We study the collinear H + FH → HF + H and D + FD → DF + D reactions on a potential-energy surface that has twin 1.75 kcal/mol saddle points. We present accurate quantal reaction probabilities over a wide energy range, including three resonance energies and three resonance widths for each isotopic case. From these we calculate accurate quantal rate constants at temperatures 75-7000 K for H + FH and 75-2400 K for D + FD; and we separate out the contributions of the lowest-energy resonance to the low-temperature rates. We present plots of S-matrix phases and eigenphases and Argand diagrams. The accurate quantal results are used to test a wide variety of approximate dynamical results: semiclassical and quantal resonance calculations based on the vibrationally adiabatic model; rate constants calculated by conventional transition-state theory, three versions of variational transition-state theory, and the unified statistical model; and vibrationally adiabatic transmission coefficients.