We note here that additional simplifications have been introduced by Min and coworkers to propose independent-trajectory algorithms derived from the exact factorization, i.e., the methods surface hopping based on the exact factorization (SHXF) and Ehrenfest dynamics based on the exact factorization (EhXF), allowing one to access complex molecular systems and processes . Also, Blumberger and coworkers recently developed CTMQC-(E)DI , where a double-intercept (DI) idea is introduced in CTMQC and in CTMQC-E to cure numerical instabilities encountered in these methods when calculating the coupling among the trajectories, thus, greatly improving energy and norm conservation. Some of these independent and coupled-trajectory algorithms are currently implemented in G-CTQMC package . Therefore, we find interesting at this stage of the computational and theoretical development of the exact factorization, to present an in-depth comparison of the performance of the exact-factorization-based algorithms, namely, CTMQC, CTMQC-E and CTTSH, with Ehrenfest and TSH, using the same molecular example. We choose for this study a three-electronic-state two-nuclear-dimensional molecular model that mimics the hydrogen dissociation in photo-excited phenol . Even though the molecular Hamiltonian is provided as analytical model potentials, the system presents some challenging features, namely (i) the presence of a conical intersection between the bright S 1 state and the dark S 2 state whose access is limited by the initial energy of the photo-excitation, (ii) the presence of two subsequent conical intersections, i.e., S 1 /S 2 and S 0 /S 1 , that are encountered along the ultrafast process that leads to hydrogen dissociation either in S 0 or in S 1 , and (iii) the activation of a periodic nuclear variable upon photo-excitation.