Formula problem

Question

I am using https://www.codecogs.com/latex/eqneditor.php

And added my latex as follows:

 \begin{equation}
 SSIM(x,y)=\frac{{\left ( 2 \mu_x\mu_y+ C_1 \right )+ \left (2 \sigma _x_y+C_2\right)}} 
{\left(\mu_x^2+\mu_y^2+C_1)(\sigma_x^2+\sigma_y^2+C_2\right)}
  \label{eq:SSMI}
\end{equation}

I expected the following formula but instead of I got the error:!Double subscript. ...y+C_1\right)+ ...

Answer 1

Double subscripts are not allowed by TeX, you should replace \sigma_x_y by \sigma_{xy}.

Also, it is preferable to use a specific operator name for such a function.

Edit: And as David Carlisle pointed out, the \left and \right commands are of no use here. It can only add unwanted additional spacing.

You can try something like this:

\documentclass[12pt]{article}
%
\usepackage{mathtools}
\DeclareMathOperator{\SSIM}{SSIM}
\begin{document}
\begin{equation}
  \SSIM(x,y) = \frac{(2\mu_x\mu_y + C_1) + (2 \sigma _{xy} + C_2)} 
    {(\mu_x^2 + \mu_y^2+C_1) (\sigma_x^2 + \sigma_y^2+C_2)}
  \label{eq:SSMI}
\end{equation}
\end{document}

Answer 2

To achieve the desired output, simply replace \sigma _x_y by \sigma _{xy}.