Comparison between the Takahashi et al. (2012) HALOFIT parameters and the new optimised results (HALOFIT+), with the bands giving the 1 and 2σ errors, where we assume that the result of EUCLIDEMULATOR2 is the truth. For both training and validation we use 200 cosmologies and 100 values of k. The dashed horizontal lines indicate an error of ±1%. The new parameters dramatically reduce the errors, particularly for k ≳ 10⁻¹ h Mpc⁻¹.