JMP jsl should have a function to find a root (zero) of a function given bracketing points, similar to uniroot() in R. Minimize(Abs(function)) is not adequate, as it doesn't know that zero is possible, and may stop way too soon. Ridders' ( Ridders' method - Wikipedia ), Brent's ( Brent's method - Wikipedia ), or Muller's ( Muller's method - Wikipedia ) methods seem to offer high efficiency. Ideally, the implementation should support discontinuities in the function, so that it can also be used to invert discrete cdf's or solve for Blaker (2000) exact discrete confidence intervals.