During each iteration of the algorithm, a hypothesis is selected with some advantage over random guessing. The weight of this hypothesis formula_3 and the "amount of time passed" formula_2 during the iteration are simultaneously solved in a system of two non-linear equations ( 1. uncorrelated hypothesis w.r.t example weights and 2. hold the potential constant) with two unknowns (weight of hypothesis formula_3 and time passed formula_2). This can be solved by bisection (as implemented in the JBoost software package) or Newton's method (as described in the original paper by Freund). Once these equations are solved, the margins of each example (formula_11 in the algorithm) and the amount of time remaining formula_12 are updated appropriately. This process is repeated until there is no time remaining.