  We present a method for ultra-fast confrontation of the WMAP cosmic microwave
background observations with theoretical models, implemented as a publicly
available software package called CMBfit, useful for anyone wishing to measure
cosmological parameters by combining WMAP with other observations. The method
takes advantage of the underlying physics by transforming into a set of
parameters where the WMAP likelihood surface is accurately fit by the
exponential of a quartic or sextic polynomial. Building on previous physics
based approximations by Hu et.al., Kosowsky et.al. and Chu et.al., it combines
their speed with precision cosmology grade accuracy. A Fortran code for
computing the WMAP likelihood for a given set of parameters is provided,
pre-calibrated against CMBfast, accurate to Delta lnL ~ 0.05 over the entire
2sigma region of the parameter space for 6 parameter ``vanilla'' Lambda CDM
models. We also provide 7-parameter fits including spatial curvature,
gravitational waves and a running spectral index.
