I downloaded an evaluation version of Mathematica, and FindFormula was able to find an exact solution to Sin(3 * Sin(x)) after around 30 seconds of computation. That probably explains why it's not available on Alpha -- way too computation intensive.

My concern now is that with anything more complicated, you can't tell if the calculation is making progress to a solution. There is also the function NonlinearModelFit which requires a structured parametric model and also works with the same limitations.

So the benefit of Eureqa is that it will provide a continuous updating of the solution, allowing one to evaluate progress. And the Excel Solver also has a continual updating of the objective function value, at any which point in time the computation can be terminated.

My concern now is that with anything more complicated, you can't tell if the calculation is making progress to a solution. There is also the function NonlinearModelFit which requires a structured parametric model and also works with the same limitations.

So the benefit of Eureqa is that it will provide a continuous updating of the solution, allowing one to evaluate progress. And the Excel Solver also has a continual updating of the objective function value, at any which point in time the computation can be terminated.