We study the projection of cognitive representations into continuous motor (reaching) responses with a computational model that unifies three influential approaches: accumulation of evidence, statistical inference, and optimal feedback control. We modeled a number comparison task that asked participants to respond with a reaching gesture. The model successfully reproduced subjects' pattern of reach and performance across varying difficulties of numerical comparison. Our model parameterized several potentially relevant cognitive variables, including a threshold, memory decay, and mental sampling rate. Remarkably, a threshold for movement was not needed for modeling human behavior when statistical inference is combined with optimal motor planning. Overall, the model indicates that the motor-system positions the effectors optimally, both biomechanically through an optimal feedback controller, and cognitively by means of continuous statistical inference on the available evidence.