MATLAB: If-statement do not respond

if statement

Hei! I am running the following function in matlab:
function trig(a,b)
format long 
x=pi/9;
a=sin(4*x)
b=4*sin(x)*cos(x)-8*sin(x).^3*cos(x)
if (a==b)
    disp('verified')
end
After calculating variables "a" and "b" I got the following values a=0.984807753012208 and b=0.984807753012208 (a=b). The problem is that my if-statment do not display "verified" after running a script. But if I type "if (a<b)" I do get 'verified'. Why is it so?
Thank you in advance.

Best Answer

Check the difference between a and b:
>>b-a
ans = 1.110223024625157e-16
This is because floating point arithmetic is not exact on a computer. You accumulate small errors which means that, with floating point numbers that have been obtained by two different methods, you can never compare for equality with ==. Use a small enough tolerance for your case:
if abs(a-b) < 1e-14
   disp('verified')
end
Also note that format only change the precision of the display. It does not affect in any way how the numbers are stored.
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