The cross section of the process $e^+ e^-topi^+pi^-$ has been measured in the Spherical Neutral Detector (SND) experiment at the VEPP-2000 $e^+e^-$ collider VEPP-2000 in the energy region $525 <sqrt[]{s} <883$ MeV. The measurement is based on data with an integrated luminosity of about 4.6 pb$^{-1}$. The systematic uncertainty of the cross section determination is 0.8 % at $sqrt{s}>0.600$ GeV. The $rho$ meson parameters are obtained as $m_rho = 775.3pm 0.5pm 0.6$ MeV, $Gamma_rho = 145.6pm 0.6pm 0.8$ MeV, $B_{rhoto e^+ e^-}times B_{rhotopi^+pi^-} = (4.89pm 0.02pm 0.04)times 10^{-5}$, and the parameters of the $e^+ e^-toomegatopi^+pi^-$ process, suppressed by $G$-parity, as $B_{omegato e^+ e^-}times B_{omegatopi^+pi^-}= (1.32pm 0.06pm 0.02)times 10^{-6} $ and $phi_{rhoomega} = 110.7pm 1.5pm1.0$ degrees.
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