We present an adaptive algorithm for effectively solving rough differential
equations (RDEs) using the log-ODE method. The algorithm is based on an error
representation formula that accurately describes the contribution of local
errors to the global error. By incorporating a cost model, our algorithm
efficiently determines whether to refine the time grid or increase the order of
the log-ODE method. In addition, we provide several examples that demonstrate
the effectiveness of our adaptive algorithm in solving RDEs