Shrink the font size of a long equation

Question

I have edited a very long equation in the eqnarray environment and broken some long lines at the appropriate positions with \nonumber\\ (see the small example below). After compiling, the equation occupied nearly one page with some long lines beyond the edge of the page.

Since the long equation is in an appendix, I want to shrink its font size only to prevent any long line from going beyond the range of the page. As mentioned above the positions of \nonumber\\ are "appropriate", which means their positions shouldn't be changed. I don't know how to do this, please give me some suggestion. Thank you in advance.

\documentclass[a4paper,12pt]{article}

\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{REVSYMB4-1}
\usepackage{latexsym}
\usepackage[a4paper, total={6in, 9in}]{geometry}

\begin{document}
\begin{eqnarray}\label{eq:longeq}
w &=& 100(\partial_x f)^3x^2
+\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2
+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
\partial_x f \partial_x^2 f \nonumber\\
&& + \epsilon\left[ 200\left( xxx\cot\theta f^3
-1\right)(\partial_x g)^2
+\left( \cot\theta- yyy^3\right)\partial_x f
-\left(4-1000\cot\theta f^3
\right)g\partial_x^2 f \right]\partial_x g +20zzz^2+500f^2
\nonumber\\
&& +\left( \cdots \right).
\end{eqnarray}

\end{document}

Answer 1

Well, you can use the usual fontsize commands like \small or \footnotesize to get a smaller font to print the equation. But in my eyes that looks ugly, I think better would be to name a term as extra variable to get the long line shorter and explain the new variable in an extra line.

However, in the following MWE I demonstrate the usage of \small and \footnotesize. Please see the leading { and the closing } to have the smaller font size only in the equation inside that {...}:

\documentclass[a4paper,12pt]{article}

\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{revsymb4-1}% <==================================== REVSYMB4-1
\usepackage{latexsym}
\usepackage[a4paper, total={6in, 9in}]{geometry}
\usepackage{blindtext} % <==================== add dummy text to document

\begin{document}
\blindtext
\begin{eqnarray}\label{eq:longeq}
w &=& 100(\partial_x f)^3x^2
+\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2
+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
\partial_x f \partial_x^2 f \nonumber\\
&& + \epsilon\left[ 200\left( xxx\cot\theta f^3
-1\right)(\partial_x g)^2
+\left( \cot\theta- yyy^3\right)\partial_x f
-\left(4-1000\cot\theta f^3
\right)g\partial_x^2 f \right]\partial_x g +20zzz^2+500f^2
\nonumber\\
&& +\left( \cdots \right).
\end{eqnarray}

{\small % <=============================================== lower fontsize
\begin{align}\label{eq:longequ} % <=====================================
w &= 100(\partial_x f)^3x^2
   +\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2 \nonumber\\ % <========
  &+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
    \partial_x f \partial_x^2 f \nonumber\\ % <=========================
  &+ \epsilon\left[ 200\left( xxx\cot\theta f^3
   -1\right)(\partial_x g)^2
   +\left( \cot\theta- yyy^3\right)\partial_x f 
   -\left(4-1000\cot\theta f^3
    \right)g\partial_x^2 f \right]\partial_x g \nonumber\\ % <==========
  &+20zzz^2+500f^2 \nonumber\\ % <======================================
  &+\left( \cdots \right).
\end{align}
} % <================================================= end lower fontsize

{\footnotesize % <======================================== lower fontsize
\begin{align}\label{eq:longequa} % <====================================
w &= 100(\partial_x f)^3x^2
   +\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2 \nonumber\\
  &+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
    \partial_x f \partial_x^2 f \nonumber\\
  &+ \epsilon\left[ 200\left( xxx\cot\theta f^3
   -1\right)(\partial_x g)^2
   +\left( \cot\theta- yyy^3\right)\partial_x f 
   -\left(4-1000\cot\theta f^3
    \right)g\partial_x^2 f \right]\partial_x g \nonumber\\
  &+20zzz^2+500f^2 \nonumber\\
  &+\left( \cdots \right).
\end{align}
} % <================================================= end lower fontsize
\blindtext
\end{document}

BTW I marked important code changings with <===========. That is the resulting pdf:

Edit:

After the comment of user @barbarabeeton I tried the following MWE (added \blindtext or free aditional text between the equations), but I can not recreate the behaviour described in the given link in the comment:

\documentclass[a4paper,12pt]{article}

\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{revsymb4-1}% <==================================== REVSYMB4-1
\usepackage{latexsym}
\usepackage[a4paper, total={6in, 9in}]{geometry}
\usepackage{blindtext} % <==================== add dummy text to document

\begin{document}
\blindtext
\begin{eqnarray}\label{eq:longeq}
w &=& 100(\partial_x f)^3x^2
+\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2
+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
\partial_x f \partial_x^2 f \nonumber\\
&& + \epsilon\left[ 200\left( xxx\cot\theta f^3
-1\right)(\partial_x g)^2
+\left( \cot\theta- yyy^3\right)\partial_x f
-\left(4-1000\cot\theta f^3
\right)g\partial_x^2 f \right]\partial_x g +20zzz^2+500f^2
\nonumber\\
&& +\left( \cdots \right).
\end{eqnarray}
This is a short blindtext to test the behaviour of \verb|\small|. 
This is a short blindtext to test the behaviour of \verb|\small|. 
This is a short blindtext to test the behaviour of fontsize command. %\blindtext
{\small % <=============================================== lower fontsize
\begin{align}\label{eq:longequ} % <=====================================
w &= 100(\partial_x f)^3x^2
   +\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2 \nonumber\\ % <========
  &+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
    \partial_x f \partial_x^2 f \nonumber\\ % <=========================
  &+ \epsilon\left[ 200\left( xxx\cot\theta f^3
   -1\right)(\partial_x g)^2
   +\left( \cot\theta- yyy^3\right)\partial_x f 
   -\left(4-1000\cot\theta f^3
    \right)g\partial_x^2 f \right]\partial_x g \nonumber\\ % <==========
  &+20zzz^2+500f^2 \nonumber\\ % <======================================
  &+\left( \cdots \right).
\end{align}
} % <================================================= end lower fontsize
This is a short blindtext to test the behaviour of \verb|\small|. 
This is a short blindtext to test the behaviour of \verb|\small|. 
This is a short blindtext to test the behaviour of fontsize command. 
{\footnotesize % <======================================== lower fontsize
\begin{align}\label{eq:longequa} % <====================================
w &= 100(\partial_x f)^3x^2
   +\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2 \nonumber\\
  &+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
    \partial_x f \partial_x^2 f \nonumber\\
  &+ \epsilon\left[ 200\left( xxx\cot\theta f^3
   -1\right)(\partial_x g)^2
   +\left( \cot\theta- yyy^3\right)\partial_x f 
   -\left(4-1000\cot\theta f^3
    \right)g\partial_x^2 f \right]\partial_x g \nonumber\\
  &+20zzz^2+500f^2 \nonumber\\
  &+\left( \cdots \right).
\end{align}
} % <================================================= end lower fontsize
\blindtext
\end{document} 

with the result:

As you can see (marked with the two red arrows) there is no interaction with the line before {\small or {\footnotesize ...

Answer 2

\documentclass[a4paper,12pt]{article}

\usepackage{mathrsfs}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{REVSYMB4-1}
\usepackage{latexsym}
\usepackage[a4paper, total={6in, 9in}]{geometry}

%---------------- show page layout. don't use in a real document!
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.15pt}
\renewcommand*\ShowFrameColor{\color{red}}
%---------------------------------------------------------------%

\begin{document}
\begin{multline}\label{eq:longeq}
w = 100(\partial_x f)^3x^2 + \cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2   
    + \bigl(z^3-150zzz^2-20\epsilon f z^2\bigr) \partial_x f \partial_x^2 f                 \\
    + \epsilon\bigl[ 200\bigl( xxx\cot\theta f^3 - 1\bigr)(\partial_x g)^2
        + \bigl( \cot\theta- yyy^3\bigr)\partial_x f                                        \\
    - \bigl(4-1000\cot\theta f^3\bigr)g\partial_x^2 f \bigr]\partial_x g +20zzz^2+500f^2    %\\
    + \bigl( \cdots \bigr).
\end{multline}

\end{document}

Answer 3

As I said in a comment, you can use \allowdisplaybreaks to enable page breaking inside a multiline equation. Here is a demo:

\documentclass[11pt]{article}
\usepackage[vmargin=2cm]{geometry}
\usepackage{amssymb,amsmath}

\usepackage{lipsum}
\allowdisplaybreaks

\begin{document}

\lipsum[1-5]

            \begin{align}
            \label{eq:S1f}
            y_1 &= a+b+c \\ & = d+e+f \\ & = g+h+ j\\
            y_2 &= a+b+c \\ & = d+e+f \\ & = g+h+j \\
            y_3 &= a+b+c \\ & = d+e+f \\ & = g+h+j \\
            y_4 &= a+b+c \\ & = d+e+f \\ & = g+h+j
            \end{align}

\end{document} 

Added:

As to the new code you posted, I would load mathtools and nccmath. Among many additions to amsmath, the first package enables to depart from an alignment in a line of an align environment, with its \EqMoveLeft command. The latter package defines medium-sized commands, which are ~ 80 % of \display style. This I propose this:

\documentclass[12pt]{article}%

\usepackage{mathrsfs}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{REVSYMB4-1}
\usepackage{nccmath}
\usepackage[a4paper, total={6in, 9in}, showframe]{geometry}

\begin{document}

\begin{align}\label{eq:longeq}
\MoveEqLeft\medmath{
w = 100(\partial_x f)^3x^2
+\cot\theta \partial_x f \partial_x fx^2-\partial_x g x^2
+ \left(z^3-150zzz^2-20\epsilon f z^2\right)
\partial_x f \partial_x^2 f} \notag\\
 & \medmath{{}+ \epsilon\Bigl[ 200\bigl( xxx\cot\theta f^3-1\bigr)(\partial_x g)^2
+\bigl( \cot\theta- yyy^3\bigr)\partial_x f -\bigl(4-1000\cot\theta f^3
\bigr)g\partial_x^2 f \Bigr]\partial_x g}\quad \notag\\
 & \medmath{{}+20zzz^2+500f^2 +( \cdots)}.
\end{align}

\end{document}