exp(log(x))-x?

Analytically, exp(log(x))-x should give zero.

But In matlab, it is not zero

x=linspace(1,10,10);
exp(log(x))-x;

for x=1 to 10, the answer is

0   
0   
-4.44089209850063e-16   
0   
0   
0   
0   
-1.77635683940025e-15   
1.77635683940025e-15    
1.77635683940025e-15

what is happening?

and how can I fix this?

[Adam]

It is 0 to within a certain precision. The results of mathematical operations involving doubles rarely produce the exact results due to the precision of the representation.

Why do you need to "fix it"? In what context are you using it?

Answer 1

[Azzi Abdelmalek]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Answer 2

[John D'Errico]

You cannot "fix" it, not as long as you work with numbers represented in floating point arithmetic. Floating point arithmetic is not mathematics. The two look a lot alike, but they are not the same.

The only fix available is in your mind, learning what you can and cannot do. Of course, if you are willing to always work in symbolic form, then you can resolve this. Your code will be painfully slow then.