The Krivine machine is an abstract machine implementing the linear head reduction of $\lambda$-calculus. Ehrhard and Regnier gave a resource sensitive version returning the annotated form of a $\lambda$-term accounting for the resources used by the linear head reduction. These annotations take the form of terms in the resource $\lambda$-calculus.

We generalize this resource-driven Krivine machine to the case of the algebraic $\lambda$-calculus. The latter is an extension of the pure $\lambda$-calculus allowing for the linear combination of $\lambda$-terms with coefficients taken from a semiring. Our machine associates a $\lambda$-term $M$ and a resource annotation $t$ with a scalar $\alpha$ in the semiring describing some quantitative properties of the linear head reduction of $M$.

In the particular case of non-negative real numbers and of algebraic terms $M$ representing probability distributions, the coefficient $\alpha$ gives the probability that the linear head reduction actually uses exactly the resources annotated by $t$. In the general case, we prove that the coefficient $\alpha$ can be recovered from the coefficient of $t$ in the Taylor expansion of $M$ and from the normal form of $t$.