Function dirty_price_of_flows_overlaid 

pub fn dirty_price_of_flows_overlaid<R: Scalar>(
    flows: &[(f64, f64)],
    y: f64,
    basis: YieldBasis,
    overlay: R,
) -> R

dirty_price_of_flows with a flat continuous overlay s on the discounting: each flow is scaled by exp(−s·t).

At s = 0 this is dirty_price_of_flows and nothing else — exp(0) is exactly one, so the multiplication is by a literal 1.0 and no price moves. The overlay exists to be seeded: ∂P/∂s at zero is the t-weighted PV moment, which is Macaulay duration once divided by the price. Taking it this way means the duration is the pricing body’s own derivative rather than a formula standing beside it.