Update benchmarks.mdh48-dfs-improvements

author: Sebastiano Tronto <sebastiano@tronto.net> 2026-01-10 05:43:36 +0100
committer: Sebastiano Tronto <sebastiano@tronto.net> 2026-01-10 05:43:36 +0100
commit: b45ce3d076537cfa2bcc2648433fbbc102d4a3d0 (patch)
tree: d6bb6de992eace566d033d0824c03da89cf7b9cb /benchmarks/benchmarks.md
parent: 639fabcc7c0b3b56f13b55c480b6c2b406154d4f (diff)
download: nissy-core-b45ce3d076537cfa2bcc2648433fbbc102d4a3d0.tar.gz
nissy-core-b45ce3d076537cfa2bcc2648433fbbc102d4a3d0.zip
1 files changed, 53 insertions, 51 deletions
diff --git a/benchmarks/benchmarks.md b/benchmarks/benchmarks.md
index 45ef29b..768a7ea 100644
--- a/benchmarks/benchmarks.md
+++ b/benchmarks/benchmarks.md
@@ -70,32 +70,32 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    0.11|    0.75|    3.43|   27.28|    19.30|
-|H48 h11   |56.5 GiB|    0.13|    0.73|    3.43|   23.28|    19.26|
+|H48 h11   |56.5 GiB|    0.09|    0.50|    2.24|   15.73|    15.55|
 |vcube 404 |31.8 GiB|    0.23|    1.24|    6.10|   59.33|   268.26|
-|H48 h10   |28.3 GiB|    0.23|    1.20|    6.18|   43.51|    48.84|
+|H48 h10   |28.3 GiB|    0.15|    0.76|    3.36|   23.51|    38.05|
 |vcube 308 |21.2 GiB|    0.17|    1.02|    6.20|   58.70|   604.35|
-|H48 h9    |14.1 GiB|    0.36|    2.47|   11.79|        |         |
+|H48 h9    |14.1 GiB|    0.24|    1.48|    6.69|        |         |
 |vcube 208 | 7.3 GiB|    0.56|    4.36|   20.58|        |         |
-|H48 h8    | 7.1 GiB|    0.79|    6.09|   25.58|        |         |
+|H48 h8    | 7.1 GiB|    0.46|    3.36|   14.13|        |         |
-|H48 h7    | 3.5 GiB|    1.07|    8.59|   42.16|        |         |
+|H48 h7    | 3.5 GiB|    0.63|    4.85|   23.25|        |         |
 |vcube 112 | 2.4 GiB|    0.96|    9.29|   40.52|        |         |
-|H48 h6    | 1.8 GiB|    2.12|   16.29|   82.24|        |         |
+|H48 h6    | 1.8 GiB|    1.25|    9.45|   46.31|        |         |
 Time per cube adjusted for table size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    6.43|   43.80|  199.38| 1587.43|  1122.73|
-|H48 h11   |56.5 GiB|    7.33|   41.47|  193.67| 1315.32|  1088.34|
+|H48 h11   |56.5 GiB|    5.21|   28.28|  126.68|  889.01|   878.77|
 |vcube 404 |31.8 GiB|    7.40|   39.47|  194.01| 1887.94|  8535.87|
-|H48 h10   |28.3 GiB|    6.60|   34.00|  174.65| 1229.18|  1379.90|
+|H48 h10   |28.3 GiB|    4.22|   21.37|   94.86|  664.22|  1075.08|
 |vcube 308 |21.2 GiB|    3.51|   21.71|  131.50| 1245.26| 12819.94|
-|H48 h9    |14.1 GiB|    5.03|   34.85|  166.51|        |         |
+|H48 h9    |14.1 GiB|    3.34|   20.97|   94.57|        |         |
 |vcube 208 | 7.3 GiB|    4.08|   31.74|  149.68|        |         |
-|H48 h8    | 7.1 GiB|    5.61|   43.02|  180.71|        |         |
+|H48 h8    | 7.1 GiB|    3.25|   23.75|   99.82|        |         |
-|H48 h7    | 3.5 GiB|    3.80|   30.34|  148.96|        |         |
+|H48 h7    | 3.5 GiB|    2.22|   17.12|   82.14|        |         |
 |vcube 112 | 2.4 GiB|    2.33|   22.53|   98.23|        |         |
-|H48 h6    | 1.8 GiB|    3.75|   28.79|  145.36|        |         |
+|H48 h6    | 1.8 GiB|    2.21|   16.70|   81.86|        |         |
 <img src="img/17moves1thread.png">
 <img src="img/18moves1thread.png">
@@ -110,32 +110,32 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    0.03|    0.27|    1.04|    7.70|   (a)   |
-|H48 h11   |56.5 GiB|    0.04|    0.22|    0.97|    6.98|     5.95|
+|H48 h11   |56.5 GiB|    0.04|    0.14|    0.60|    3.97|     4.19|
 |vcube 404 |31.8 GiB|    0.07|    0.30|    1.65|   16.17|   (a)   |
-|H48 h10   |28.3 GiB|    0.07|    0.36|    1.79|   12.42|    14.03|
+|H48 h10   |28.3 GiB|    0.05|    0.20|    0.91|    6.65|     9.81|
 |vcube 308 |21.2 GiB|    0.05|    0.35|    1.78|   16.61|   (a)   |
-|H48 h9    |14.1 GiB|    0.11|    0.70|    3.48|   25.61|    25.37|
+|H48 h9    |14.1 GiB|    0.07|    0.39|    1.74|   12.54|    18.96|
 |vcube 208 | 7.3 GiB|    0.16|    1.47|    5.86|        |   (a)   |
-|H48 h8    | 7.1 GiB|    0.23|    1.74|    7.19|        |         |
+|H48 h8    | 7.1 GiB|    0.13|    0.90|    3.71|        |         |
-|H48 h7    | 3.5 GiB|    0.32|    2.45|   12.12|        |         |
+|H48 h7    | 3.5 GiB|    0.17|    1.28|    6.12|        |         |
 |vcube 112 | 2.4 GiB|    0.29|    3.13|   11.95|        |   (a)   |
-|H48 h6    | 1.8 GiB|    0.61|    4.61|   24.22|        |         |
+|H48 h6    | 1.8 GiB|    0.33|    2.47|   12.22|        |         |
 Time per cube adjusted for table size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    2.03|   15.69|   60.25|  447.97|   (a)   |
-|H48 h11   |56.5 GiB|    2.53|   12.71|   54.58|  394.33|   336.47|
+|H48 h11   |56.5 GiB|    2.04|    8.17|   33.77|  224.59|   236.92|
 |vcube 404 |31.8 GiB|    2.32|    9.50|   52.46|  514.50|   (a)   |
-|H48 h10   |28.3 GiB|    2.11|   10.23|   50.61|  350.78|   396.48|
+|H48 h10   |28.3 GiB|    1.37|    5.76|   25.83|  187.88|   277.18|
 |vcube 308 |21.2 GiB|    1.02|    7.52|   37.82|  352.36|   (a)   |
-|H48 h9    |14.1 GiB|    1.57|    9.96|   49.23|  361.85|   358.45|
+|H48 h9    |14.1 GiB|    1.03|    5.45|   24.58|  177.17|   267.79|
 |vcube 208 | 7.3 GiB|    1.18|   10.69|   42.63|        |   (a)   |
-|H48 h8    | 7.1 GiB|    1.66|   12.27|   50.82|        |         |
+|H48 h8    | 7.1 GiB|    0.92|    6.39|   26.20|        |         |
-|H48 h7    | 3.5 GiB|    1.11|    8.67|   42.83|        |         |
+|H48 h7    | 3.5 GiB|    0.62|    4.53|   21.62|        |         |
 |vcube 112 | 2.4 GiB|    0.69|    7.59|   28.97|        |   (a)   |
-|H48 h6    | 1.8 GiB|    1.08|    8.16|   42.81|        |         |
+|H48 h6    | 1.8 GiB|    0.59|    4.37|   21.61|        |         |
 (a) vcube cannot parallelize on a single scramble, the results for the
 superflip are going to be the same as in the single thread case.
@@ -153,32 +153,32 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    0.02|    0.13|    0.45|    2.84|   (a)   |
-|H48 h11   |56.5 GiB|    0.02|    0.08|    0.33|    2.22|     2.41|
+|H48 h11   |56.5 GiB|    0.02|    0.06|    0.22|    1.33|     1.84|
 |vcube 404 |31.8 GiB|    0.04|    0.14|    0.65|    6.08|   (a)   |
-|H48 h10   |28.3 GiB|    0.03|    0.13|    0.58|    4.21|     5.56|
+|H48 h10   |28.3 GiB|    0.03|    0.08|    0.33|    2.34|     4.18|
 |vcube 308 |21.2 GiB|    0.03|    0.19|    0.78|    6.67|   (a)   |
-|H48 h9    |14.1 GiB|    0.04|    0.25|    1.10|    8.05|    10.77|
+|H48 h9    |14.1 GiB|    0.04|    0.15|    0.64|    4.45|     8.09|
 |vcube 208 | 7.3 GiB|    0.08|    0.79|    2.43|        |   (a)   |
-|H48 h8    | 7.1 GiB|    0.08|    0.57|    2.40|        |         |
+|H48 h8    | 7.1 GiB|    0.06|    0.34|    1.36|        |         |
-|H48 h7    | 3.5 GiB|    0.11|    0.83|    4.00|        |         |
+|H48 h7    | 3.5 GiB|    0.07|    0.47|    2.20|        |         |
 |vcube 112 | 2.4 GiB|    0.15|    1.63|    5.10|        |   (a)   |
-|H48 h6    | 1.8 GiB|    0.21|    1.51|    7.74|        |         |
+|H48 h6    | 1.8 GiB|    0.13|    0.91|    4.39|        |         |
 Time per cube adjusted for table size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
 |vcube 212 |58.2 GiB|    0.95|    7.83|   26.04|  165.03|   (a)   |
-|H48 h11   |56.5 GiB|    1.12|    4.61|   18.90|  125.27|   136.10|
+|H48 h11   |56.5 GiB|    1.34|    3.48|   12.19|   74.93|   103.98|
 |vcube 404 |31.8 GiB|    1.21|    4.60|   20.76|  193.43|   (a)   |
-|H48 h10   |28.3 GiB|    0.86|    3.61|   16.47|  118.85|   157.13|
+|H48 h10   |28.3 GiB|    0.74|    2.37|    9.46|   66.13|   118.23|
 |vcube 308 |21.2 GiB|    0.67|    4.01|   16.48|  141.49|   (a)   |
-|H48 h9    |14.1 GiB|    0.60|    3.51|   15.57|  113.71|   152.21|
+|H48 h9    |14.1 GiB|    0.51|    2.15|    8.98|   62.92|   114.31|
 |vcube 208 | 7.3 GiB|    0.56|    5.78|   17.68|        |   (a)   |
-|H48 h8    | 7.1 GiB|    0.59|    4.03|   16.98|        |         |
+|H48 h8    | 7.1 GiB|    0.40|    2.40|    9.59|        |         |
-|H48 h7    | 3.5 GiB|    0.41|    2.94|   14.12|        |         |
+|H48 h7    | 3.5 GiB|    0.26|    1.66|    7.77|        |         |
 |vcube 112 | 2.4 GiB|    0.35|    3.95|   12.37|        |   (a)   |
-|H48 h6    | 1.8 GiB|    0.38|    2.67|   13.68|        |         |
+|H48 h6    | 1.8 GiB|    0.23|    1.61|    7.76|        |         |
 (a) vcube cannot parallelize on a single scramble, the results for the
 superflip are going to be the same as in the single thread case.
@@ -197,32 +197,34 @@ Time per cube (in seconds, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11   |56.5 GiB|    0.05|    0.41|    3.69|   31.65|    21.80|
+|H48 h11   |56.5 GiB|    0.04|    0.26|    2.22|   18.96|    16.95|
-|H48 h10   |28.3 GiB|    0.07|    0.70|    6.73|   58.61|    48.62|
+|H48 h10   |28.3 GiB|    0.05|    0.42|    3.82|   34.42|    36.80|
-|H48 h9    |14.1 GiB|    0.12|    1.28|   12.93|        |         |
+|H48 h9    |14.1 GiB|    0.08|    0.73|    7.28|        |         |
-|H48 h8    | 7.1 GiB|    0.25|    2.72|   27.42|        |         |
+|H48 h8    | 7.1 GiB|    0.15|    1.56|   15.41|        |         |
-|H48 h7    | 3.5 GiB|    0.37|    4.24|   47.10|        |         |
+|H48 h7    | 3.5 GiB|    0.21|    2.38|   26.52|        |         |
-|H48 h6    | 1.8 GiB|    0.69|    8.18|   91.85|        |         |
+|H48 h6    | 1.8 GiB|    0.39|    4.67|   53.00|        |         |
 Time per cube adjusted for table size (in seconds \* GiB, lower is better).
 |  Solver  |  Size  |17 moves|18 moves|19 moves|20 moves|Superflip|
 |:---------|:-------|-------:|-------:|-------:|-------:|--------:|
-|H48 h11   |56.5 GiB|    2.57|   23.07|  208.71| 1788.12|  1231.86|
+|H48 h11   |56.5 GiB|    2.11|   14.55|  125.21| 1071.23|   957.47|
-|H48 h10   |28.3 GiB|    2.01|   19.77|  190.14| 1655.95|  1373.79|
+|H48 h10   |28.3 GiB|    1.48|   11.96|  107.83|  972.35|  1039.73|
-|H48 h9    |14.1 GiB|    1.72|   18.07|  182.67|        |         |
+|H48 h9    |14.1 GiB|    1.08|   10.29|  102.88|        |         |
-|H48 h8    | 7.1 GiB|    1.74|   19.21|  193.74|        |         |
+|H48 h8    | 7.1 GiB|    1.03|   10.99|  108.87|        |         |
-|H48 h7    | 3.5 GiB|    1.29|   14.98|  166.41|        |         |
+|H48 h7    | 3.5 GiB|    0.74|    8.41|   93.69|        |         |
-|H48 h6    | 1.8 GiB|    1.21|   14.47|  162.36|        |         |
+|H48 h6    | 1.8 GiB|    0.70|    8.25|   93.68|        |         |
 </details>
 ## Comments on the results
-* Adjusting for table size, vcube generally is a bit faster than H48,
+* Adjusting for table size, H48 is generally faster than vcube.
-  except for 20 moves scrambles where H48 is a clear winner.
+* The gap between the two solvers is larger for scrambles with
+  longer optimal solutions.
 * On sets of 25 scrambles, H48 performs better than vcube when using
-  multiple threads. However, this advantage will likely disappear (or
+  multiple threads, compared to their single-threaded performance.
+  However, this advantage will likely disappear (or
  even invert) if we increase the size of the set.
 ## Other notes
author	Sebastiano Tronto <sebastiano@tronto.net>	2026-01-10 05:43:36 +0100
committer	Sebastiano Tronto <sebastiano@tronto.net>	2026-01-10 05:43:36 +0100
commit	b45ce3d076537cfa2bcc2648433fbbc102d4a3d0 (patch)
tree	d6bb6de992eace566d033d0824c03da89cf7b9cb /benchmarks/benchmarks.md
parent	639fabcc7c0b3b56f13b55c480b6c2b406154d4f (diff)
download	nissy-core-b45ce3d076537cfa2bcc2648433fbbc102d4a3d0.tar.gz nissy-core-b45ce3d076537cfa2bcc2648433fbbc102d4a3d0.zip

diff --git a/benchmarks/benchmarks.md b/benchmarks/benchmarks.md index 45ef29b..768a7ea 100644 --- a/benchmarks/benchmarks.md +++ b/benchmarks/benchmarks.md
@@ -70,32 +70,32 @@ Time per cube (in seconds, lower is better).
70	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	70	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
71	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	71	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
72	\|vcube 212 \|58.2 GiB\| 0.11\| 0.75\| 3.43\| 27.28\| 19.30\|	72	\|vcube 212 \|58.2 GiB\| 0.11\| 0.75\| 3.43\| 27.28\| 19.30\|
73	\|H48 h11 \|56.5 GiB\| 0.13\| 0.73\| 3.43\| 23.28\| 19.26\|	73	\|H48 h11 \|56.5 GiB\| 0.09\| 0.50\| 2.24\| 15.73\| 15.55\|
74	\|vcube 404 \|31.8 GiB\| 0.23\| 1.24\| 6.10\| 59.33\| 268.26\|	74	\|vcube 404 \|31.8 GiB\| 0.23\| 1.24\| 6.10\| 59.33\| 268.26\|
75	\|H48 h10 \|28.3 GiB\| 0.23\| 1.20\| 6.18\| 43.51\| 48.84\|	75	\|H48 h10 \|28.3 GiB\| 0.15\| 0.76\| 3.36\| 23.51\| 38.05\|
76	\|vcube 308 \|21.2 GiB\| 0.17\| 1.02\| 6.20\| 58.70\| 604.35\|	76	\|vcube 308 \|21.2 GiB\| 0.17\| 1.02\| 6.20\| 58.70\| 604.35\|
77	\|H48 h9 \|14.1 GiB\| 0.36\| 2.47\| 11.79\| \| \|	77	\|H48 h9 \|14.1 GiB\| 0.24\| 1.48\| 6.69\| \| \|
78	\|vcube 208 \| 7.3 GiB\| 0.56\| 4.36\| 20.58\| \| \|	78	\|vcube 208 \| 7.3 GiB\| 0.56\| 4.36\| 20.58\| \| \|
79	\|H48 h8 \| 7.1 GiB\| 0.79\| 6.09\| 25.58\| \| \|	79	\|H48 h8 \| 7.1 GiB\| 0.46\| 3.36\| 14.13\| \| \|
80	\|H48 h7 \| 3.5 GiB\| 1.07\| 8.59\| 42.16\| \| \|	80	\|H48 h7 \| 3.5 GiB\| 0.63\| 4.85\| 23.25\| \| \|
81	\|vcube 112 \| 2.4 GiB\| 0.96\| 9.29\| 40.52\| \| \|	81	\|vcube 112 \| 2.4 GiB\| 0.96\| 9.29\| 40.52\| \| \|
82	\|H48 h6 \| 1.8 GiB\| 2.12\| 16.29\| 82.24\| \| \|	82	\|H48 h6 \| 1.8 GiB\| 1.25\| 9.45\| 46.31\| \| \|
83		83
84	Time per cube adjusted for table size (in seconds \* GiB, lower is better).	84	Time per cube adjusted for table size (in seconds \* GiB, lower is better).
85		85
86	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	86	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
87	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	87	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
88	\|vcube 212 \|58.2 GiB\| 6.43\| 43.80\| 199.38\| 1587.43\| 1122.73\|	88	\|vcube 212 \|58.2 GiB\| 6.43\| 43.80\| 199.38\| 1587.43\| 1122.73\|
89	\|H48 h11 \|56.5 GiB\| 7.33\| 41.47\| 193.67\| 1315.32\| 1088.34\|	89	\|H48 h11 \|56.5 GiB\| 5.21\| 28.28\| 126.68\| 889.01\| 878.77\|
90	\|vcube 404 \|31.8 GiB\| 7.40\| 39.47\| 194.01\| 1887.94\| 8535.87\|	90	\|vcube 404 \|31.8 GiB\| 7.40\| 39.47\| 194.01\| 1887.94\| 8535.87\|
91	\|H48 h10 \|28.3 GiB\| 6.60\| 34.00\| 174.65\| 1229.18\| 1379.90\|	91	\|H48 h10 \|28.3 GiB\| 4.22\| 21.37\| 94.86\| 664.22\| 1075.08\|
92	\|vcube 308 \|21.2 GiB\| 3.51\| 21.71\| 131.50\| 1245.26\| 12819.94\|	92	\|vcube 308 \|21.2 GiB\| 3.51\| 21.71\| 131.50\| 1245.26\| 12819.94\|
93	\|H48 h9 \|14.1 GiB\| 5.03\| 34.85\| 166.51\| \| \|	93	\|H48 h9 \|14.1 GiB\| 3.34\| 20.97\| 94.57\| \| \|
94	\|vcube 208 \| 7.3 GiB\| 4.08\| 31.74\| 149.68\| \| \|	94	\|vcube 208 \| 7.3 GiB\| 4.08\| 31.74\| 149.68\| \| \|
95	\|H48 h8 \| 7.1 GiB\| 5.61\| 43.02\| 180.71\| \| \|	95	\|H48 h8 \| 7.1 GiB\| 3.25\| 23.75\| 99.82\| \| \|
96	\|H48 h7 \| 3.5 GiB\| 3.80\| 30.34\| 148.96\| \| \|	96	\|H48 h7 \| 3.5 GiB\| 2.22\| 17.12\| 82.14\| \| \|
97	\|vcube 112 \| 2.4 GiB\| 2.33\| 22.53\| 98.23\| \| \|	97	\|vcube 112 \| 2.4 GiB\| 2.33\| 22.53\| 98.23\| \| \|
98	\|H48 h6 \| 1.8 GiB\| 3.75\| 28.79\| 145.36\| \| \|	98	\|H48 h6 \| 1.8 GiB\| 2.21\| 16.70\| 81.86\| \| \|
99		99
100	<img src="img/17moves1thread.png">	100	<img src="img/17moves1thread.png">
101	<img src="img/18moves1thread.png">	101	<img src="img/18moves1thread.png">
@@ -110,32 +110,32 @@ Time per cube (in seconds, lower is better).
110	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	110	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
111	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	111	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
112	\|vcube 212 \|58.2 GiB\| 0.03\| 0.27\| 1.04\| 7.70\| (a) \|	112	\|vcube 212 \|58.2 GiB\| 0.03\| 0.27\| 1.04\| 7.70\| (a) \|
113	\|H48 h11 \|56.5 GiB\| 0.04\| 0.22\| 0.97\| 6.98\| 5.95\|	113	\|H48 h11 \|56.5 GiB\| 0.04\| 0.14\| 0.60\| 3.97\| 4.19\|
114	\|vcube 404 \|31.8 GiB\| 0.07\| 0.30\| 1.65\| 16.17\| (a) \|	114	\|vcube 404 \|31.8 GiB\| 0.07\| 0.30\| 1.65\| 16.17\| (a) \|
115	\|H48 h10 \|28.3 GiB\| 0.07\| 0.36\| 1.79\| 12.42\| 14.03\|	115	\|H48 h10 \|28.3 GiB\| 0.05\| 0.20\| 0.91\| 6.65\| 9.81\|
116	\|vcube 308 \|21.2 GiB\| 0.05\| 0.35\| 1.78\| 16.61\| (a) \|	116	\|vcube 308 \|21.2 GiB\| 0.05\| 0.35\| 1.78\| 16.61\| (a) \|
117	\|H48 h9 \|14.1 GiB\| 0.11\| 0.70\| 3.48\| 25.61\| 25.37\|	117	\|H48 h9 \|14.1 GiB\| 0.07\| 0.39\| 1.74\| 12.54\| 18.96\|
118	\|vcube 208 \| 7.3 GiB\| 0.16\| 1.47\| 5.86\| \| (a) \|	118	\|vcube 208 \| 7.3 GiB\| 0.16\| 1.47\| 5.86\| \| (a) \|
119	\|H48 h8 \| 7.1 GiB\| 0.23\| 1.74\| 7.19\| \| \|	119	\|H48 h8 \| 7.1 GiB\| 0.13\| 0.90\| 3.71\| \| \|
120	\|H48 h7 \| 3.5 GiB\| 0.32\| 2.45\| 12.12\| \| \|	120	\|H48 h7 \| 3.5 GiB\| 0.17\| 1.28\| 6.12\| \| \|
121	\|vcube 112 \| 2.4 GiB\| 0.29\| 3.13\| 11.95\| \| (a) \|	121	\|vcube 112 \| 2.4 GiB\| 0.29\| 3.13\| 11.95\| \| (a) \|
122	\|H48 h6 \| 1.8 GiB\| 0.61\| 4.61\| 24.22\| \| \|	122	\|H48 h6 \| 1.8 GiB\| 0.33\| 2.47\| 12.22\| \| \|
123		123
124	Time per cube adjusted for table size (in seconds \* GiB, lower is better).	124	Time per cube adjusted for table 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	\|vcube 212 \|58.2 GiB\| 2.03\| 15.69\| 60.25\| 447.97\| (a) \|	128	\|vcube 212 \|58.2 GiB\| 2.03\| 15.69\| 60.25\| 447.97\| (a) \|
129	\|H48 h11 \|56.5 GiB\| 2.53\| 12.71\| 54.58\| 394.33\| 336.47\|	129	\|H48 h11 \|56.5 GiB\| 2.04\| 8.17\| 33.77\| 224.59\| 236.92\|
130	\|vcube 404 \|31.8 GiB\| 2.32\| 9.50\| 52.46\| 514.50\| (a) \|	130	\|vcube 404 \|31.8 GiB\| 2.32\| 9.50\| 52.46\| 514.50\| (a) \|
131	\|H48 h10 \|28.3 GiB\| 2.11\| 10.23\| 50.61\| 350.78\| 396.48\|	131	\|H48 h10 \|28.3 GiB\| 1.37\| 5.76\| 25.83\| 187.88\| 277.18\|
132	\|vcube 308 \|21.2 GiB\| 1.02\| 7.52\| 37.82\| 352.36\| (a) \|	132	\|vcube 308 \|21.2 GiB\| 1.02\| 7.52\| 37.82\| 352.36\| (a) \|
133	\|H48 h9 \|14.1 GiB\| 1.57\| 9.96\| 49.23\| 361.85\| 358.45\|	133	\|H48 h9 \|14.1 GiB\| 1.03\| 5.45\| 24.58\| 177.17\| 267.79\|
134	\|vcube 208 \| 7.3 GiB\| 1.18\| 10.69\| 42.63\| \| (a) \|	134	\|vcube 208 \| 7.3 GiB\| 1.18\| 10.69\| 42.63\| \| (a) \|
135	\|H48 h8 \| 7.1 GiB\| 1.66\| 12.27\| 50.82\| \| \|	135	\|H48 h8 \| 7.1 GiB\| 0.92\| 6.39\| 26.20\| \| \|
136	\|H48 h7 \| 3.5 GiB\| 1.11\| 8.67\| 42.83\| \| \|	136	\|H48 h7 \| 3.5 GiB\| 0.62\| 4.53\| 21.62\| \| \|
137	\|vcube 112 \| 2.4 GiB\| 0.69\| 7.59\| 28.97\| \| (a) \|	137	\|vcube 112 \| 2.4 GiB\| 0.69\| 7.59\| 28.97\| \| (a) \|
138	\|H48 h6 \| 1.8 GiB\| 1.08\| 8.16\| 42.81\| \| \|	138	\|H48 h6 \| 1.8 GiB\| 0.59\| 4.37\| 21.61\| \| \|
139		139
140	(a) vcube cannot parallelize on a single scramble, the results for the	140	(a) vcube cannot parallelize on a single scramble, the results for the
141	superflip are going to be the same as in the single thread case.	141	superflip are going to be the same as in the single thread case.
@@ -153,32 +153,32 @@ Time per cube (in seconds, lower is better).
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	\|vcube 212 \|58.2 GiB\| 0.02\| 0.13\| 0.45\| 2.84\| (a) \|	155	\|vcube 212 \|58.2 GiB\| 0.02\| 0.13\| 0.45\| 2.84\| (a) \|
156	\|H48 h11 \|56.5 GiB\| 0.02\| 0.08\| 0.33\| 2.22\| 2.41\|	156	\|H48 h11 \|56.5 GiB\| 0.02\| 0.06\| 0.22\| 1.33\| 1.84\|
157	\|vcube 404 \|31.8 GiB\| 0.04\| 0.14\| 0.65\| 6.08\| (a) \|	157	\|vcube 404 \|31.8 GiB\| 0.04\| 0.14\| 0.65\| 6.08\| (a) \|
158	\|H48 h10 \|28.3 GiB\| 0.03\| 0.13\| 0.58\| 4.21\| 5.56\|	158	\|H48 h10 \|28.3 GiB\| 0.03\| 0.08\| 0.33\| 2.34\| 4.18\|
159	\|vcube 308 \|21.2 GiB\| 0.03\| 0.19\| 0.78\| 6.67\| (a) \|	159	\|vcube 308 \|21.2 GiB\| 0.03\| 0.19\| 0.78\| 6.67\| (a) \|
160	\|H48 h9 \|14.1 GiB\| 0.04\| 0.25\| 1.10\| 8.05\| 10.77\|	160	\|H48 h9 \|14.1 GiB\| 0.04\| 0.15\| 0.64\| 4.45\| 8.09\|
161	\|vcube 208 \| 7.3 GiB\| 0.08\| 0.79\| 2.43\| \| (a) \|	161	\|vcube 208 \| 7.3 GiB\| 0.08\| 0.79\| 2.43\| \| (a) \|
162	\|H48 h8 \| 7.1 GiB\| 0.08\| 0.57\| 2.40\| \| \|	162	\|H48 h8 \| 7.1 GiB\| 0.06\| 0.34\| 1.36\| \| \|
163	\|H48 h7 \| 3.5 GiB\| 0.11\| 0.83\| 4.00\| \| \|	163	\|H48 h7 \| 3.5 GiB\| 0.07\| 0.47\| 2.20\| \| \|
164	\|vcube 112 \| 2.4 GiB\| 0.15\| 1.63\| 5.10\| \| (a) \|	164	\|vcube 112 \| 2.4 GiB\| 0.15\| 1.63\| 5.10\| \| (a) \|
165	\|H48 h6 \| 1.8 GiB\| 0.21\| 1.51\| 7.74\| \| \|	165	\|H48 h6 \| 1.8 GiB\| 0.13\| 0.91\| 4.39\| \| \|
166		166
167	Time per cube adjusted for table size (in seconds \* GiB, lower is better).	167	Time per cube adjusted for table size (in seconds \* GiB, lower is better).
168		168
169	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	169	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
170	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	170	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
171	\|vcube 212 \|58.2 GiB\| 0.95\| 7.83\| 26.04\| 165.03\| (a) \|	171	\|vcube 212 \|58.2 GiB\| 0.95\| 7.83\| 26.04\| 165.03\| (a) \|
172	\|H48 h11 \|56.5 GiB\| 1.12\| 4.61\| 18.90\| 125.27\| 136.10\|	172	\|H48 h11 \|56.5 GiB\| 1.34\| 3.48\| 12.19\| 74.93\| 103.98\|
173	\|vcube 404 \|31.8 GiB\| 1.21\| 4.60\| 20.76\| 193.43\| (a) \|	173	\|vcube 404 \|31.8 GiB\| 1.21\| 4.60\| 20.76\| 193.43\| (a) \|
174	\|H48 h10 \|28.3 GiB\| 0.86\| 3.61\| 16.47\| 118.85\| 157.13\|	174	\|H48 h10 \|28.3 GiB\| 0.74\| 2.37\| 9.46\| 66.13\| 118.23\|
175	\|vcube 308 \|21.2 GiB\| 0.67\| 4.01\| 16.48\| 141.49\| (a) \|	175	\|vcube 308 \|21.2 GiB\| 0.67\| 4.01\| 16.48\| 141.49\| (a) \|
176	\|H48 h9 \|14.1 GiB\| 0.60\| 3.51\| 15.57\| 113.71\| 152.21\|	176	\|H48 h9 \|14.1 GiB\| 0.51\| 2.15\| 8.98\| 62.92\| 114.31\|
177	\|vcube 208 \| 7.3 GiB\| 0.56\| 5.78\| 17.68\| \| (a) \|	177	\|vcube 208 \| 7.3 GiB\| 0.56\| 5.78\| 17.68\| \| (a) \|
178	\|H48 h8 \| 7.1 GiB\| 0.59\| 4.03\| 16.98\| \| \|	178	\|H48 h8 \| 7.1 GiB\| 0.40\| 2.40\| 9.59\| \| \|
179	\|H48 h7 \| 3.5 GiB\| 0.41\| 2.94\| 14.12\| \| \|	179	\|H48 h7 \| 3.5 GiB\| 0.26\| 1.66\| 7.77\| \| \|
180	\|vcube 112 \| 2.4 GiB\| 0.35\| 3.95\| 12.37\| \| (a) \|	180	\|vcube 112 \| 2.4 GiB\| 0.35\| 3.95\| 12.37\| \| (a) \|
181	\|H48 h6 \| 1.8 GiB\| 0.38\| 2.67\| 13.68\| \| \|	181	\|H48 h6 \| 1.8 GiB\| 0.23\| 1.61\| 7.76\| \| \|
182		182
183	(a) vcube cannot parallelize on a single scramble, the results for the	183	(a) vcube cannot parallelize on a single scramble, the results for the
184	superflip are going to be the same as in the single thread case.	184	superflip are going to be the same as in the single thread case.
@@ -197,32 +197,34 @@ Time per cube (in seconds, lower is better).
197		197
198	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	198	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
199	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	199	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
200	\|H48 h11 \|56.5 GiB\| 0.05\| 0.41\| 3.69\| 31.65\| 21.80\|	200	\|H48 h11 \|56.5 GiB\| 0.04\| 0.26\| 2.22\| 18.96\| 16.95\|
201	\|H48 h10 \|28.3 GiB\| 0.07\| 0.70\| 6.73\| 58.61\| 48.62\|	201	\|H48 h10 \|28.3 GiB\| 0.05\| 0.42\| 3.82\| 34.42\| 36.80\|
202	\|H48 h9 \|14.1 GiB\| 0.12\| 1.28\| 12.93\| \| \|	202	\|H48 h9 \|14.1 GiB\| 0.08\| 0.73\| 7.28\| \| \|
203	\|H48 h8 \| 7.1 GiB\| 0.25\| 2.72\| 27.42\| \| \|	203	\|H48 h8 \| 7.1 GiB\| 0.15\| 1.56\| 15.41\| \| \|
204	\|H48 h7 \| 3.5 GiB\| 0.37\| 4.24\| 47.10\| \| \|	204	\|H48 h7 \| 3.5 GiB\| 0.21\| 2.38\| 26.52\| \| \|
205	\|H48 h6 \| 1.8 GiB\| 0.69\| 8.18\| 91.85\| \| \|	205	\|H48 h6 \| 1.8 GiB\| 0.39\| 4.67\| 53.00\| \| \|
206		206
207	Time per cube adjusted for table size (in seconds \* GiB, lower is better).	207	Time per cube adjusted for table size (in seconds \* GiB, lower is better).
208		208
209	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|	209	\| Solver \| Size \|17 moves\|18 moves\|19 moves\|20 moves\|Superflip\|
210	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|	210	\|:---------\|:-------\|-------:\|-------:\|-------:\|-------:\|--------:\|
211	\|H48 h11 \|56.5 GiB\| 2.57\| 23.07\| 208.71\| 1788.12\| 1231.86\|	211	\|H48 h11 \|56.5 GiB\| 2.11\| 14.55\| 125.21\| 1071.23\| 957.47\|
212	\|H48 h10 \|28.3 GiB\| 2.01\| 19.77\| 190.14\| 1655.95\| 1373.79\|	212	\|H48 h10 \|28.3 GiB\| 1.48\| 11.96\| 107.83\| 972.35\| 1039.73\|
213	\|H48 h9 \|14.1 GiB\| 1.72\| 18.07\| 182.67\| \| \|	213	\|H48 h9 \|14.1 GiB\| 1.08\| 10.29\| 102.88\| \| \|
214	\|H48 h8 \| 7.1 GiB\| 1.74\| 19.21\| 193.74\| \| \|	214	\|H48 h8 \| 7.1 GiB\| 1.03\| 10.99\| 108.87\| \| \|
215	\|H48 h7 \| 3.5 GiB\| 1.29\| 14.98\| 166.41\| \| \|	215	\|H48 h7 \| 3.5 GiB\| 0.74\| 8.41\| 93.69\| \| \|
216	\|H48 h6 \| 1.8 GiB\| 1.21\| 14.47\| 162.36\| \| \|	216	\|H48 h6 \| 1.8 GiB\| 0.70\| 8.25\| 93.68\| \| \|
217		217
218	</details>	218	</details>
219		219
220	## Comments on the results	220	## Comments on the results
221		221
222	* Adjusting for table size, vcube generally is a bit faster than H48,	222	* Adjusting for table size, H48 is generally faster than vcube.
223	except for 20 moves scrambles where H48 is a clear winner.	223	* The gap between the two solvers is larger for scrambles with
		224	longer optimal solutions.
224	* On sets of 25 scrambles, H48 performs better than vcube when using	225	* On sets of 25 scrambles, H48 performs better than vcube when using
225	multiple threads. However, this advantage will likely disappear (or	226	multiple threads, compared to their single-threaded performance.
		227	However, this advantage will likely disappear (or
226	even invert) if we increase the size of the set.	228	even invert) if we increase the size of the set.
227		229
228	## Other notes	230	## Other notes