Faster than Binary search, Spllie Point, JAVA net beans

I have a NURBS spline function that computes a point on a spline. As you may know a spline function returns the x and y coordinate pair for a given t parameter of the spline. What I need is a function that takes the x coordinate as input and returns the t parameter. In the past I have done this with a binary search, but need something much faster that can do it in fewer steps. The shape of the spline makes it easy as the shape goes from left to right without reversal (monotonic). I will provide the spline function. You will make a function computes the required t input to get the desired return of x from the spline function. I need it in JAVA using net beans with a simple dialog that has the following inputs and returns. input field for the x parameter input field for the tolerance (how close x must be) execute button return field for the t parameter return field reporting the number of steps required to find t return field reporting the time required to compute it