In the machine a number is represented as $$\begin{equation} fl(x)= x(1+\epsilon) \tag{7} \end{equation}$$

where $|\epsilon| \leq \epsilon_M$ and $\epsilon$ is given by the specified precision, $10^{-7}$ for single and $10^{-16}$ for double precision, respectively. $\epsilon_M$ is the given precision. In case of a subtraction $a=b-c$, we have $$\begin{equation} fl(a)=fl(b)-fl(c) = a(1+\epsilon_a), \tag{8} \end{equation}$$ or $$\begin{equation} fl(a)=b(1+\epsilon_b)-c(1+\epsilon_c), \tag{9} \end{equation}$$