the calculation, it is important to collect incremental contributions to sensitivities when going backwards through the computation.

The theoretical maximum effort factor of $5$ can be traced back to the effort required to handle multiplication/division of intermediate values. Evidently, if the sensitivity of the result on the intermediate quantity $I_k$ is known in $\bar I_k$, and $I_k$ was obtained as the sum of $I_i+I_j$, then the sensitivities of $I_i$ and $I_i$ must be increased by $\bar I_k$ (for if e.g. $I_j$ gets used multiple times, then $\bar I_j$ receives multiple increments). If, however, $I_k$ is the *product* of $I_i$ and $I_j$, then $\bar
I_i$ must be increased by $I_j\cdot \bar I_k$ and vice versa – the combined read/add/store operations give rise to a bounded multiplicative factor for the total effort.

In practice, the corresponding calculations are even considerably simpler than what the general theory of algorithmic differentiation suggests, as the partial derivatives $\partial E/\partial g_j$ with respect to the geometry parameters $g_j$ are, at least for simple surfaces, obtainable directly as a by-product of the forward calculation. Comparing the Worldline method with the remarkable approach discovered by Rodriguez, Ibannescu, Iannuzzi, Capasso, Joannopoulos, and Johnson [@2007PhRvL..99h0401R; @2007PhRvA..76c2106R] or for that matter 