With RK4 the expressions become $$\tilde{x}=x_2+\epsilon+O((h)^{6}),$$ with $$\epsilon = \frac{|x_1-x_2|}{15}.$$ The estimate is one order higher than the original RK4. But this method is normally rather inefficient since it requires a lot of computations. We solve typically the equation three times at each time step. However, we can compare the estimate $\epsilon$ with some by us given accuracy $\xi$. We can then ask the question: what is, with a given $x_j$ and $t_j$, the largest possible step size $\tilde{h}$ that leads to a truncation error below $\xi$? We want $$C\tilde{h} \le \xi,$$ which leads to $$\left(\frac{\tilde{h}}{h}\right)^{M+1}\frac{|x_1-x_2|}{(1-2^{-M})}\le \xi,$$ meaning that $$\tilde{h}=h\left(\frac{\xi}{\epsilon}\right)^{1+1/M}.$$