  We present a new approach to measuring cosmic expansion history and growth
rate of large scale structure using the anisotropic two dimensional galaxy
correlation function (2DCF) measured from data; it makes use of the empirical
modeling of small-scale galaxy clustering derived from numerical simulations by
Zheng et al. (2013). We validate this method using mock catalogues, before
applying it to the analysis of the CMASS sample from the Sloan Digital Sky
Survey Data Release 10 (DR10) of the Baryon Oscillation Spectroscopic Survey
(BOSS). We find that this method enables accurate and precise measurements of
cosmic expansion history and growth rate of large scale structure. Modeling the
2DCF fully including nonlinear effects and redshift space distortions (RSD) in
the scale range of 16 to 144 Mpc/h, we find H(0.57)r_s(z_d)/c=0.0459 +/-
0.0006, D_A(0.57)/r_s(z_d)=9.011 +/- 0.073, and f_g(0.57)\sigma_8(0.57)=0.476
+/- 0.050, which correspond to precisions of 1.3%, 0.8%, and 10.5%
respectively. We have defined r_s(z_d) to be the sound horizon at the drag
epoch computed using a simple integral, f_g(z) as the growth rate at redshift
z, and \sigma_8(z) as the matter power spectrum normalization on 8Mpc/h scale
at z. We find that neglecting the small-scale information significantly weakens
the constraints on H(z) and D_A(z), and leads to a biased estimate of f_g(z).
Our results indicate that we can significantly tighten constraints on dark
energy and modified gravity by reliably modeling small-scale galaxy clustering.
