% Math 5610/6860 - Numerical Analysis I
% Computer lab #2, problem 3

% here is a demonstration of a series of operations where the relative error is
% not guaranteed to be less than machine epsilon
x = 1; y=2^-54; z=1;

% this is rounded to 1 since y < machine epsilon
fprintf('x+y= %e     (rounding takes out y) \n',x+y); 

% therefore the following gives the wrong answer!!
fprintf('(x+y)-z= %e (wrong answer)\n',(x+y)-z);

% note: in Matlab you can find out what is machine epsilon by using the
% builtin function eps:
fprintf('machine epsilon is: %e and should be %e\n',eps,2^-52);