Suppose I have n generally nonlinear equations for n variables, like e.g. for n=2 the system F(x,y)=0

x^2 + 2*y - 4 = 0
sqrt(8)*x + y^2 - 5 = 0

By introducing variables for intermediate results, I can transform this into an (almost, at least, up to some additional singularities, which I don't care about for my question) equivalent set of equations with more variables, like e.g. the set of 4 equations for 4 variables G(x,y,z,w)=0

x^2*w = 1
z*w = 1
z + 2*y - 4 = 0
sqrt(8)*x + y^2 - 5 = 0

Now I want to solve a system like this numerically, say e.g., with a Newton-Krylov-Solver like KINSOL.

Is there any expectable or even provable advantage regarding convergence in using the system with redundant variables G over using the reduced system F? Or is it normally rather worse?

If this question can be answered at all, is the answer sensitive to choosing a different solver?

With hand-waving arguments I can equally well come to opposite speculations:

1. The more variables, the more freedom the algorithm has for finding the roots, and doesn't get stuck so easily in difficult regions (like locally bad condition number or high curvature)
2. The more variables, the higher dimensional the search space, and so the more likely it is that the algorithm can go astray

I can't imagine that this problem has never been dealt with before. But obviously I don't know the right keywords.