Accurate classical dynamical fixed-energy reaction probabilities and fixed-temperature rate constants are calculated for the collinear reaction H + FH on a low-barrier model potential energy surface. The calculations cover energies from 0.1 to 100 kcal/mol above threshold and temperatures of 100-10000 K. The accurate results are used to test five approximate theories: conventional transition-state theory (TST), canonical variational theory (CVT), improved canonical variational theory (ICVT), microcanonical variational theory (μVT), and the unified statistical model (US). The first four of these theories involve a single dividing surface in phase space, and the US theory involves three dividing surfaces. The tests are particularly interesting because the potential energy surface has two identical saddle points. At temperatures from 100 to 2000 K, the μVT is the most accurate theory, with errors in the range 11-14%; for temperatures from 2000 to 10000 K, the US theory is the most successful, with errors in the range 3-14%. Over the whole range, a factor of 100 in temperature, both theories have errors of 35% or less. Even TST has errors of 47% or less over the whole factor-of-100 temperature range. Although the US model should become exact at threshold for this system, it already underestimates the reaction probability by a factor of 0.64 at 0.1 kcal/mol above threshold. TST and μVT agree with each other within 12% up to an energy 13 kcal/mol above the saddle point energy.