  The rate of magnetic field diffusion plays an essential role in several
astrophysical plasma processes. It has been demonstrated that the omnipresent
turbulence in astrophysical media induces fast magnetic reconnection, which
consequently leads to large-scale magnetic flux diffusion at a rate independent
of the plasma microphysics. This process is called ``reconnection diffusion''
(RD) and allows for the diffusion of fields which are dynamically important.
The current theory describing RD is based on incompressible magnetohydrodynamic
(MHD) turbulence. In this work, we have tested quantitatively the predictions
of the RD theory when magnetic forces are dominant in the turbulence dynamics
(Alfv\'{e}nic Mach number $M_A < 1$). We employed the \textsc{Pencil Code} to
perform numerical simulations of forced MHD turbulence, extracting the values
of the diffusion coefficient $\eta_{RD}$ using the Test-Field method. Our
results are consistent with the RD theory ($\eta_{RD} \sim M_A^{3}$ for $M_A <
1$) when turbulence approaches the incompressible limit (sonic Mach number $M_S
\lesssim 0.02$), while for larger $M_S$ the diffusion is faster ($\eta_{RD}
\sim M_A^{2}$). This work shows for the first time simulations of compressible
MHD turbulence with the suppression of the cascade in the direction parallel to
the mean magnetic field, which is consistent with incompressible weak
turbulence theory. We also verified that in our simulations the energy
cascading time does not follow the scaling with $M_A$ predicted for the weak
regime, in contradiction with the RD theory assumption. Our results generally
support and expand the RD theory predictions.
