Chapter 12.7, Problem 60E

Floating-point operations In general, real numbers (with infinite decimal expansions) cannot be represented exactly in a computer by floating-point numbers (with finite decimal expansions). Suppose that floating-point numbers on a particular computer carry an error of at most 10^–16. Estimate the maximum error that is committed in doing the following arithmetic operations. Express the error in absolute and relative (percent) terms.

a.    f(x, y) = xy

b.     $f\left(x,y\right)=x/y$

c.    F(x, y, z) = xz

d.     $F\left(x,y,z\right)=\left(x/y\right)/z$