Assume I have a real valued function $f(x_1,\ldots ,x_N)$ of some variables $x_i$ which I want to evaluate numerically. In general the formula for $f$ can contain products, rationals, trancendental functions etc. and  will be to long to investigate its numerical stability analytically. Or it will at least be to time consuming to do it in practice. Assume I do not have a shorter equivalent with guaruanteed stability. Is there a methodical procedure to analyse the numerical stability of $f$. I think of comparing it to arbitrary precission results obtained using a computer algebra system. Say the function will be implemented in C using stdlib functions and single or double precision. Which quantities should I compare to quantify the quality of the approximation at finite precission? How do I determine critical values of the variables? How can I choose the compiler and the compiler optimizations so other people can easily reproduce the results? ... I know that the problem setting is probably to generic to give good answers. But I still think that this is a common problem in computer science and wonder if there are references which propose standards to perform such analysis.