The rate of divergence would not be steady or linear. Particular events would accelerate it or lead to sudden insights or changes of approach for either of you.
You can only predict it after you've run the simulation once, and after you have let the simulated person do what they want to for the first time. During the first run, free will is unpredictable.
Only after you have run it can you say "if I run the simulation again with the exact same parameters, I know what they will do next".
And if you find a way to create a faster version of the simulated person algorithm, then the problem just devolves to the faster version. How can you predict what the fast-free-will person will do before you let it do what it wants to do? And so on.