The extremely large magnetoresistance (XMR) observed in many topologically nontrivial and trivial semimetals has attracted much attention in relation to its underlying physical mechanism. In this paper, by combining the band structure and Fermi surface (FS) calculations with the Hall resistivity and de Haas-Van Alphen (dHvA) oscillation measurements, we studied the anisotropy of magnetoresistance (MR) of ReO$_3$ with a simple cubic structure, an ordinary nonmagnetic metal considered previously. We found that ReO$_3$ exhibits almost all the characteristics of XMR semimetals: the nearly quadratic field dependence of MR, a field-induced upturn in resistivity followed by a plateau at low temperatures, high mobilities of charge carriers. It was found that for magnetic field emph{H} applied along the emph{c} axis, the MR exhibits an unsaturated emph{H}$^{1.75}$ dependence, which was argued to arise from the complete carrier compensation supported by the Hall resistivity measurements. For emph{H} applied along the direction of 15$^circ$ relative to the emph{c} axis, an unsaturated emph{H}$^{1.90}$ dependence of MR up to 9.43~$times$~$10^3$$%$ at 10~K and 9~T was observed, which was explained by the existence of electron open orbits extending along the $k_{x}$ direction. Two mechanisms responsible for XMR observed usually in the semimetals occur also in the simple metal ReO$_3$ due to its peculiar FS (two closed electron pockets and one open electron pocket), once again indicating that the details of FS topology are a key factor for the observed XMR in materials.
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