function [y] = detpep108d(xx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% DETTE & PEPELYSHEV (2010) 8-DIMENSIONAL FUNCTION
%
% Authors: Sonja Surjanovic, Simon Fraser University
%          Derek Bingham, Simon Fraser University
% Questions/Comments: Please email Derek Bingham at dbingham@stat.sfu.ca.
%
% Copyright 2013. Derek Bingham, Simon Fraser University.
%
% THERE IS NO WARRANTY, EXPRESS OR IMPLIED. WE DO NOT ASSUME ANY LIABILITY
% FOR THE USE OF THIS SOFTWARE.  If software is modified to produce
% derivative works, such modified software should be clearly marked.
% Additionally, this program is free software; you can redistribute it 
% and/or modify it under the terms of the GNU General Public License as 
% published by the Free Software Foundation; version 2.0 of the License. 
% Accordingly, this program is distributed in the hope that it will be 
% useful, but WITHOUT ANY WARRANTY; without even the implied warranty 
% of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 
% General Public License for more details.
%
% For function details and reference information, see:
% http://www.sfu.ca/~ssurjano/
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% INPUT:
%
% xx = [x1, x2, ..., x8]
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

x1 = xx(1);
x2 = xx(2);
x3 = xx(3);

term1 = 4 * (x1 - 2 + 8*x2 - 8*x2^2)^2;
term2 = (3 - 4*x2)^2;
term3 = 16 * sqrt(x3+1) * (2*x3-1)^2;

outer = 0;
for ii = 4:8
    inner = 0;
    for jj = 3:ii
        xj = xx(jj);
        inner = inner + xj;
    end
    new = ii * log(1+inner);
    outer = outer + new;
end

y = term1 + term2 + term3 + outer;

end