# Quick evaluation of floating point Absolute Error

I need to to find a quick and dirty way to estimate the absolute error introduced by a series of agebraic operations of IEEE single precision floating point numbers, a pessimistic result is ok.

The way I am doing it, is to evaluate the biggest possible value that can be obtained during the chain of operations, find the power of two immediately greater than that number, and multiply such power of two by the number of algebraic operations performed and by the value of the least significant bit in the significand assuming exponent 1 (which is 0.00000011920928955078125)

Does it look like a sensible approach, or am I missing something?

• You could do this with interval arithmetic. Generally, what you're asking for is called validated numerics. Also, I must say it's not very clear why the approach you describe would produce a valid bound. Isn't something like $(x^{1/2^n})^{2^n}$, $0\leq x\leq 1$, evaluated with $n$ repeated square roots and $n$ repeated squares a counterexample? It seems like you could be making some specific assumptions that aren't valid in general. This is potentially a difficult problem, so a quick and dirty way might not exist and be useful at the same time. – Kirill May 17 '17 at 15:30