Concerning 'numerical instability': with a sufficiently advanced type system you should be able to save yourself from something like numerical instability. You

Concerning 'numerical instability': with a sufficiently advanced type system you should be able to save yourself from something like numerical instability. You could e.g. ensure all numbers have an 'order of magnitude type' and define operations between 'order of magnitude' types to raise errors for certain (ranges of) combinations. However, there is (AFAIK) no convenient way to express this in any language, let alone without performance suffering greatly.