I am attempting to use the Wolfram Language to derive a function f(x,z), where x is the desired accuracy in base-2 digits and z is the input, to model the convergence rate of a continued fraction used to approximate $e^z$. I have generated a CSV file containing millions of sample entries, where each row represents f(x,z),z,x. I uploaded the csv file to my website if you want a peek at it: https://jackgiffin.com/main/mischelppages/cont-fraction-convergence-e-samples.txt.

However, I have ran into three problems, one of which I can find no solution to.

1. FindFormula does not seem to be able to generate a function with multiple inputs
2. FindFormula return piecewise equations, which are bad for projecting much higher approximations. My partial solution is just to generate a lot of formulas and select the first one that is not piecewise.
3. FindFormula does not seem to have an overestimate option. Ideally, there would be an option to make FindFormula find a formula which is never less than the true value. My partial solution id just a to add 1 or 2 to the resulting equations.

Here is the code I am currently using to generate one-input function: