I’m not sure what you ultimately want to do but its quite common to start with
a simple tractable system so you can compare exact and numerical results.
The FE code isn’t magic, you can compare the Simpson results to the
PO elements maybe.
I don’t know what kind of code FF actually generates and how slow it is
vs modern FPU exception handling, probably including div by zero ,
but the latter can be very slow. I couple
decades ago, we had some audio code that had to work in real time
and it generally did well but stopped keeping up ( 8jhz sample rate lol with
an ACELP decoder and maybe a high-order elliptic filter ). IIRC, the problem
was feeding the FPU denomral numbers. Checking the intel data books
these don’t seem to be handled too quickly 