  Evaluating higher-order functional programs through abstract machines
inspired by the geometry of the interaction is known to induce $\textit{space}$
efficiencies, the price being $\textit{time}$ performances often poorer than
those obtainable with traditional, environment-based, abstract machines.
Although families of lambda-terms for which the former is exponentially less
efficient than the latter do exist, it is currently unknown how \emph{general}
this phenomenon is, and how far the inefficiencies can go, in the worst case.
We answer these questions formulating four different well-known abstract
machines inside a common definitional framework, this way being able to give
sharp results about the relative time efficiencies. We also prove that
non-idempotent intersection type theories are able to precisely reflect the
time performances of the interactive abstract machine, this way showing that
its time-inefficiency ultimately descends from the presence of higher-order
types.
