Each function or subroutine has a declared performance characteristic, these represent how the performance of a function can be predicted.
The function always executes around the same amount of instructions. Depending upon the actual values passed in the arguments there might be insignificant variations but do not contain any iterative solver. The behavior of standard library functions used is not considered for this performance classification.
The function uses an iterative root finding algorithm to compute the result. In the library all functions which use iterative solvers have a maximum amount of iterations, after which they will fail.
Iterative solvers are usually non-linear root finding methods such as Newton-Rapshon, False Position or Bisection style solvers or can be solvers for differential equations such as Runge-Kutta methods as described in [DKahaner1988].