We propose to replace the exact amplitudes used in Monte Carlo event generators for trained machine learning regressors, with the aim of speeding up the evaluation of slow amplitudes. As a proof of concept, we study the process gg → ZZ, whose leading-order amplitude is loop induced. We show that gradient boosting machines like XGBoost can predict the fully differential distributions with errors below 0.1%, and with prediction times O(10³) faster than the evaluation of the exact function. This is achieved with training times ∼ 23  minutes and regressors of size ≲ 22  Mb. We also find that xgboost performs well over the entire phase space, while interpolation gives much larger errors in regions where the function is peaked. These results suggest a possible new avenue to speed up Monte Carlo event generators.