Nonlinear optical frequency conversion is of fundamental importance in photonics and underpins countless of its applications: Sum- and difference-frequency generation in media with quadratic nonlinearity permits reaching otherwise inaccessible wavelength regimes, and the dramatic effect of supercontinuum generation through cubic nonlinearities has resulted in the synthesis of broadband multi-octave spanning spectra, much beyond what can be directly achieved with laser gain media. Chip-integrated waveguides permit to leverage both quadratic and cubic effects at the same time, creating unprecedented opportunities for multi-octave spanning spectra across the entire transparency window of a nonlinear material. Designing such waveguides often relies on numeric modeling of the underlying nonlinear processes, which, however, becomes exceedingly challenging when multiple and cascading nonlinear processes are involved. Here, to address this challenge, we report on a novel numeric simulation tool for mixed and cascaded nonlinearities that uses anti-aliasing strategies to avoid spurious light resulting from a finite simulation bandwidth. A dedicated fifth-order interaction picture Runge-Kutta solver with adaptive step-size permits efficient numeric simulation, as required for design parameter studies. The simulation results are shown to quantitatively agree with experimental data, and the simulation tool is available as an open-source Python package (pychi).