Evaluating polynomials to 5 significant figures but only 1 sig fig returns - Maple Programming

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For example, A polynomial is defined as follows:

f := (x, y) -> 333.75y^6 + x^2(11x^2y^2 - y^6 - 12y^4 - 2) + 5.5y^8 + 1/2*x/y

In maple, I look to evaluate this to 5 significant figures like so:

evalf[5](f(77617,33096))

And obtain a value that is: 1*10^32.

Why is this not to 5 sig fig? Why is this not close to a value of 7.878 * 10^29 as you increase the number of sig fig required?

Thanks!

polynomials maple
1 Answers

Don't reduce the working precision that low, especially if you are trying to compute an accurate answer (and then round it for convenience).

More importantly, for compound expressions the floating-point working precision (Digits, or the index of an evalf call) is just that: a specification of working precision and not an accuracy request.

By lowering the working precision so much you are seeing greater roundoff error in the floating-point computation.

restart;
f := (x, y) -> 333.75*y^6
    + x^2*(11*x^2*y^2 - y^6 - 12*y^4 - 2)
    + 5.5*y^8 + 1/2*x/y:

for d from 5 to 15 do
    evalf[5](evalf[d](f(77617,33096)));
end do;

                   32
               1 10  

                   31
              -3 10  

                   30
               1 10  

                   29
               8 10  

                    29
              7.9 10  

                    29
             7.88 10  

                     29
             7.878 10  

                     29
            7.8784 10  

                     29
            7.8785 10  

                     29
            7.8785 10  

                     29
            7.8785 10
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