The formulas are published in a programming language called M. There is an open source implementation [1].
> There is currently no legal guarantee of any kind about the correctness of the code produced by the Mlang compiler, or by the results produced by the interpreter of Mlang. However, authors have been in contact with DGFiP to validate Mlang, and the system passes all the private DGFiP tests as of Sept. 2022 for the version of the source files responsible for computing the tax on the 2018, 2019, 2020 and 2021 income.