The description below sounds intriguing.
In numerical analysis, the ITP method, short for Interpolate Truncate and Project, is the first root-finding algorithm that achieves the superlinear convergence of the secant method[1] while retaining the optimal[2] worst-case performance of the bisection method.[3] It is also the first method with guaranteed average performance strictly better than the bisection method under any continuous distribution.[3] In practice it performs better than traditional interpolation and hybrid based strategies (Brent's Method, Ridders, Illinois), since it not only converges super-linearly over well behaved functions but also guarantees fast performance under ill-behaved functions where interpolations fail.[3]