Proof with auto with typeclass_instances.
intros x Hx.
apply relative_error_lt_conversion...
apply bpow_gt_0.
intros _; now apply relative_error_FLT.
Qed.
Variable choice : Z -> bool.

Theorem relative_error_N_FLT :
forall x,
(bpow (emin + prec - 1) <= Rabs x)%R ->
(Rabs (round beta (FLT_exp emin prec) (Znearest choice) x - x) <= /2 * bpow (-prec + 1) * Rabs x)%R.