How to automatically shrink lines in align block to fit hbox?

Question

I have written the following latex

\documentclass{article}
\usepackage[utf8]{inputenc}

\usepackage{amsmath}
\renewcommand{\P}{\mathcal{P}}
\date{May 2019}

\begin{document}

\begin{align*}
    &H_{n + 1}= \\
    &-\sum_{x_{n + 1}} \P(x_{n + 1} | x_n) \sum_{x_1, x_2, \dots, x_{n}} \P(x_1, x_2, \dots, x_n) \log(\P(x_1, x_2, \dots, x_n)\P(x_{n + 1} | x_n)) =\\
    &-\sum_{x_{n + 1}} \P(x_{n + 1} | x_n) \sum_{x_1, x_2, \dots, x_{n}} \P(x_1, x_2, \dots, x_n) (\log(\P(x_1, x_2, \dots, x_n)) + \log(\P(x_{n + 1} | x_n))) =\\
    &-\sum_{x_{n + 1}} \P(x_{n + 1} | x_n) H_n - \sum_{x_1, x_2, \dots, x_{n + 1}} \P(x_1, x_2, \dots, x_{n + 1}) \log(\P(x_{n + 1} | x_n))) =
\end{align*}

\end{document}

This gives me an overfull hbox warning. Is there a way to automatically shrink each line so that it fits inside the hbox?

Note: I am willing to accept a solution that tells me how to shrink everything in the align contents, but I would greatly prefer an answer that automatically shrinks each line dynamically, and I would love an answer that explains how to do both.

Answer 1

The simplest solution would be to load the geometry package, to have more sensible margins and use the \smashoperator command from mathtools (needless to load amsmath in this case). Without geometry, you'll have to break the second row, for instance with multlined:

\documentclass{article}
\usepackage{showframe}
\renewcommand*{\ShowFrameLinethickness}{0.3pt}
\usepackage[utf8]{inputenc}%
\usepackage{mathtools}

\renewcommand{\P}{\mathcal{P}}
\date{May 2019}

\begin{document}

\begin{align*}
    &H_{n + 1}= \\
    &-\sum_{x_{n + 1}} \P(x_{n + 1}\mid x_n) \smashoperator{\sum_{x_1, x_2, \dots, x_{n}}} \P(x_1, x_2, \dots, x_n) \log(\P(x_1, x_2, \dots, x_n)\P(x_{n + 1} \mid x_n)) =\\
    &-\begin{multlined}\smash[b]{\sum_{x_{n + 1}}} \P(x_{n + 1}\mid x_n) \smash[b]{\smashoperator{\sum_{x_1, x_2, \dots, x_{n}}}} \P(x_1, x_2, \dots, x_n)\bigl (\log(\P(x_1, x_2, \dots, x_n)) \\+ \log(\P(x_{n + 1}\mid x_n))\bigr) =
    \end{multlined}\\
    &-\sum_{x_{n + 1}} \P(x_{n + 1}\mid x_n) H_n -\smashoperator{ \sum_{x_1, x_2, \dots, x_{n + 1}}} \P(x_1, x_2, \dots, x_{n + 1}) \log(\P(x_{n + 1}\mid x_n))) =
\end{align*}

\end{document}

Unrelated: I replaced the occurrences of | in probabilities with \mid to have a better horizontal spacing.