Context : An accurate assessment of white dwarf cooling times is paramount to place white dwarf cosmochronology of Galactic populations on more solid grounds .
This issue is particularly relevant in view of the enhanced observational capabilities provided by the next generation of Extremely Large Telescopes , that will offer more avenues to employ white dwarfs as probes of Galactic evolution and test-beds of fundamental physics .

Aims : We estimate for the first time the consistency of results obtained from independent evolutionary codes for white dwarf models with fixed mass and chemical stratification , when the same input physics is employed in the calculations .

Methods : We compute and compare cooling times obtained from two independent and widely used stellar evolution codes – BaSTI and LPCODE evolutionary codes – using exactly the same input physics , for 0.55 M _ { \sun } white dwarf models with both pure carbon and uniform carbon-oxygen ( 50/50 mass fractions ) core , and pure hydrogen layers with mass fraction q _ { H } = 10 ^ { -4 } M _ { WD } on top of a pure helium buffer of mass q _ { He } = 10 ^ { -2 } M _ { WD } .

Results : Using the same radiative and conductive opacities , photospheric boundary conditions , neutrino energy loss rates and equation of state , cooling times from the two codes agree within \sim 2 \% at all luminosities , except when \log ( L / L _ { \sun } ) > -1.5 where differences up to \sim 8 \% do appear , due to the different thermal structure of the first white dwarf converged models at the beginning of the cooling sequence .
This agreement is true for both pure carbon and uniform carbon-oxygen stratification core models , and also when the release of latent heat and carbon-oxygen phase separation are considered .
We have also determined quantitatively and explained the effect of varying equation of state , low-temperature radiative opacities and electron conduction opacities in our calculations ,

Conclusions : We have assessed for the first time the maximum possible accuracy in the current estimates of white dwarf cooling times , resulting only from the different implementations of the stellar evolution equations and homogeneous input physics in two independent stellar evolution codes .
This accuracy amounts to \sim 2 \% at luminosities lower than \log ( L / L _ { \sun } ) \sim - 1.5 .
This difference is smaller than the uncertainties in cooling times due to the present uncertainties in the white dwarf chemical stratification .
Finally , we extend the scope of our work by providing tabulations of our cooling sequences and the required input physics , that can be used as a comparison test of cooling times obtained from other white dwarf evolutionary codes .