Issue using resizebox within equation and split environments

Why resizing? One line more is sufficient.

documentclass{article}
usepackage{amsmath,amssymb}

makeatletter
newcommand{tf}[1]{operatorname{#1}} % text function
newcommand{tv}[1]{mathit{newmcodes@ #1}} % text variable
makeatother

begin{document}

begin{equation}label{eq:word}
begin{split}
tf{quality}(w_{i})
  &= log(1 + tf{similarity}(a,b)) + log(1 + tf{familiarity}(w_{i}))  
  &quad + log(1+tf{familiarity}(min{(e,3)})) 
  &quad + log(1 + tf{expectedness}(w_i|w_{i-1})) 
  &quad - log(1+tf{tts-experience}(tv{subject}))
         + tf{quality}(w_{i-1}) + mathcal{A} 
end{split}
end{equation}

end{document}

I chose to represent function names with operatorname, so upright, and variables in italics (but text italic, rather than math italic). The newmcodes@ trick is to make hyphens also in variables to be normal and not minus signs.

I wouldn't align the operation signs under the equals. In case you like it better, here's the correct code.

documentclass{article}
usepackage{amsmath,amssymb}

makeatletter
newcommand{tf}[1]{operatorname{#1}} % text function
newcommand{tv}[1]{mathit{newmcodes@ #1}} % text variable
makeatother

begin{document}

begin{equation}label{eq:word}
begin{split}
tf{quality}(w_{i})
  ={}   & !log(1 + tf{similarity}(a,b)) + log(1 + tf{familiarity}(w_{i}))  
  {}+{} & !log(1+tf{familiarity}(min{(e,3)})) 
  {}+{} & !log(1 + tf{expectedness}(w_i|w_{i-1})) 
  {}-{} & !log(1+tf{tts-experience}(tv{subject}))
          + tf{quality}(w_{i-1}) + mathcal{A} 
end{split}
end{equation}

end{document}

The ! bits are necessary because of the “empty atom” that split inserts after &, which causes a following operator to be preceded by a thin space that we need to remove.

Scaling equations makes incompatible font sizes and is usually best avoided.

Here the equation is wider than it need be as math italic spaces out the letters to make them a product of variables, not a word, with that change it already fits on the page, but the equation number is moved down, here I add an additional line break so that the equation number can stay centred.

documentclass{article}
usepackage[utf8]{inputenc}
usepackage{amsmath,amssymb}
usepackage{parskip}
usepackage[numbers]{natbib}
bibliographystyle{plainnat}
usepackage{graphicx}

begin{document}

begin{gather}
    label{eq:word}
     begin{split}
        operatorname{quality}(w_{i}) ={}hspace{-50pt}&
     &log(1 + operatorname{similarity}(a,b)) + log(1 + operatorname{familiarity}(w_{i}))  
        & + log(1+operatorname{familiarity}(min{(e,3)})) +
        log(1 + operatorname{expectedness}(w_i|w_{i-1})) 
        & - log(1+operatorname{tts-experience}(mathrm{subject})) + 
        operatorname{quality}(w_{i-1}) + mathcal{A} 
   end{split}
    end{gather}

end{document}