  Whether the number of beta-steps in the lambda-calculus can be taken as a
reasonable cost model (that is, polynomially related to the one of Turing
machines) is a delicate problem, which depends on the notion of evaluation
strategy. Since the nineties, it is known that weak (that is, out of
abstractions) call-by-value evaluation is a reasonable strategy while L\'evy's
optimal parallel strategy, which is strong (that is, it reduces everywhere), is
not. The strong case turned out to be subtler than the weak one. In 2014
Accattoli and Dal Lago have shown that strong call-by-name is reasonable, by
introducing a new form of useful sharing and, later, an abstract machine with
an overhead quadratic in the number of beta-steps.
  Here we show that strong call-by-value evaluation is also reasonable, via a
new abstract machine realizing useful sharing and having a linear overhead.
Moreover, our machine uses a new mix of sharing techniques, adding on top of
useful sharing a form of implosive sharing, which on some terms brings an
exponential speed-up. We give an example of family that the machine executes in
time logarithmic in the number of beta-steps.
