% Rounding Error Example % % Ken Jackson 8 Sept. 2008 format long e x = 1.e-13 y = 1. + x - 1. ry = (y - x) / x z = 4. + x - 4. rz = (z - x) / x % In exact arithmetic, x = y = z, but the computed values are not equal? % If you run the program above you will get % % x = 1.000000000000000e-13 % % y = 9.992007221626409e-14 % % ry = -7.992778373591440e-04 % % z = 1.003641614261142e-13 % % rz = 3.641614261141482e-03 % % Can you explain why the relative errors are so large?