Numerical simulations that I know of, all use steps or iterations of some type. Even if we start with theoretical infinite/perfect precision of the double pendulum, the numerical simulation will diverge from (ideal frictionless!) reality.

Two simulations of chaotic systems (starting identically) with different step sizes will always diverge (The difference in eventual positions does not stabilise as steps are made smaller). For this reason, I am not even sure if infinitesimal steps would avoid divergence from (ideal) reality. Plus y'know, the whole issue of a simulation with infinitesimal steps never making ANY progress, regardless of how fast it runs.

Therefore, I conclude that infinite degrees of precision is not the issue or solution for numerical explanation of chaotic behavior.