Obvious Result Wrong in Matlab

[knowLittle]

clf;
clear all;
syms x
%t=linspace(0, pi);
%x=t;

f=@(x) exp(-x).*cos(2*x)

h1=ezplot(f,[ 0, pi]); %plots the function f

f(pi./4)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
My output gives me:

f =

@(x)exp(-x).*cos(2*x)


ans =

2.7918e-017
%%%%%%%%%%%%%%%%%
But, the real answer is 0.

I'm clueless. Please, help.

 

[jhae2.718]

Your result is equivalent to zero within the precision of double precision floating point arithmetic.

 

[knowLittle]

Ok. Could you explain me, how to read 2.7918e-017?

 

[Dickfore]

$$2.7918 \times 10^{-17} = 1.000000011_{2} \times 2^{-55}$$

 

[jhae2.718]

It's $2.7918\times10^{-17}$, which is an order of magnitude less than the minimum number representable under double precision, which is of the order 10^-16. This value is called the machine epsilon, and you can find it using the MATLAB eps command.

 

[knowLittle]

Thank you.

 

[jhae2.718]

If you're interested in floating point arithmetic, most computers conform to the IEEE754 standard.

 

[knowLittle]

Thank you, I'll take a look.