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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 $$ x_1, x_2 \in [1E-5,\ 1E+5] $$

aban
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  • How can you answer this without knowing the distribution of the roundoff of the factors ? –  Apr 29 '19 at 06:54
  • The word distribution is normally used in the context of stochastic variables. Even after the edit it is not clear what you mean. – Carl Christian Apr 30 '19 at 18:34

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