.tar.gz nissy-core-147b0c3c4615c32478a4923242909b8ae5a30d03.zip

diff --git a/benchmarks/benchmarks.md b/benchmarks/benchmarks.md index f84ddb3..33e8288 100644 --- a/benchmarks/benchmarks.md +++ b/benchmarks/benchmarks.md
@@ -71,9 +71,9 @@ Time per cube (in seconds, lower is better).
71		71
72	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	72	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
73	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	73	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
74	\|H48 h11 k2\|56.1GiB \| 0.23 \| 1.15 \| 5.08 \| 31.30 \| 278.47 \|	74	\|H48 h11 k2\|56.1GiB \| 0.23 \| 1.15 \| 5.08 \| 31.30 \| 53.67 \|
75	\|vcube 404 \|31.8GiB \| 0.30 \| 1.25 \| 6.87 \| 57.49 \| 291.31 \|	75	\|vcube 404 \|31.8GiB \| 0.30 \| 1.25 \| 6.87 \| 57.49 \| 291.31 \|
76	\|H48 h10 k2\|28.1GiB \| 0.34 \| 1.80 \| 7.77 \| \| \|	76	\|H48 h10 k2\|28.1GiB \| 0.34 \| 1.80 \| 7.77 \| \| 81.89 \|
77	\|vcube 308 \|21.2GiB \| 0.20 \| 1.11 \| 6.92 \| \| \|	77	\|vcube 308 \|21.2GiB \| 0.20 \| 1.11 \| 6.92 \| \| \|
78	\|H48 h9 k2 \|14.1GiB \| 0.42 \| 2.84 \| 12.86 \| \| \|	78	\|H48 h9 k2 \|14.1GiB \| 0.42 \| 2.84 \| 12.86 \| \| \|
79	\|vcube 208 \| 7.3GiB \| 0.57 \| 4.41 \| 20.75 \| \| \|	79	\|vcube 208 \| 7.3GiB \| 0.57 \| 4.41 \| 20.75 \| \| \|
@@ -86,9 +86,9 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
86		86
87	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	87	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
88	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	88	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
89	\|H48 h11 k2\|56.1GiB \| 12.90 \| 64.51 \| 284.99 \|1755.93 \|15622.17 \|	89	\|H48 h11 k2\|56.1GiB \| 12.90 \| 64.51 \| 284.99 \|1755.93 \| 3010.89 \|
90	\|vcube 404 \|31.8GiB \| 9.54 \| 39.75 \| 218.47 \|1828.18 \| 9263.66 \|	90	\|vcube 404 \|31.8GiB \| 9.54 \| 39.75 \| 218.47 \|1828.18 \| 9263.66 \|
91	\|H48 h10 k2\|28.1GiB \| 9.55 \| 50.58 \| 218.34 \| \| \|	91	\|H48 h10 k2\|28.1GiB \| 9.55 \| 50.58 \| 218.34 \| \| 2301.11 \|
92	\|vcube 308 \|21.2GiB \| 4.24 \| 23.53 \| 146.70 \| \| \|	92	\|vcube 308 \|21.2GiB \| 4.24 \| 23.53 \| 146.70 \| \| \|
93	\|H48 h9 k2 \|14.1GiB \| 5.92 \| 40.04 \| 181.33 \| \| \|	93	\|H48 h9 k2 \|14.1GiB \| 5.92 \| 40.04 \| 181.33 \| \| \|
94	\|vcube 208 \| 7.3GiB \| 4.16 \| 32.19 \| 151.48 \| \| \|	94	\|vcube 208 \| 7.3GiB \| 4.16 \| 32.19 \| 151.48 \| \| \|
@@ -110,11 +110,11 @@ Time per cube (in seconds, lower is better).
110		110
111	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	111	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
112	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	112	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
113	\|H48 h11 k2\|56.1GiB \| 0.06 \| 0.31 \| 1.31 \| 7.96 \| 77.81 \|	113	\|H48 h11 k2\|56.1GiB \| 0.06 \| 0.31 \| 1.31 \| 7.96 \| 14.01 \|
114	\|vcube 404 \|31.8GiB \| 0.10 \| 0.38 \| 1.88 \| 16.98 \| (a) \|	114	\|vcube 404 \|31.8GiB \| 0.10 \| 0.38 \| 1.88 \| 16.98 \| (a) \|
115	\|H48 h10 k2\|28.1GiB \| 0.10 \| 0.47 \| 2.00 \| 13.54 \| 114.35 \|	115	\|H48 h10 k2\|28.1GiB \| 0.10 \| 0.47 \| 2.00 \| 13.54 \| 21.96 \|
116	\|vcube 308 \|21.2GiB \| 0.06 \| 0.42 \| 1.95 \| 17.73 \| (a) \|	116	\|vcube 308 \|21.2GiB \| 0.06 \| 0.42 \| 1.95 \| 17.73 \| (a) \|
117	\|H48 h9 k2 \|14.1GiB \| 0.14 \| 0.83 \| 3.82 \| 25.98 \| 162.72 \|	117	\|H48 h9 k2 \|14.1GiB \| 0.14 \| 0.83 \| 3.82 \| 25.98 \| 31.68 \|
118	\|vcube 208 \| 7.3GiB \| 0.17 \| 1.49 \| 5.88 \| \| (a) \|	118	\|vcube 208 \| 7.3GiB \| 0.17 \| 1.49 \| 5.88 \| \| (a) \|
119	\|H48 h8 k2 \| 7.1GiB \| 0.27 \| 2.02 \| 7.94 \| \| \|	119	\|H48 h8 k2 \| 7.1GiB \| 0.27 \| 2.02 \| 7.94 \| \| \|
120	\|H48 h7 k2 \| 3.6GiB \| 0.35 \| 2.59 \| 12.41 \| \| \|	120	\|H48 h7 k2 \| 3.6GiB \| 0.35 \| 2.59 \| 12.41 \| \| \|
@@ -125,11 +125,11 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
125		125
126	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	126	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
127	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	127	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
128	\|H48 h11 k2\|56.1GiB \| 3.37 \| 17.39 \| 73.49 \| 446.56 \| 4365.92 \|	128	\|H48 h11 k2\|56.1GiB \| 3.37 \| 17.39 \| 73.49 \| 446.56 \| 785.96 \|
129	\|vcube 404 \|31.8GiB \| 3.80 \| 12.08 \| 59.78 \| 539.96 \| (a) \|	129	\|vcube 404 \|31.8GiB \| 3.80 \| 12.08 \| 59.78 \| 539.96 \| (a) \|
130	\|H48 h10 k2\|28.1GiB \| 2.81 \| 13.21 \| 56.20 \| 380.47 \| 3213.24 \|	130	\|H48 h10 k2\|28.1GiB \| 2.81 \| 13.21 \| 56.20 \| 380.47 \| 617.08 \|
131	\|vcube 308 \|21.2GiB \| 1.27 \| 8.90 \| 41.34 \| 375.88 \| (a) \|	131	\|vcube 308 \|21.2GiB \| 1.27 \| 8.90 \| 41.34 \| 375.88 \| (a) \|
132	\|H48 h9 k2 \|14.1GiB \| 1.97 \| 11.70 \| 53.86 \| 366.32 \| 2294.35 \|	132	\|H48 h9 k2 \|14.1GiB \| 1.97 \| 11.70 \| 53.86 \| 366.32 \| 446.69 \|
133	\|vcube 208 \| 7.3GiB \| 1.24 \| 10.88 \| 42.92 \| \| (a) \|	133	\|vcube 208 \| 7.3GiB \| 1.24 \| 10.88 \| 42.92 \| \| (a) \|
134	\|H48 h8 k2 \| 7.1GiB \| 1.92 \| 14.34 \| 56.37 \| \| \|	134	\|H48 h8 k2 \| 7.1GiB \| 1.92 \| 14.34 \| 56.37 \| \| \|
135	\|H48 h7 k2 \| 3.6GiB \| 1.26 \| 9.32 \| 44.68 \| \| \|	135	\|H48 h7 k2 \| 3.6GiB \| 1.26 \| 9.32 \| 44.68 \| \| \|
@@ -152,11 +152,11 @@ Time per cube (in seconds, lower is better).
152		152
153	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	153	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
154	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	154	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
155	\|H48 h11 k2\|56.1GiB \| 0.02 \| 0.10 \| 0.43 \| 2.48 \| 26.29 \|	155	\|H48 h11 k2\|56.1GiB \| 0.02 \| 0.10 \| 0.43 \| 2.48 \| 5.67 \|
156	\|vcube 404 \|31.8GiB \| 0.03 \| 0.16 \| 0.67 \| 6.36 \| (a) \|	156	\|vcube 404 \|31.8GiB \| 0.03 \| 0.16 \| 0.67 \| 6.36 \| (a) \|
157	\|H48 h10 k2\|28.1GiB \| 0.03 \| 0.16 \| 0.74 \| 4.43 \| \|	157	\|H48 h10 k2\|28.1GiB \| 0.03 \| 0.16 \| 0.74 \| 4.43 \| 8.81 \|
158	\|vcube 308 \|21.2GiB \| 0.04 \| 0.22 \| 0.89 \| 9.53 \| (a) \|	158	\|vcube 308 \|21.2GiB \| 0.04 \| 0.22 \| 0.89 \| 9.53 \| (a) \|
159	\|H48 h9 k2 \|14.1GiB \| 0.04 \| 0.26 \| 1.18 \| 8.31 \| \|	159	\|H48 h9 k2 \|14.1GiB \| 0.04 \| 0.26 \| 1.18 \| 8.31 \| 13.20 \|
160	\|vcube 208 \| 7.3GiB \| 0.08 \| 0.80 \| 2.38 \| \| (a) \|	160	\|vcube 208 \| 7.3GiB \| 0.08 \| 0.80 \| 2.38 \| \| (a) \|
161	\|H48 h8 k2 \| 7.1GiB \| 0.08 \| 0.60 \| 2.48 \| \| \|	161	\|H48 h8 k2 \| 7.1GiB \| 0.08 \| 0.60 \| 2.48 \| \| \|
162	\|H48 h7 k2 \| 3.6GiB \| 0.11 \| 0.81 \| 3.91 \| \| \|	162	\|H48 h7 k2 \| 3.6GiB \| 0.11 \| 0.81 \| 3.91 \| \| \|
@@ -167,11 +167,11 @@ Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
167		167
168	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	168	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
169	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	169	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
170	\|H48 h11 k2\|56.1GiB \| 1.12 \| 5.61 \| 24.12 \| 139.13 \| 1474.87 \|	170	\|H48 h11 k2\|56.1GiB \| 1.12 \| 5.61 \| 24.12 \| 139.13 \| 318.09 \|
171	\|vcube 404 \|31.8GiB \| 1.08 \| 5.09 \| 21.31 \| 202.25 \| (a) \|	171	\|vcube 404 \|31.8GiB \| 1.08 \| 5.09 \| 21.31 \| 202.25 \| (a) \|
172	\|H48 h10 k2\|28.1GiB \| 0.84 \| 4.50 \| 20.79 \| 124.48 \| \|	172	\|H48 h10 k2\|28.1GiB \| 0.84 \| 4.50 \| 20.79 \| 124.48 \| 247.56 \|
173	\|vcube 308 \|21.2GiB \| 0.85 \| 4.66 \| 18.87 \| 202.04 \| (a) \|	173	\|vcube 308 \|21.2GiB \| 0.85 \| 4.66 \| 18.87 \| 202.04 \| (a) \|
174	\|H48 h9 k2 \|14.1GiB \| 0.56 \| 3.67 \| 16.64 \| 117.17 \| \|	174	\|H48 h9 k2 \|14.1GiB \| 0.56 \| 3.67 \| 16.64 \| 117.17 \| 186.12 \|
175	\|vcube 208 \| 7.3GiB \| 0.58 \| 5.84 \| 17.37 \| \| (a) \|	175	\|vcube 208 \| 7.3GiB \| 0.58 \| 5.84 \| 17.37 \| \| (a) \|
176	\|H48 h8 k2 \| 7.1GiB \| 0.57 \| 4.26 \| 17.60 \| \| \|	176	\|H48 h8 k2 \| 7.1GiB \| 0.57 \| 4.26 \| 17.60 \| \| \|
177	\|H48 h7 k2 \| 3.6GiB \| 0.40 \| 2.92 \| 14.07 \| \| \|	177	\|H48 h7 k2 \| 3.6GiB \| 0.40 \| 2.92 \| 14.07 \| \| \|
@@ -196,25 +196,25 @@ Average time for finding all optimal solutions.
196		196
197	Time per cube (in seconds, lower is better).	197	Time per cube (in seconds, lower is better).
198		198
199	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|	199	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
200	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|	200	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
201	\|H48 h11 k2\|56.1GiB \| 0.05 \| 0.50 \| 4.24 \| 19.75 \|	201	\|H48 h11 k2\|56.1GiB \| 0.05 \| 0.50 \| 4.24 \| 19.75 \| 52.99 \|
202	\|H48 h10 k2\|28.1GiB \| 0.08 \| 0.88 \| 6.94 \| \|	202	\|H48 h10 k2\|28.1GiB \| 0.08 \| 0.88 \| 6.94 \| \| \|
203	\|H48 h9 k2 \|14.1GiB \| 0.13 \| 1.39 \| 13.50 \| \|	203	\|H48 h9 k2 \|14.1GiB \| 0.13 \| 1.39 \| 13.50 \| \| \|
204	\|H48 h8 k2 \| 7.1GiB \| 0.25 \| 2.85 \| \| \|	204	\|H48 h8 k2 \| 7.1GiB \| 0.25 \| 2.85 \| \| \| \|
205	\|H48 h7 k2 \| 3.6GiB \| 0.36 \| 4.24 \| \| \|	205	\|H48 h7 k2 \| 3.6GiB \| 0.36 \| 4.24 \| \| \| \|
206	\|H48 h6 k2 \| 1.8GiB \| 0.69 \| 8.20 \| \| \|	206	\|H48 h6 k2 \| 1.8GiB \| 0.69 \| 8.20 \| \| \| \|
207		207
208	Time per cube adjusted for tables size (in seconds \* GiB, lower is better).	208	Time per cube adjusted for tables size (in seconds \* GiB, lower is better).
209		209
210	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|	210	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
211	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|	211	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
212	\|H48 h11 k2\|56.1GiB \| 2.81 \| 28.05 \| 237.86 \|1107.98 \|	212	\|H48 h11 k2\|56.1GiB \| 2.81 \| 28.05 \| 237.86 \|1107.98 \| 2972.74 \|
213	\|H48 h10 k2\|28.1GiB \| 2.25 \| 24.73 \| 195.01 \| \|	213	\|H48 h10 k2\|28.1GiB \| 2.25 \| 24.73 \| 195.01 \| \| \|
214	\|H48 h9 k2 \|14.1GiB \| 1.83 \| 19.60 \| 190.35 \| \|	214	\|H48 h9 k2 \|14.1GiB \| 1.83 \| 19.60 \| 190.35 \| \| \|
215	\|H48 h8 k2 \| 7.1GiB \| 1.77 \| 20.24 \| \| \|	215	\|H48 h8 k2 \| 7.1GiB \| 1.77 \| 20.24 \| \| \| \|
216	\|H48 h7 k2 \| 3.6GiB \| 1.30 \| 15.26 \| \| \|	216	\|H48 h7 k2 \| 3.6GiB \| 1.30 \| 15.26 \| \| \| \|
217	\|H48 h6 k2 \| 1.8GiB \| 1.24 \| 14.76 \| \| \|	217	\|H48 h6 k2 \| 1.8GiB \| 1.24 \| 14.76 \| \| \| \|
218		218
219	## Comments on the results	219	## Comments on the results
220		220