Re-examining representation of primitive numerical types

I've discovered the work of Oskar Mencer at Imperial College. He is examining ways to vary number representation using FPGAs. Instead of simplying choosing an Integer or a Floating Point type in your language of choice, he is started to take advantage of the reconfigurable FPGA to find optimal representation of each type against specific metrics.

One important point he does make is in calculating a primitive function like sin(x). Many researchers have published methods to compute sin(x), yet there is no mention when to use which method. Furthermore, even after you choose the method, there are many options that can be adjusted. How do you choose which options to adjust?