given any two floating numbers on a PC. what is the distribution of the roundoff error of their multiplication?
Using math
let $x_1$ and $x_2$ be two floating numbers, the true value of their multiplications is $x=x_1 x_2$, the number represented on a PC is $\hat{x}$. What is the distribution of
$$ \frac{|\hat{x} - x|}{|x|} \text{?} $$
[update]
let's set the range of $x_1$ and $x_2$ as $$ x_1, x_2 \in [1E-5,\ 1E+5] $$