  Measuring the radio emission from cosmic ray particle cascades has proven to
be a very efficient method to determine their properties such as the mass
composition. Efficient modeling of the radio emission from air showers is
crucial in order to extract the cosmic ray physics parameters from the measured
radio emission. MGMR3D is a fast semi-analytic code that calculates the
complete radio footprint, i.e.\ intensity, polarization, and pulse shapes, for
a parametrized shower-current density and can be used in a chi-square
optimization to fit a given radio data. It is many orders of magnitude faster
than its Monte Carlo counterparts. We provide a detailed comparative study of
MGMR3D to Monte Carlo simulations, where, with improved parametrizations, the
shower maximum $\Xmax$ is found to have very strong agreement with a small
dependency on the incoming zenith angle of the shower. Another interesting
feature we observe with MGMR3D is sensitivity to the shape of the longitudinal
profile in addition to $\Xmax$. This is achieved by probing the distinguishable
radio footprint produced by a shower having a different longitudinal profile
than usual. Furthermore, for the first time, we show the results of
reconstructing shower parameters for LOFAR data using MGMR3D, and obtaining a
$\Xmax$ resolution of 22 g/cm$^2$ and energy resolution of 19\%.
