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Simulating strong-field quantum electrodynamics (QED) processes in extreme plasmas traditionally requires memory-intensive precomputed lookup tables and expensive numerical inversion of cumulative probability distributions. To eliminate this bottleneck, this work models the auxiliary rate functions and cumulative probabilities for synchrotron radiation and nonlinear Breit–Wheeler pair production using specialized Padé approximants. The resulting formulation inverts event probabilities via an exact closed-form quartic equation, reproducing exact QED particle spectra within 1% error without tables, interpolation, or iterative root-finding.
Extreme-field QED simulations can abandon memory-bound lookup tables and iterative root-finding entirely: tailored Padé approximants collapse event sampling to an exact closed-form quartic solve with sub-1% error.
Monte Carlo sampling of strong-field quantum electrodynamics processes underpins simulations of high-intensity laser experiments and of astrophysical compact-object magnetospheres. Sampling an event requires the total rate of the process together with the cumulative probability that determines how energy is partitioned between the produced particles. Simulations typically tabulate both in advance and invert the tabulated probability numerically. Here we replace this procedure with elementary-function approximations for synchrotron radiation and the nonlinear Breit--Wheeler process. For each process, we approximate the auxiliary function that sets the total rate, as well as the cumulative probability, with Pad\'e approximants chosen so that the inversion reduces to a quartic equation. This yields the sampled quantum parameter---electron $\chi_e$ or photon $\chi_\gamma$---in closed form. The approximations and the particle spectra sampled from them agree with the exact results to within $1\%$. The procedure requires no lookup tables, no interpolation, and no numerical root finding, and can be inserted directly into radiative particle-in-cell codes.