"how numbers are stored in computers""how numbers are stored in computers"
The rounding error incurred when using the following formula to compute the area of a triangle:
is at most , provided that subtraction is performed with a guard digit, , and square roots are computed to within ulp.
The condition that is true for virtually every real floating-point system. For example, when , ensures that , and when , is sufficient.
A formal way to write the relative error of this expression is