tokens: the mass, metallicity, effective temperature and individual frequencies in the same manner as before and computed masses and radii using the scaling relations iteratively with the reference functions described in equations ( 3 ) and ( 4 ). The results are shown in Figs 3 and A3 . These figures show that the reference functions that we present here indeed remove trends that are present in the mass and radius determinations as a function of max and mitigate the biases to a large extent. However, the standard deviations from using either equation ( 3 ) or ( 4 ) are very similar and significantly larger than in the ideal case, showing the impact of uncertainties in the observations. Figure 3. Same as Fig. 2 but now with the initial values of T eff , max and [Fe/H] perturbed with typical uncertainties (see the text for more detail). 4.1 Hare-and-hound validation We have thus far demonstrated that the new functions improve mass and radius estimations for the data they fit. In order to prove the general efficacy of our new corrections, we appraise the performance of the functions on data to which they have not been exposed. We perform a series of hare-and-hound validations using stellar models calculated with two additional evolution codes. We used garstec (Weiss Schlattl 2008 ) and mesa (Paxton etal. 2011 ) to compute grids of stellar tracks from which we draw testing data. Over 1000 models from each grid were extracted to serve as hares with the requirement that each selected model falls within the verified mass, metallicity and max ranges of the correction functions. The choice of microphysics and modelling assumptions differ between these two codes and they also differ from the code used to calculate the training data in yrec . Thus, mass and radius predictions of the hares will indicate the degree of stellar evolution code dependence in our function. Both the garstec and mesa grids were computed using OPAL opacities (Iglesias Rogers 1996 ) in conjunction with Ferguson etal. ( 2005 ) tables at low temperatures. We utilized the updated 2005 tables for the OPAL equation of state (Rogers Nayfonov 2002 ) along with the assumption of an Eddington plane-parallel atmosphere. We have taken the recommended nuclear reaction rates from the NACRE collaboration in combination with those from Caughlan Fowler ( 1988 ). The treatment of convection follows the mixing length theory as described by Kippenhahn, Weigert Weiss ( 2012 ) and models were computed with the respective solar-calibrated mixing lengths. Radial mode frequencies were calculated with the adipls pulsation package (Christensen-Dalsgaard 2008 ) for the garstec models and with the gyre pulsation package (Townsend Teitler 2013 ) for the mesa models. The large frequency separation was determined using a weighted median around the scaled max as per Bellinger etal. ( 2016 ). The grids differ in that the garstec models assume Asplund etal. ( 2009 ) solar abundances and were computed without
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