%% Annotated Matlab transcript -- 1/30
%% CS 323 - Doug DeCarlo

% loss of significance error example
% comparing x*(sqrt(x+1)-sqrt(x)) against
%           x/(sqrt(x+1)+sqrt(x))

% Ok for this interval...
x = 0:1:1000;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'b',x,x./(sqrt(x+1)+sqrt(x)),'g');
x = 0:1e3:1e6;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'b',x,x./(sqrt(x+1)+sqrt(x)),'g');
x = 0:1e10:1e12;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'b',x,x./(sqrt(x+1)+sqrt(x)),'g');
% Now problems become apparent and just get worse...
x = 0:1e12:1e14;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'b',x,x./(sqrt(x+1)+sqrt(x)),'g');
x = 0:1e14:1e16;
plot(x,x.*(sqrt(x+1)-sqrt(x)),'b',x,x./(sqrt(x+1)+sqrt(x)),'g');