  To understand the role that AGN feedback plays in galaxy evolution we need
in-depth studies of the multi-phase structure and energetics of galaxy-wide
outflows. In this work we present new, deep ($\sim$50 hr) NOEMA CO(1-0) line
observations of the molecular gas in the powerful outflow driven by the AGN in
the ultra-luminous infrared galaxy IRAS F08572+3915. We spatially resolve the
outflow, finding that its most likely configuration is a wide-angle bicone
aligned with the kinematic major axis of the rotation disk. The molecular gas
in the wind reaches velocities up to approximately $\pm$1200 km s$^{-1}$ and
transports nearly 20% of the molecular gas mass in the system. We detect a
second outflow component located $\sim$6 kpc north-west from the galaxy moving
away at $\sim$900 km s$^{-1}$, which could be the result of a previous episode
of AGN activity. The total mass and energetics of the outflow, which includes
contributions from the ionized, neutral, warm and cold molecular gas phases is
strongly dominated by the cold molecular gas. In fact, the molecular mass
outflow rate is higher than the star formation rate, even if we only consider
the gas in the outflow that is fast enough to escape the galaxy, which accounts
for about $\sim$40% of the total mass of the outflow. This results in an
outflow depletion time for the molecular gas in the central $\sim$1.5 kpc
region of only $\sim3$ Myr, a factor of $\sim2$ shorter than the depletion time
by star formation activity.
