Time for conversion to Legendre basis as a function of number of points and order of accuracy (or depth, ). Each trace corresponds to a fixed number of dimensions with the depth increasing. (a) Time versus number of points showing nonlinear dependence on , particularly in dimensions 3 and 6, for which the maximum depth is 10 and 9, respectively. (b) The same data scaled to give time per point of evaluation and is shown as a function of . Perfect linear scaling of time with number of points would imply that the time per point is the same for a given value of , independent of dimension. Apart from fixed overhead costs that skew the results for small , the time per point is nearly constant over a large range of feasible values of .