Distributions of the residuals in the recovered atmospheric parameters (Δθ = θ_rec − θ_real) for a subsample of cool random spectra with G_RVS = 8.4, 10.3, and 12.6 (i.e. S/N values of 350, 125, and 20, from top to bottom, respectively) and defined by 4000 <T_eff< and 8000 K. The different colours represent the different tested methods: FERRE, ANN, and MATISSE_G in red, green and blue, respectively.