New hex-axes search 2x faster than triple-axes search

One interesting option in Kociemba's Cube Explorer is the Triple Search option. This option searches along three axes at once, instead of just one. How much does Triple Search help? For random cubes, when searching for a length 20 solution, it helps tremendously. I implemented my own Kociemba solver with single-axis search, triple-axis search, and a new "six-axis" search, and compared the amount of time needed to find length 20 or better solutions for 3,000 random cubes. This program was single-threaded (Kociemba's cube explorer is multi-threaded), runs only from the command line, and is brand new code (so it has not been heavily optimized yet). The time to run is as follows:
Single-axis search  17m50s    2.8 sols/s
Triple-axes search   3m55s   12.8 sols/s
Hex-axes search      1m40s   30.0 sols/s
This shows that for this specific problem, triple-axes search is much faster than single-axis search, and hex-axes search is faster yet. What is hex-axes search? It is simply solving the three axes of the original position in parallel with the three axes of the *inverse* position. (Of course you should check that the original position is not isomorphic to the inverse position.) If anyone else has a Kociemba solver and would like to confirm these results, that would be greatly appreciated.

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Made some improvements in speed, so the numbers are now, this time to run 30,000 random cubes:
Single-axis  24m9s  20.7 sols/s
Triple-axes  3m56s   127 sols/s
Hex-axes      2m5s   240 sols/s
So things are much faster now, but the relative speeds of the strategies remain approximately the same.