$$\epsilon=log_{10}\left(\left|\frac{f''_{\mbox{computed}}-f''_{\mbox{exact}}} {f''_{\mbox{exact}}}\right|\right),$$ $$\epsilon_{\mbox{tot}}=\epsilon_{\mbox{approx}}+\epsilon_{\mbox{ro}}.$$

For the computed second derivative we have $$f_0''=\frac{ f_h -2f_0 +f_{-h}}{h^2}-2\sum_{j=1}^{\infty}\frac{f_0^{(2j+2)}}{(2j+2)!}h^{2j},$$ and the truncation or approximation error goes like $$\epsilon_{\mbox{approx}}\approx \frac{f_0^{(4)}}{12}h^{2}.$$