Years ago I participated in a CTF where one of the challenges was to produce Fractran programs that met certain requirements. They were relatively simple-sounding things like computing the nth power of two, but even that is a bit of a pain in Fractran. I initially tried something similar to this article, manually compiling programs that use only the (Turing-complete) JZDEC instruction on paper. Unfortunately, there was a length limitation which made this approach impossible as it did not produce fraction lists nearly as small as one can write by hand. I ended up finding it easier to write a program to brute force all possible Fractran programs under the length limit until one of them had the correct behavior than to actually write useful Fractran code by hand.