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Which function is more accurate?

  1. Jan 28, 2010 #1
    1. The problem statement, all variables and given/known data
    You have a number system in base 10 with a precision of 5 digits. Which function is more accurate: x^2-y^2 or (x-y)(x+y)?

    2. Relevant equations
    None really.

    3. The attempt at a solution
    My intuition would tell me that (x-y)(x+y) is more accurate, since multiplication is less accurate than addition or subtraction (unless the two numbers are very close). But look at x = 1.0000, y = 0.00001:

    Actual value: 0.999999999

    x^2 = 1, y^2 = 1e-10 ~ 0

    x-y = 0.99999
    x+y = 1.00001 ~ 1
    (x-y)(x+y) = 0.99999

    So x^2-y^2 is more accurate, at least in this situation. I have no idea why, though.
  2. jcsd
  3. Jan 28, 2010 #2
    Which class is this for? If it's a programming class/computer architecture class/etc. the answer probably has to do with floating point errors and accumulated rounding errors.
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