What is wrong with my Simpson algorithm?

Question

I was trying to write an algorithm to approximate integrals with Simpson's method. When I try to plot it in a loglog plot, however, I don't get the correct order of accuracy which is O(h^4) (I get O(n)). I can't find any errors though. This is my code:

%Reference solution with Simpson's method (the reference solution works well)
yk = 0;
yj = 0;
href = 0.0001;
mref = (b-a)/href;

for k=2:2:mref-1
    yk=yk+y(k*href+a);
end

for j=1:2:mref
    yj=yj+y(href*j+a);
end
Iref=(href/3)*(y(a)+y(b)+2*yk+4*yj);

%Simpson's method
iter = 1;
Ehmatrix = 0;
for n = 0:nmax
    h = b/(2^n+1);
    x = a:h:b;
    xodd = x(2:2:end-1);
    xeven = x(3:2:end);
    yodd = y(xodd);
    yeven = y(xeven);
    Isimp = (h/3)*(y(x(1))+4*sum(yodd)+2*sum(yeven)+y(b));
    E = abs(Isimp-Iref);
    Ehmatrix([iter],1) = [E];
    Ehmatrix([iter],2) = [h];
    iter = iter + 1;
end

figure
loglog(Ehmatrix(:,2),Ehmatrix(:,1))

a and b are the integration limits and y is the integrand that we want to approximate.

Answer 1

Taking into account Geoff's suggestions, and making a few other changes, it all works as expected.

%Reference solution with Simpson's method (the reference solution works well)
a=0;
b=1;
y=@(x) cos(x);
nmax=10;

%Simpson's method
Ehmatrix = [];
for n = 0:nmax
    x = linspace(a,b,2^n+1);
    h = x(2)-x(1);
    xodd = x(2:2:end-1);
    xeven = x(3:2:end-1);
    yodd = y(xodd);
    yeven = y(xeven);
    Isimp = (h/3)*(y(x(1))+4*sum(yodd)+2*sum(yeven)+y(b));
    E = abs(Isimp-integral(y,0,1));
    Ehmatrix(n+1,:) = [E h];
end

loglog(Ehmatrix(:,2),Ehmatrix(:,1))

P=polyfit(log(Ehmatrix(:,2)),log(Ehmatrix(:,1)),1);    
OrderofAccuracy=P(1)

You were getting O(h) accuracy because xeven=x(3:2:end) was wrong. Replacing it by xeven=x(3:e:end-1) fixes the code, and thus the accuracy.