Truncated series aim to approximate continuous functions with a satisfying trade-off between accuracy and computational effort. In the case of ordinary differential equations, Runge–Kutta schemes and their generalization called B-series are known to be an efficient technique. In a validated algorithm, the error generated by the truncation must be taken into account. However, computing such error is expensive; thus few techniques have been proposed to compute it such as Runge–Kutta pairs, rooted trees, and symbolic or automatic differentiation. We first propose to symbolically optimize the truncation error formula, and we show that the order conditions can be relaxed, if the truncation error is appropriately computed. Following this idea, a novel type of series named AB-series is proposed.