  On a closed and connected symplectic manifold, the group of Hamiltonian
diffeomorphisms has the structure of an infinite dimensional Fr\'echet Lie
group, where the Lie algebra is naturally identified with the space of smooth
and zero-mean normalized functions, and the adjoint action is given by
pullbacks. We show that this action is flexible: for a non-zero smooth and
zero-mean normalized function $ u $, any other smooth and zero-mean normalized
function $ f $ can be written as a finite sum of elements in the orbit of $u$
under the adjoint action. Additionally, the number of elements in this sum is
dominated from above by the uniform norm of $f$. This result can be interpreted
as a (bounded) infinitesimal version of the Banyaga's theorem on simplicity of
the group of Hamiltonian diffeomorphisms. Moreover, it allows to remove the
$C^{\infty}$-continuity assumption from the Buhovsky-Ostrover theorem on the
uniqueness of Hofer's metric.
