fsolve or nSolve with the option bisection_solver

This algorithm of dichotomy is the simplest but also generically the slowest. It encloses the zero of a function on an interval. Each iteration, cuts the interval into two parts. We compute the middle point value. The function sign at this point, gives us the half-interval on which the next iteration will be performed.
Input :

fsolve((cos(x))=x,x,-1.. 1,bisection_solver)

Output :

[0.739085078239,0.739085137844]