The above subraction is thus $$ \begin{equation} \frac{ |fl(a)-a|}{a}=\frac{ |fl(b)-fl(c)-(b-c)|}{a}, \tag{13} \end{equation} $$ yielding $$ \begin{equation} \frac{ |fl(a)-a|}{a}=\frac{ |b\epsilon_b- c\epsilon_c|}{a}. \tag{14} \end{equation} $$ The relative error is the quantity of interest in scientific work. Information about the absolute error is normally of little use in the absence of the magnitude of the quantity being measured.