Quality of the label recovery using the same PSM approximation as in Figure 1, based on 250 (open circles) and 1000 (full circles) a.i. model calculations, respectively. Shown is the rms difference between the labels of the PSM approximation that best matches the exact a.i. model spectrum in a χ²-sense and the actual labels of the exact spectrum: PSM-induced errors in the label recovery by the PSM approximation are typically 0.02 dex (when considering the label range of the APOGEE survey). The dashed and solid lines show the theoretically achievable label precision at S/N = 100 (the Cramer–Rao bound; see T16), when using the APOGEE wavelength windows, or the full spectrum. A single PSM approximation can be used for fitting all labels simultaneously across much of the APOGEE survey, without inducing serious systematic errors. The red line indicates typical APOGEE DR12 precisions. The quality of the label recovery remains (to within ∼10% of each label’s accuracy), even if a number of spectral continuum and line-spread parameters are also fit simultaneously.