The growing complexity of Cyber-Physical Systems (CPS), together with increasingly available parallelism provided by multi-core chips, fosters the parallelization of simulation. Simulation speed-ups are expected from co-simulation and parallelization based on model splitting into weakly coupled sub-models, as for instance in the framework of Functional Mockup Interface (FMI). However, slackened synchronization between sub-models and their associated solvers running in parallel introduces integration errors, which must be kept inside acceptable bounds. CHOPtrey denotes a forecasting framework enhancing the performance of complex system co-simulation, with a trivalent articulation. First, we consider the framework of a Computa-tionally Hasty Online Prediction system (CHOPred). It allows to improve the trade-off between integration speed-ups, needing large communication steps, and simulation precision, needing frequent updates for model inputs. Second, smoothed adaptive forward prediction improves co-simulation accuracy. It is obtained by past-weighted extrapolation based on Causal Hopping Oblivious Polynomials (CHOPoly). And third, signal behavior is segmented to handle the discon-tinuities of the exchanged signals: the segmentation is performed in a Contextual & Hierarchical Ontology of Patterns (CHOPatt). Implementation strategies and simulation results demonstrate the framework ability to adap-tively relax data communication constraints beyond synchronization points which sensibly accelerate the simulation. The CHOPtrey framework extends the range of applications of standard Waring-Lagrange polynomial extrapolation, often deemed unstable. The embedding of predictions in lag-dependent smoothing and discontinuity handling demonstrates its practical efficiency.