Merge the "solver-experiments" branch that I have been working on for

a few weeks. This include mainly three things:

1. Various tweaks for a total performance gain of around 30%.
2. Take into account symmetries and avoid repeated work. This
   required a re-work of the splitting into tasks before the solve.
3. Add a second fallback table (eoesep). This gives huge performance
   gains for particular scrambles (e.g. superflip).

After merging this commit, remove and re-generate all pruning tables.

Squashed commit of the following:

commit 60f0705d2d69050e6a30581a2810f686d6f69b80
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Sat Dec 7 16:06:48 2024 +0100

    Fix indentation

commit cc5d489a251812b6188c0ba264ac6cb2236f1afe
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Sat Dec 7 15:56:19 2024 +0100

    Updated documentation

commit a3f605dd628546e52564f82b139feb473b0725f3
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Sat Dec 7 14:01:11 2024 +0100

    use eoesep table as second fallback

commit c75e43c9116c64f97e92b0fe038be8a032925a72
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Fri Dec 6 16:13:23 2024 +0100

    First commit for gendata_eoesep

commit fea7688ab8bdc5ae0c3480622e2510a3bcd39248
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Dec 3 17:31:00 2024 +0100

    Add scramble to tool

commit 66866cb71dea4ca8278ecb9e90ff4295771feb42
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Dec 3 17:22:59 2024 +0100

    Added tool to check multiple solutions

commit ef65611c772c3996bddca8d181da3538e0af1674
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Dec 3 17:16:20 2024 +0100

    Write all solutions for symmetric positions

commit e3ded26db7d7d4ae7c0e2488151ed14f581f7b8e
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Nov 26 09:14:54 2024 +0100

    Added symmetry filter (TODO: print excluded solutions)

commit 864c437a9751c58d58562650ca9eba4a9e6ad3eb
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Mon Nov 25 14:51:13 2024 +0100

    Improved task split

commit b88926d36d7ab0c64c5fe3bb954fd15d41267fba
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Fri Nov 22 19:06:41 2024 +0100

    Reworked tasks for multi-threading in view of symmetry filter

commit 26fa653f97df8cd601aecb80eaf89f0a00e9ba9f
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Thu Oct 31 15:37:43 2024 +0100

    Added transform move

commit 19f655ef94d658eaa2fefb5cea3c167a3ec58db6
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Thu Oct 31 09:29:15 2024 +0100

    Clarified doc

commit 3b0fe1e5ef8b628854e30f0f0067300e2763c954
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Thu Oct 31 08:36:58 2024 +0100

    Handle solved cube correctly

commit 57705cbc4982e3abe97a36ed64871738d4f721c0
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Thu Oct 31 08:24:30 2024 +0100

    Close file

commit fc7d462b58bcf3d3a3fbf26c1f3bd04c640a4898
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Oct 29 15:05:48 2024 +0100

    Removed stats tool

commit 359bf7cb49ef405ee76ed662207d47cb2abcc5a9
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Oct 29 15:01:51 2024 +0100

    Updated theory doc

commit 39c315af562bc4ce896f41004388a4c34d475d37
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Oct 29 14:51:40 2024 +0100

    Remove unused constants

commit 57a5d24538aa59a4df9221dad2f99e9f0286bd9d
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Tue Oct 29 10:20:38 2024 +0100

    Add tool to solve scrambles from file

commit 07e2918c216636891b1fa6adecc9756086a901e9
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Mon Oct 28 17:00:00 2024 +0100

    Add make table to tool

commit f5e5266c654eb027a5a35c57cc618555246f5e5e
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Mon Oct 28 09:35:49 2024 +0100

    Remove old solver, other small things

commit a1ec78025b7959dbb845213f7f4e6851ecebc204
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Sun Oct 27 02:00:29 2024 +0200

    Improvements

commit 8eea23dbe888d923e662e24ae969130e2c67b999
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Sat Oct 26 12:24:19 2024 +0200

    Makefile fix

commit 3fc3927beacc78971cefeb42da8d71fe6c015fc1
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Fri Oct 25 18:25:09 2024 +0200

    More performance gains

commit 7b4efa1f9af9722de1ab9ccfc27899825a0d12c4
Author: Sebastiano Tronto <sebastiano@tronto.net>
Date:   Fri Oct 25 15:53:20 2024 +0200

    Alternative solver implementation, small performance gain

2 files changed, 29 insertions, 5 deletions

diff --git a/doc/h48.md b/doc/h48.md
index 323453a..678e160 100644
--- a/doc/h48.md
+++ b/doc/h48.md
@@ -230,9 +230,8 @@ can be one of three kinds:
   If the base value is `b`, a pruning value of 1, 2 or 3 can be used directly
   as a lower bound of b+1, b+2 and b+3 respectively. However, a value of 0
   could mean that the actual lower bound is anything between 0 and b, so we
-  cannot take b as a lower bount. Instead we have to use a pruning value from
-  another table, for example the corner-only table mentioned in the previous
-  section, or a completely new one.
+  cannot take b as a lower bound. Instead we have to use a pruning value from
+  another table - see the section "Fallback tables" below.
 * 1 bit per entry, or `k1`: With one bit per entry, the only information we
   can get from the pruning table is wether or not the current position
   requires more or fewer moves than a fixed base value b. This can still be
@@ -240,6 +239,24 @@ can be one of three kinds:
   pruning values.
   (Work in progress - `k1` tables not available in the code yet)
 
+### Fallback tables
+
+When a pruning table does not store the exact lower bound value, for
+example in the case of `k2` table as described above, we need to refine
+our estimate using another table, which we call *fallback table*.
+In the current implementation, we actually use two different tables:
+
+* **h0** table: for larger `k2` tables we get a fallback value from the full
+  table for the **h0** coordinate.
+* edges-only table: to improve the pruning value for certain specific
+  scrambles, namely whose with solved corners such as the superflip,
+  we employ a second table that takes into account the edges of a full
+  **h11** coordinate. This table is small (around 1MB).
+
+More tables could be used to refine the fallback estimate, but each
+additional table leads to longer lookup times, especially if it is
+too large to fit in cache.
+
 ### Estimation refinements
 
 After computing the pruning value, there are a number of different tricks
@@ -285,6 +302,12 @@ as described above. For doing this, we need to replace the cube with its
 inverse, and keep track of the moves done from now on so that we can
 invert them at the end to construct the final solution.
 
+When this technique is used, it is also possible to avoid some table
+lookups: if the last move applied to the cube is a 180° move *on the
+inverse position*, then the coordinate on the normal position has not
+changed. Thus if we keep track of the last computed pruning value,
+we can reuse it and avoid an expensive table lookup.
+
 ### Other optimizations
 
 Other possible (low-level) optimizations include:
@@ -344,7 +367,7 @@ don't have this much memory.
 
 ### 2 bits tables with for h0 and h11
 
-(Work in progress - currently I there is no specialized routine for
+(Work in progress - currently there is no specialized routine for
 computing 2 bits table for "real" coordinates; instead, an optimized
 version of the generic method explained below is used)
 
diff --git a/doc/transformations.md b/doc/transformations.md
index a180ce6..65212ea 100644
--- a/doc/transformations.md
+++ b/doc/transformations.md
@@ -6,4 +6,5 @@ For example, to apply the transformation RBm (mirrored RB) to a cube C:
         1. Apply a mirror along the M plane to the solved cube
         2. Rotate the mirrored cube with z' y2
         3. Apply the cube C to the transformed solved cube
-        4. Apply the transformations of step 1a and 1b in reverse
+        4. Apply the transformations of step 2 in reverse
+        5. Apply the transformations of step 1 in reverse