@kwdef struct MonitoredBackTracking{B, V}
    linesearch::B = BackTracking()
    dz_tmp::V = []
    z_tmp::V = []
end

"""
MonitoredBackTracing is a thin wrapper of BackTracking, making sure that
the BackTracking relaxation is rejected if it results in a residual increase
"""
function OrdinaryDiffEq.relax!(
    dz,
    nlsolver::AbstractNLSolver,
    integrator::DEIntegrator,
    f,
    linesearch::MonitoredBackTracking,
)
    (; linesearch, dz_tmp, z_tmp) = linesearch

    # Store step before relaxation
    @. dz_tmp = dz

    # Apply relaxation and measure the residu change
    @. z_tmp = nlsolver.z + dz
    resid_before = resid(z_tmp, integrator, nlsolver, f) # The function resid mimicks this one: https://github.com/SciML/OrdinaryDiffEq.jl/blob/e3af6419b02810ea3b762ab0511cda0e4bcf245c/lib/OrdinaryDiffEqNonlinearSolve/src/newton.jl#L426
    relax!(dz, nlsolver, integrator, f, linesearch)
    @. z_tmp = nlsolver.z + dz
    resid_after = resid(z_tmp, integrator, nlsolver, f)

    # If the residu increased due to the relaxation, reject it
    if resid_after > resid_before
        @. dz = dz_tmp
    end
end