Figure 1

(a) Violin plot of the prediction errors (PE) of 9 formulas. The formulas with the smallest PEs were Kane-K (− 1.373 ± 0.78 D), Kane-TK (− 0.64 ± 0.61 D), and EVO-K (− 0.53 ± 0.50 D), and the formulas with the largest PEs were Shammas-TK (1.58 ± 0.68 D), BTK-TK (1.46 ± 0.71 D), and m-Masket-TK (0.96 ± 0.54 D). (b) Violin plot of the absolute prediction errors (AE) of 9 formulas. The formulas with the lowest AEs were EVO-TK (0.40 ± 0.29, range 0–1.23, MedAE = 0.36 D), BTK-K (0.41 ± 0.26, range 0.01–1.19, MedAE = 0.35), and Masket-K (0.44 ± 0.33, range 0.02–1.39, MedAE = 0.37).