Pseudocode search for intersection of y = x and y = cos(x)

Parts of the graphs of two functions, $f(x) = x$ and $g(x) = \cos(x)$, are shown below, where $x$ is measured in radians.

The pseudocode below describes a simple algorithm to find the point where the two functions intersect.

define intersect(x0, x1):
    x ← x0
    while x < x1
        if -0.01 < cos(x) - x < 0.01 then
            return x
        end if
        x ← x + 0.01
    end while
    return "No intersection found"