Figure 3. Cost of time underlying saccades, as inferred from data reported by Collewijn et al. (1988). *a*, Infinitesimal CoT *g*(*t*). To infer this cost, we used either the linear regression or the true data points exhibiting a growth larger than linear for amplitudes >40 degrees (see Collewijn et al., 1988). Dotted traces represent extrapolated parts of the CoT. Solid lines indicate values inferred using our inverse methodology. Our approach does not require fitting parameters or hypothesizing the shape of the time cost. *b*, Integral CoT *G*(*t*). The concavity of the CoT is obvious; and in particular, linear/convex costs can be ruled out (Shadmehr et al., 2010). *c*, Fitting of the infinitesimal CoT. We fitted *g* on the actual range of durations of observed saccades (i.e., from 36.5 to 295 ms). We considered both exponential and hyperbolic candidate functions. Best fitting parameters were as follows: (α, β) = (1.3, 4.3) and (α, β) = (0.9, 5.5) for the hyperbolic and exponential fits, respectively. *d*, Simulations in the stochastic case with different levels of signal-dependent noise (from *k*_{SDN} to *nk*_{SDN} with *n* = 2, 3, and 4, denoted by × *n* in the figure). RMSE is reported for hyperbolic (hyp.) and exponential (exp.) functions, respectively. With larger multiplicative noise, the CoT gets closer to the hyperbolic class of CoT. *e*, Verification of the amplitude–duration relationship as obtained from free time optimal control simulations with the CoT depicted in *b* (black trace). White-filled circles represent true data points (i.e., target values for the model). Black crosses represent simulated data (i.e., reconstructed values from the model). Both series of points matched perfectly because the methodology provides an exact solution to the problem of identifying the CoT associated with the observed amplitude–duration relationship. *f*, Velocity profiles of saccades of different amplitudes as predicted by the optimal control model.