how to round a rational number based on a given difference range

Hi,

I am taking two inputs from a user, VCR and x_diff. VCR can be integer or decimal, I used format rat to change it to Num/Den format. Then, this will be used later for other codes. My issue now, I want to round these Num and Den values based on a given acceptable difference range (x_diff), so for example VCR=0.76 and x_diff=0.02 would result in assiging VCR=0.75 which is 3/4 instead of 19/25 (0.76) The minimum Num and Den values the better for my problem. Another example, VCR=0.1 and using x_diff=0.1, the assigned new VCR is 0.2 which is 1/5 instead of 1/10 previously.

I have developed the code as following:

 function [VCR_new]= Rat_test(VCR, x_diff)
 % VCR= Gain, x_diff is acceptable difference
 F=[1 1 2 3 5 8 13 21 34 55 89 144]; % Fibonnacci series
 format rat  % change VCR to rational VCR=Num/Den
 for m=1:size(VCR,2);
    [Num(m), Den(m)] = numden(sym(VCR(m))); % Num of simplest form of VCR

    i=1; j=1; % initialization   
    if  x_diff~= 0
        while F(i)< Den(m) % to make sure assigned new number does not exceeding the Den(m)
            Den_new = i;

            for j=1: Den(m)
                VCRx_New = j/i;

                if  abs(VCRx_New- Num(m)/Den(m)) <= x_diff
                    Num(m)= j; Den(m)=i;
                    x_diff = 0;
                else
                end 
             end
            i=i+1;
        end
    else
end
    VCR_new (m)= Num(m)/Den(m);
end

My concern: Is there any way to minimize/optimize this code?

Thanks