  We present a method that calibrates a semi-analytic model to the Renaissance
Simulations, a suite of cosmological hydrodynamical simulations with
high-redshift galaxy formation. This approach combines the strengths of
semi-analytic techniques and hydrodynamical simulations, enabling the extension
to larger volumes and lower redshifts inaccessible to simulations due to
computational expense. Using a sample of Renaissance star formation histories
(SFHs) from an average density region of the Universe, we construct a four
parameter prescription for metal-enriched star formation characterized by an
initial bursty stage followed by a steady stage where stars are formed at
constant efficiencies. Our model also includes a treatment of Population III
star formation where a minimum halo mass and log-normal distribution of stellar
mass are adopted to match the numerical simulations. Star formation is
generally well reproduced for halos with masses $\lesssim$$10^{9}
M_{\mathrm{\odot}}$. Between $11<z<25$ our model produces metal-enriched star
formation rate densities (SFRDs) that typically agree with Renaissance within a
factor of $\sim$2 for the average density region. Additionally, the total
metal-enriched stellar mass only differs from Renaissance by about $10\%$ at $z
\sim 11$. For regions that are either more overdense or rarefied not included
in the calibration, we produce metal-enriched SFRDs that agree with Renaissance
within a factor of $\sim$2 at high-$z$, but eventually differ by higher factors
for later times. This is likely due to environmental dependencies not included
in the model. Our star formation prescriptions can easily be adopted in other
analytic or semi-analytic works to match our calibration to Renaissance.
