An SBV solution to the bit-precise puzzle of shuffling the bits in a 64-bit word in a custom order. The idea is to take a 64-bit value:

1.......2.......3.......4.......5.......6.......7.......8.......

And turn it into another 64-bit value, that looks like this:

12345678........................................................

We do not care what happens to the bits that are represented by dots. The problem is to do this with one mask and one multiplication.

Apparently this operation has several applications, including in programs that play chess of all things. We use SBV to find the appropriate mask and the multiplier.

Note that this is an instance of the program synthesis problem, where we "fill in the blanks" given a certain skeleton that satisfy a certain property, using quantified formulas.