> In my training, it was basically assumed that floating point errors were negligible these days Yeah, that's what most of us think initially. The problem is t

> In my training, it was basically assumed that floating point errors were negligible these days Yeah, that's what most of us think initially. The problem is that the effects of error can compound in many ways -- nonlinearities, feedback, etc. can all wreck your accuracy enough to make the results meaningless. A really instructive counterexample for me was solving quadratics. Easy, right? Just try writing a solver for ax^2 + bx + c = 0. Now try breaking it. If all you did was use the quadratic formula, you should find that it's quite easy to break it, and surprisingly difficult to write a robust solver. (If you're completely stuck, consider the most obvious edge case: what if a ≈ 0? Any other scenarios you can think of?)