  We perform a joint determination of the distance-redshift relation and cosmic
expansion rate at redshifts z = 0.44, 0.6 and 0.73 by combining measurements of
the baryon acoustic peak and Alcock-Paczynski distortion from galaxy clustering
in the WiggleZ Dark Energy Survey, using a large ensemble of mock catalogues to
calculate the covariance between the measurements. We find that D_A(z) = (1205
+/- 114, 1380 +/- 95, 1534 +/- 107) Mpc and H(z) = (82.6 +/- 7.8, 87.9 +/- 6.1,
97.3 +/- 7.0) km/s/Mpc at these three redshifts. Further combining our results
with other baryon acoustic oscillation and distant supernovae datasets, we use
a Monte Carlo Markov Chain technique to determine the evolution of the Hubble
parameter H(z) as a stepwise function in 9 redshift bins of width dz = 0.1,
also marginalizing over the spatial curvature. Our measurements of H(z), which
have precision better than 7% in most redshift bins, are consistent with the
expansion history predicted by a cosmological-constant dark-energy model, in
which the expansion rate accelerates at redshift z < 0.7.
