Before revision:  In the appendix, we test the good performance of New Q-Newton's method on various benchmark test functions such as Rastrigin, Askley, Rosenbroch and many other, against algorithms such as Newton's method, BFGS, Adaptive Cubic Regularization, Random damping Newton's method and Inertial Newton's method, as well as Unbounded Two-way Backtracking Gradient Descent.
After revision:  We test the good performance of New Q-Newton's method on various benchmark test functions such as Rastrigin, Askley, Rosenbroch and many other, against algorithms such as Newton's method, BFGS, Adaptive Cubic Regularization, Random damping Newton's method and Inertial Newton's method, as well as Unbounded Two-way Backtracking Gradient Descent.