Hi, unfortunately nlsolve claims it is converged when the iterations do not make progress (and xtol==0).Thus, you should also (or only) check f_converged:
res = nlsolve(f!, j!, [ 0.0];method =:anderson,show_trace=false,beta=1.0,ftol=1E-10,xtol=1E-12)
all_converged(res) = res.x_converged && res.f_converged
@show all_converged(res)
The Anderson method stability depends on its parameters. Setting beta=0.1 seems to make it work. The Anderson method is probably not the best choice for your problem.