The problem is that the only item getting placed in the lower half of the \splitdfrac
was the +
symbol, and everything else was being placed on a single line. It’s easier to see in a screenshot of the fraction (this was taken in landscape):

Look at how the +
appears to be typeset below everything else, and then the rest of the numerator continues on a different baseline.
Here's a cleaned up version of the code, that is hopefully a little easier to read/follow and compiles to a slightly less wide/more compact fraction:
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
-\frac{1}{128 \pi^2}
\left[
\frac{
\splitfrac{
4 (m_1+m_3) \cos\delta \sin\theta_{12} \sin\theta_{13}
(\cos\delta \cos\theta_{12} (2\,y_e^2 - y_\mu^2 - y_\tau^2
}{
+ (y_\mu^2 - y_\tau^2) \cos 2\theta_{23})) \sin\theta_{13}
+ (-y_\mu^2 + y_\tau^2) \sin\theta_{12} \sin 2\theta_{23}
}
}{
m_1 - m_3
}
\right]
\end{equation}
\end{document}
Here's a screenshot of the new equation:

And some other comments:
As David Carlisle says in the comments, you should be using \sin
or \cos
for math operators; not just typing out the words in italic maths font. Additionally, don’t use non-breaking spaces (the tildes ~
) in maths mode. Instead, consider using maths-spaces (such as the thin space \,
that I’ve used above).
Consider breaking your fraction up into multiple lines, to make it easier to read and debug. That was the first thing I did, and then the out-of-place +
leapt out at me. The scheme above perhaps isn't perfect, but I claim it’s better than a single monolithic line.
You don't need curly braces around exponents with a single character (e.g. y^2
rather than y^{2}
). Again, might make things easier to read (but that's a personal preference).
{}
button but please make it a complete document (not least so we see same margins that you see)sin
andcos
using the math italic font, use\sin
and\cos
or define similar commands if you really need the mixed case versions.