Unless you have optimized your code as much as possible to run on x86 or GPU and still find that you need a prohibitively expensive amount of processing power t

Unless you have optimized your code as much as possible to run on x86 or GPU and still find that you need a prohibitively expensive amount of processing power to accomplish the task, then and only then is an FPGA worth it. It is literally a DIY CPU architecture. So, unless you know exactly what it is about your current CPU's architecture that is holding you back, you won't be able to benefit from an FPGA-based design.