This is a follow-up of a previous question.
Let $p$ be a polynomial with floating-point coefficients.
Is there a method for finding intervals where evaluating $p$ in floating-point arithmetic always gives the correct sign?
I want to find (ideally, maximal) disjoint interval $I_1, \dots, I_m$ such that for all floating-point numbers $a \in I_k$, the sign of $f(a)$ is always correct.
This is clearly related to isolating the zeros of $f$.
A standard example, where the sign of $f$ is wrong around a zero is $f(x)=x^6 - 6 x^5 + 15 x^4 - 20 x^3 + 15 x^2 - 6 x + 1$ near the multiple zero $x=1$. Note the $f(x)$ is the expansion of $(x-1)^6$.