  It is known that the main component of the Kontsevich's moduli space of
elliptic stable maps is singular. There are two different desingularizations.
One is Vakil-Zinger's desingularization and the other is the moduli space of
logarithmic stable maps. When the degree is less then or equal to 3 and the
target is $\mathbb{P}^{n}$, we show that the moduli space of logarithmic stable
maps can be obtained by blowing up Vakil-Zinger's desingularization.
