The role of compressible fluctuations in Hall MHD (HMHD) turbulence is investigated using direct numerical simulations and in-situ spacecraft in the near-Earth space. A focus is put on verifying the new exact third-order law derived recently for compressible isothermal HMHD turbulence (Andrés, Galtier and Sahraoui, 2017). The numerical simulations use a 3D compressible HMHD code in the isothermal limit (gamma = 1) with low sonic Mach numbers (Ms < 1). The main goal is to estimate the energy cascade rate of turbulence over a broad range of scales that span both the inertial and sub-ion (dispersive) ranges. Preliminary comparison with observations from the recently launched multispacecraft NASA/MMS (Magnetospheric MultiScale) mission in the solar wind are made.