  In this work we use a refined entropic sampling technique based on the
Wang-Landau method to study the spin-$1/2$ Baxter-Wu model. The static critical
exponents were determined as $\alpha=0.6545(68)$, $\beta=0.0818(30)$,
$\gamma=1.18193(77)$, and $\nu=0.66341(47)$. The estimate for the critical
temperature was $T_c=2.269194(45)$. We compare the present results with those
obtained from other well established approaches and we find a startling
closeness with the exact values, besides the high precision reached for the
critical temperature. We also calculate the coefficients $a$ and $b$ for the
divergence of the microcanonical inverse temperature at the ground state
achieving an excellent agreement in comparison with the simulation estimates.
