I recently had an interesting conversation with Xin Yi, of NUDT, about accurately evaluating the polynomial \(P(x) = 5x^2 - 3\) near its root \(x = \sqrt{3/5}\). He wanted to know: what's the most accurate way to evaluate this polynomial, and why doesn't Herbie find it? Error in evaluating polynomials Evaluating a polynomial P(x) at one of its roots is bound to be inaccurate. If you pick a floating point input x, think of it as representing a range (x-ε, x+ε). and very close to a zero, P(x-...
