  We present the QCD corrections of order $\alpha_s^3$ to the decay rate of $b
\to u \ell \bar \nu_\ell$, with $\ell = e,\mu$, originating from diagrams with
closed fermion loops and neglecting the mass of the up quark. Our calculation
relies on integration-by-parts reduction of Feynman integrals with one
propagator raised to a symbolic power in Kira and the numerical evaluation of
master integrals with AMFlow. This allows us to obtain results for the
fermionic contributions to the total semileptonic rate with an accuracy of more
than thirty digits.
