  Fitting half-integer generalized Laguerre functions to the evolved,
real-space dark matter and halo correlation functions provides a simple way to
reconstruct their initial shapes. We show that this methodology also works well
in a wide variety of realistic, assembly biased, velocity biased and
redshift-space distorted mock galaxy catalogs. We use the linear point feature
in the monopole of the redshift-space distorted correlation function to
quantify the accuracy of our approach. We find that the linear point estimated
from the mock galaxy catalogs is insensitive to the details of the biasing
scheme at the sub-percent level. However, the linear point scale in the
nonlinear, biased, and redshift-space distorted field is systematically offset
from its scale in the unbiased linear density fluctuation field by more than
1%. In the Laguerre reconstructed correlation function, this is reduced to
sub-percent values, so it provides comparable accuracy and precision to methods
that reconstruct the full density field before estimating the distance scale.
The linear point in the reconstructed density fields provided by these other
methods is likewise precise, accurate, and insensitive to galaxy bias. All
reconstructions depend on some input parameters, and marginalizing over
uncertainties in the input parameters required for reconstruction can degrade
both accuracy and precision. The linear point simplifies the marginalization
process, enabling more realistic estimates of the precision of the distance
scale estimate for negligible additional computational cost. We show this
explicitly for Laguerre reconstruction.
