Consider the problem of computing $\backslash$alpha $=$ ab $+$ cd $=0$ in a finite decimal system F with

the unit roundoff $\backslash$mu $,$ where a$,$ b$,$ c$,$ d in F$.$ Let $\backslash$alpha $=$ f l$($ab $+$ cd$)$ be the computed value of

$\backslash$alpha with the rounding policy. It has the form

$\backslash$alpha $=$ ab$(1+\backslash$delta $1)+$ cd$(1+\backslash$delta $2),|\backslash$delta $1|,|\backslash$delta $2|<=2\backslash$mu $,$

where $\backslash$mu is the machine precision. Derive an upper bound for the relative error

$\backslash$alpha $\backslash$alpha

$\backslash$alpha