\documentclass{article}
\usepackage{amsmath}
\title{pdfdiff Test Document}
\author{Test Author}
\date{2024}

\begin{document}
\maketitle

\section{Introduction}

This is the original version of the test document.
It contains several sentences that will be changed in the modified version.

The quick brown fox jumps over the lazy dog.
This sentence will be deleted entirely in the modified version.

\section{Methods}

We used a straightforward approach to solve the problem.
The algorithm runs in linear time with respect to the input size.
All experiments were conducted on a standard desktop machine.

The loss function is defined as
\begin{equation}
    \mathcal{L} = \frac{1}{N} \sum_{i=1}^{N} \left( y_i - \hat{y}_i \right)^2
\end{equation}
where $y_i$ is the true label and $\hat{y}_i = f(x_i; \theta)$ is the model prediction.

We update parameters using gradient descent with learning rate $\alpha = 0.01$.

\section{Results}

The results show a modest improvement over the baseline.
Our method achieves an accuracy of 72\% on the test set.

The overall score is computed as
\begin{equation}
    S = \frac{1}{n} \sum_{i=1}^{n} \mathbf{1}[\hat{y}_i = y_i]
\end{equation}

\section{Conclusion}

In conclusion, the proposed method works reasonably well.
Future work will focus on improving performance.

\end{document}
