If u and y are floating-point numbers, then the evaluation of f(x,y) = -r-V 22 y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic for parts (a) and (b) below. (a) Let I = 123.4 = 0.1234 x 103 and y = -1.234 = -0.1234 x 10', evaluate fi (F(1, y)) and determine the relative error. (b) Now let x = -123.4 = -0.1234 x 103 and y = 1.234 = 0.1234 x 101, evaluate fl(fr, y)) and determine the relative error. (c) Based on the above results and similar kinds of computations (you might do some more computations, but it is not necessary to hand them in), specify which ranges of values of u and y are such that the computation of f(f(z,y) will always be very inaccurate? (Your ranges can be loosely deifned, that is, you do not have to give specific numeric bounds. You may say things like "large x, or "large y", or "small positive x, etc.) If u and y are floating-point numbers, then the evaluation of f(x,y) = -r-V 22 y in a floating point system may be very inaccurate due to cancellation. To illustrate, use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic for parts (a) and (b) below. (a) Let I = 123.4 = 0.1234 x 103 and y = -1.234 = -0.1234 x 10', evaluate fi (F(1, y)) and determine the relative error. (b) Now let x = -123.4 = -0.1234 x 103 and y = 1.234 = 0.1234 x 101, evaluate fl(fr, y)) and determine the relative error. (c) Based on the above results and similar kinds of computations (you might do some more computations, but it is not necessary to hand them in), specify which ranges of values of u and y are such that the computation of f(f(z,y) will always be very inaccurate? (Your ranges can be loosely deifned, that is, you do not have to give specific numeric bounds. You may say things like "large x, or "large y", or "small positive x, etc.)