I have implemented Quine-McCluskey method of boolean function simplification. I ended up with the table of prime implicants:

As you can see my results are the same as these on wikipedia. However now I need to create the simplest formula using the implicants. I found out about Petrick's method. To me, it seems very human-intuitive, though quite long - but I can't think how should computer apply this method. It seems really like a calculating equation. Computers need a lot of help to deal with equations.
Is there a different way to think about it?