We measure the deflagration behavior of energetic materials at extreme conditions (up to 520 K and 1 GPa) in the LLNL High Pressure Strand Burner, thereby obtaining reaction rate data for prediction of violence of thermal explosions. The apparatus provides both temporal pressure history and flame time-of-arrival information during deflagration, allowing direct calculation of deflagration rate as a function of pressure. Samples may be heated before testing. Here we report the deflagration behavior of several HMX-based explosives at pressures of 10-600 MPa and temperatures of 300-460 K. We find that formulation details are very important to overall deflagration behavior. Formulations with high binder content ( greater than or equal to 15 wt%) deflagrate smoothly over the entire pressure range regardless of particle size, with a larger particle size distribution leading to a slower reaction. The deflagration follows a power law function with the pressure exponent being unity. Formulations with lower binder content (less than or equal to 10 wt% or less) show physical deconsolidation at pressures over 100-200 MPA, with transition to a rapid erratic deflagration 10-100 times faster. High temperatures have a relatively minor effect on the deflagration rate until the HMX beta-->delta phase transition occurs, after which the deflagration rate increases by more than a factor of 10.