Golden Section Search--When to use it?

I have some x inside an interval say [a,b] where I know that my solution lies. Due to the nonlinearity of the problem solving it by traditional agorithms is not possible. I can evaluate each point inside the interval.

I wish to do a search applying the compostion of a few functions to points within the interval until I reached some value close enough to some Epsilon (haven't decided how close I need to be).

I've explored bisecting the interval until I reach the solution, but I was wondering if the Golden section search would be a better choice. Does this converge any faster or am I wasting my time exploring this method? Suggestions anyone?

Thanks,

just2peachy