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\section{Abstract}  Various MHD (magnetohydrodynamic) equilibrium tools, some of which being recently developped or considerably updated, are used on the medium-size COMPASS tokamak \cite{P_nek_2006}. MHD equilibrium is a fundamental property of the tokamak plasma, whose knowledge is required for many diagnostics and modelling tools. Proper benchmarking and validation of equilibrium tools is thus key for interpretting and plannig tokamak experiments. We present here benchmarks and comparisons to experimental data of the EFIT++ reconstruction code [?], the free-boundary equilibrium code FREEBIE [?], and the rapid plasma boundary reconstruction part of the EQUINOX code \cite{doi:10.1016/j.jcp.2011.04.005}. We demonstrate that FREEBIE can determine calculate  the equilibrium and corresponding poloidal field (PF) coils currents for given plasma parameters. Both EFIT++ and EQUINOX can reconstruct the equilibrium equilibria generated by FREEBIE  from synthetic diagnostic data (with (including  an artificial noise) from FREEBIE. noise).  Optimum reconstruction parameters are estimated; in addition, possible enhancements using more diagnostics are discussed and simulated using synthetic diagnostics. FREEBIE can also calculate the temporal evolution of the poloidal field coils currents for a whole plasma scenario.  The accuracy of the reconstruction depends on the noise level and certain numerical parameters. For example, EFIT++ reconstruction with a low-order $p'\left(\psi\right)$ and $ff'\left(\psi\right)$ is not perfect even with no noise. The recent EFIT++ version 6 is several times faster compared to version 4.