The problem of inverting the implicit function $$y=f(x)$$ in the form of power-series $$x = a + \sum_{k=1}^{\infty} b_k (y-f(a))^k$$ around a point of interest $x=a$, has a long history. Lagrange obtained a theoretical inversion formula [1]https://mathworld.wolfram.com/LagrangeInversionTheorem.html, yet efficient implementations are relatively recent [2]Brent, Richard P., and Hsiang T. Kung. “Fast algorithms for manipulating formal …