Relative error distribution for the ionisation (top) and heating (bottom) rates, for the PWPL (reds) and PWC (blues) approximation. The left panel corresponds to the redshift dependent UVB spectrum and the right panel to the age dependent SSP spectrum for population ages below 8 Myr. Different line styles show the error distribution for HI (solid), HeI (dashed), and HeII (dot-dashed). The errors are calculated relative to the numerical integration of Eqs. (1) and (2).