There's a general phonomena that is shown here. Higher order methods tend to be more efficient when you need less error. However, anything below 3rd order tends to generally be not useful, and for most problems it has been found that 5th order or above is the most efficient. The Euler method, being a first order discretization, converges far too slow and simply takes too many timesteps in order to bring the error down to satisfying levels. Even the "standard" RK4 method which is taught in a lot of classes is shown here to not be very efficient, at least in comparison to the methods commonly used in production-quality ODE solvers. Notice that due to the log scaling, Vern9 and Tsit5 are almost 10x faster that RK4 for get about 6 digits of accuracy! There's a lot of reasons for that, but you can browse Hairer's Solving Ordinary Differential Equations I for why different Runge-Kutta methods can be vastly different in efficiency (it has to do with choosing coefficients s.t. the principle truncation error term is minimized).