I know how 8 move comms work, and I can follow the pieces through the solve, but I don't understand how to make the commutators cancel moves with the solution. I would just be sticking in an 8 mover during the solve and hoping for some good luck.
For instance my recent solve leaving three corners was:-
R' U' F R' F' L F L' F2 . R2 D R D' U F L F' L' F' D2 B D' F D2
So stepping through I found
Insert @ . = D' L' D R2 D' L D R2 = 3 cancellations
So insert the commutator there and the solve can then be written as
[First part of original solve][Inserted Commutator][Last part of the original solve], ie
[R' U' F R' F' L F L' F2
] [D' L' D R2 D' L D
R2] [R2 D R D' U F L F' L' U' F' D2 B D' F D2
]
But there is no point doing R2 following by R2 because R2 and R2 cancel themselves out so we remove both of them as the net effect is the two moves didn't do anything to the cube:-
R' U' F R' F' L F L' F2 D' L' D R2 D' L
D D R D' U F L F' L' U' F' D2 B D' F D2
And now we see D followed by D, well that is exactly the same is writing D2 so:-
Final Solution = R' U' F R' F' L F L' F2 D' L' D R2 D' L D2 R D' U F L F' L' U' F' D2 B D' F D2 = 30 HTM
....
So you are looking for as many of the moves at the beginning and end of the commutator to match the moves in the solution at the insert point. As you step through you can tell if the first move of the comm is the same face you just stepped and the same goes for the last move of the comm and the next move you would make. Hope that clarifies somewhat.
Edit: Say you were lucky enough to find the following insert:-
[R' U' F R' F' L D L D] [D' L' D R2 D' L D R2] [R2 D' L' U F L F' L' U' F' D2 B D' F D2]
Well lets look at the start of the comm D' cancels with the D before it. Both can be removed = 2 cancellations. So after those two moves are removed the L' and L cancel = 2 more cancellations. Now we see a D and a D, that can be changed to D2 for another single cancellation. Now to the end of the comm. Well R2 and R2 cancel = 2, D and D' for another 2, then L and L' for another 2, then its D' and U. So 11 cancellations. In this very lucky case inserting the commutator actually resulted in the final solve being shorter than the original skeleton, we added 8 moves and ended up removing 11 moves. Definately worth looking for
