LaTeX generation quality — math typesetting, document layout, compilation correctness
| Model | Avg Score |
|---|---|
| gpt-4.1-mini | 95.8 |
| gemini-2.5-flash | 93.9 |
| gpt-4.1-nano | 85.5 |
\documentclass{article}
\usepackage{amsmath}
\begin{document}
The solutions to a quadratic equation $ax^2 + bx + c = 0$ are given by the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}\label{eq:euler}
e^{i \pi} + 1 = 0
\end{equation}
\end{document}\documentclass{article}
\usepackage{amsmath}
\begin{document}
The solutions to a quadratic equation $ax^2 + bx + c = 0$ are given by the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
\begin{equation}
\label{eq:euler}
e^{i\pi} + 1 = 0
\end{equation}
\end{document}\documentclass{article}
\usepackage{amsmath} % Required for the 'equation' environment
\begin{document}
\begin{equation} \label{eq:euler}
e^{i\pi} + 1 = 0
\end{equation}
\end{document}\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align}
2x + 3 &= 7 \\
2x &= 7 - 3 \\
x &= \frac{7 - 3}{2} = 2
\end{align}
\end{document}\documentclass{article}
\usepackage{amsmath} % Required for mathematical typesetting
\begin{document}
The solutions to a quadratic equation $ax^2 + bx + c = 0$ are given by the quadratic formula $x \documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
2x + 3 &= 7 \\[6pt]
2x &= 7 - 3 \\[6pt]
2x &= 4 \\[6pt]
x &= \frac{4}{2} \\[6pt]
x &= 2
\end{align*}
\end{document}\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\begin{bmatrix}
x_1 \\
x_2 \\
x_3
\end{bmatrix\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
2x + 3 &= 7 \\
2x &= 4 \\
x &= 2
\end{align*}
\end{document}\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2 \\
x_3
\end{pmatrix}
=
\begin{pmatrix}
b\documentclass{article}
\usepackage{amsmath} % Required for pmatrix environment
\begin{document}
\[
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{pmatrix}
\begin{pmatrix}
x_1 \\
x_2 \\
x_\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation}
f(x) = \begin{cases}
x^2, & \text{if } x \geq 0, \\
- x, & \text{if } x < 0.
\end{cases}
\end{equa\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
f(x) =
\begin{cases}
x^2, & x \geq 0, \\
-x, & x < 0.
\end{cases}
\end{equation}
\end{document}\documentclass{article}
\usepackage{amsmath} % Required for the 'cases' environment
\begin{document}
\section*{Piecewise Function Example} % Just for a title, not strictly required by the prompt
He\documentclass{article}
\usepackage{amsmath, amssymb}
\begin{document}
\[
\int_a^b f'(x) \, dx = f(b) - f(a)
\]
\[
\int_{\partial \Omega} \omega = \int_{M} d\omega
\]
\end{document}\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation}
\label{eq:FTC}
\int_a^b f'(x)\, dx = f(b) - f(a)
\end{equation}
\vspace{1em}
\begin{equation}
\l\documentclass{article}
\usepackage{amsmath} % Required for mathematical environments like gather*
\usepackage{amssymb} % Required for symbols like \partial and \Omega
\begin{document}
\begin{gather\documentclass{article}
\usepackage{booktabs}
\usepackage{array}
\usepackage{caption}
\usepackage{float}
\begin{document}
\begin{table}[H]
\centering
\begin{tabular}{l c c}
\toprule
Model & Accuracy\documentclass{article}
\usepackage{booktabs} % For professional table rules
\begin{document}
\begin{center}
\begin{tabular}{lrr}
\toprule
Model & Accuracy (\%) & Parameters (M) \\
\midr\documentclass{article}
\usepackage{booktabs}
\usepackage{array}
\usepackage{caption}
\begin{document}
\begin{table}[ht]
\centering
\caption{Benchmark Results}
\begin{tabular}{lcc}
\toprule
Model & \documentclass{article}
\usepackage{amsmath, amsthm}
\begin{document}
\newtheorem{theorem}{Theorem}
\begin{theorem}
In a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), we have
\[
a^2\documentclass{article}
\usepackage{booktabs}
\usepackage{caption}
\begin{document}
\begin{table}[ht]
\centering
\caption{Comparison of Models Across Tasks}
\begin{tabular}{lcccc}
\toprule
& \multi\documentclass{article}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{multicol}
\usepackage{array}
\begin{document}
\begin{table}[ht]
\centering
\begin{tabular}{lccccc}
\toprule
\multicolu\documentclass{article}
\usepackage{booktabs} % For professional looking tables
\usepackage{amsmath} % Often useful, though not strictly needed here
\usepackage{amssymb} % Often useful, though not s\documentclass{article}
\usepackage{amsmath,amsthm}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}
In a right triangle with legs $a$ and $b$ and hypotenuse $c$, we have
\[
a^2 + b^2\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm} % Required for \newtheorem and proof environment
% Define a theorem style and a theorem environment
\theoremstyle{plain} % This is the\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}
\usepackage{mtreatmal}
\usepackage{thmtools}
% Define custom environments
\declaretheorem[style=definition,name=Definition]{de\documentclass{article}
\usepackage{amsmath,amssymb,amsthm}
\newtheorem{definition}{Definition}
\newtheorem{lemma}{Lemma}
\newtheorem{remark}{Remark}
\begin{document}
\begin{definition}
A \emph{met\documentclass{article}
\usepackage[ruled,vlined]{algorithm2e}
\begin{document}
\begin{algorithm}[H]
\SetKwFunction{QuickSort}{QuickSort}
\SetKwFunction{Partition}{Partition}
\SetKwInOut{Input}{Inpu\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage[linesnumbered,ruled,vlined]{algorithm2e}
\begin{document}
\begin{algorithm}[H]
\caption{Quicksort Algorithm}
\KwIn{$A$ (array), $lo$\documentclass{article}
\usepackage{amsmath} % For math environments and commands like \iff
\usepackage{amssymb} % For symbols like \mathbb, \forall, \in
\usepackage{amsthm} % For \newtheorem
\documentclass{article}
\usepackage{amsmath}
\usepackage[ruled,vlined]{algorithm2e}
\begin{document}
\begin{algorithm}[H]
\caption{Mini-batch Stochastic Gradient Descent with Momentum}
\KwIn{Initial\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\section{Requirements}
\begin{enumerate}
\item The software shall support user authentication via username and password.
\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{booktabs}
\usepackage{algorithm2e}
\usepackage{tikz}
\begin{document}
\section{Requirements}
\begin{enumerate}
\item The softwar\documentclass{article}
\usepackage{amsmath}
\usepackage[ruled,vlined]{algorithm2e}
\begin{document}
\begin{algorithm}[H]
\SetAlgoLined
\KwIn{Initial parameters $\theta$, learning rate $\alpha$, mom\documentclass{article}
\usepackage{amsmath} % Not strictly needed but often included, so keeping it standard
\usepackage{amssymb} % Not strictly needed but often included, so keeping it standard
% No\documentclass{article}
\usepackage{amsmath,amssymb}
\title{A Brief Survey of Optimization Methods}
\author{Jane Smith}
\date{March 2026}
\begin{document}
\maketitle
\begin{abstract}
Optimization \documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage{booktabs}
\usepackage{algorithm2e}
\usepackage{tikz}
\usepackage{hyperref}
\title{A Brief Survey of Optim\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\title{A Brief Survey of Optimization Methods}
\author{Jane Smith}
\date{March 2026}
\begin{document}
\maketitle
\begin{abstract}
\documentclass{article}
\usepackage{amsmath} % Required for mathematical symbols like \nabla, \leftarrow, \| \cdot \|
\usepackage[ruled,vlined]{algorithm2e} % Required for pseudocode, with ruled style\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[ruled,vlined]{algorithm2e} % Use ruled and vlined for a standard appearance
\begin{document}
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, shapes.geometric}
\begin{document}
\begin{tikzpicture}[
node/.style={rectangle, rounded corners=8pt, draw, minimum width=3cm,\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, positioning, shapes.geometric}
\begin{document}
\begin{tikzpicture}[
node distance=2.5cm and 4cm,
box/.style={
rectangl\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{tikzpicture}[node/.style={circle, draw=black, minimum size=0.8cm},
>=\documentclass{article}
\usepackage{url}
\begin{document}
Deep learning \cite{goodfellow2016}, attention mechanisms \cite{vaswani2017}, and BERT \cite{devlin2019} have significantly advanced natural\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage{booktabs}
\usepackage{algorithm2e}
\usepackage{tikz}
\usepackage{hyperref}
\begin{document}
This is a sa\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning}
\begin{document}
\begin{center}
\begin{tikzpicture}[node distance=1.5cm and 2cm, every node/.style={circle, draw, minimum size=\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
\end{equation}
\begin{equation}
\prod_{k=1}^{n} k = n!
\end{equation}
\begin{equa\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{equation}
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
\end{equation}
\begin{equation}
\prod_{k=1}^{n} k = n!
\end{e\documentclass{article}
\usepackage{hyperref} % For clickable references (good practice)
\begin{document}
\section*{Introduction}
Recent advancements in deep learning \cite{goodfellow2016} have revo\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\sum_{i=1}^{n} i = \frac{n(n+1)}{2}
\end{equation}
\begin{equation}
\prod_{k=1}^{n} k = n!
\end{equation}
\be\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{gather}
\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \mathbf{B} = 0 \\
\nabla \times\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\begin{document}
\begin{gather}
\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0} \\
\nabla \cdot \vec{B} = 0 \\
\nabla \times \vec{\documentclass{article}
\usepackage{amsmath} % Required for the gather environment
\usepackage{amssymb} % Required for \nabla
\begin{document}
\section*{Maxwell's Equations (Differential Form)}
Her\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning, arrows.meta} % 'positioning' for 'below=of', 'arrows.meta' for enhanced arrow tips like 'stealth'
\begin{document}
\begin{cente\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
1 + \cfrac{1}{
2 + \cfrac{1}{
3 + \cfrac{1}{
4 + \cfrac{1}{5}
}
}
}
\]
\[
\frac{\displaystyle \frac{a}{b} + \frac{c\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
1 + \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{5}}}}
\]
\[
\frac{\frac{a}{b} + \frac{c}{d}}{\frac{e}{f} - \frac{g}{h}}
\]
\documentclass{article}
\usepackage{tikz} % Required for TikZ diagrams
\begin{document}
\begin{center}
\begin{tikzpicture}[
% Define horizontal separation between layers
layersep=3cm,
%\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[
1 + \cfrac{1}{2 + \cfrac{1}{3 + \cfrac{1}{4 + \cfrac{1}{5}}}}
\]
\[
\frac{\frac{a}{b} + \frac{c}{d}}{\frac{e}{f} - \frac{g}{h}}
\]
\documentclass{article}
\usepackage{tikz}
\usepackage{subcaption}
\begin{document}
\begin{figure}
\centering
\begin{subfigure}[t]{0.45\textwidth}
\centering
\begin{tikzpicture}
\dr\documentclass{article}
\usepackage{tikz}
\usepackage{subcaption}
\usepackage{graphicx}
\begin{document}
\begin{figure}[htbp]
\centering
\begin{subfigure}[b]{0.45\textwidth}
\centering
\\documentclass{article}
\usepackage{amsmath,amssymb}
\newcommand{\R}{\mathbb{R}}
\newcommand{\norm}[1]{\left\lVert#1\right\rVert}
\newcommand{\inner}[2]{\left\langle #1, #2 \right\rangle}
\newcommand\documentclass{article}
\usepackage{amsmath, amssymb}
\newcommand{\R}{\mathbb{R}}
\newcommand{\norm}[1]{\left\| #1 \right\|}
\newcommand{\inner}[2]{\left\langle #1, #2 \right\rangle}
\newcommand{\E}{\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage{booktabs}
\usepackage{hyperref}
\begin{document}
\section{Introduction to Statistical Testing}\label{sec:intro}
Statistical testing\documentclass{article}
\usepackage{tikz} % For creating vector graphics
\usepackage{subcaption} % For subfigures and subcaptions
\usepackage{graphicx} % Generally useful for figures, though not stric\documentclass{article}
\usepackage{amsmath} % For math environments and commands
\usepackage{amssymb} % For \mathbb (blackboard bold)
% Define custom commands
\newcommand{\R}{\mathbb{R}} % Real numb\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{booktabs}
\begin{document}
\section{Statistical Hypothesis Testing}\label{sec:hypothesis-testing}
Statistical hypothesi\documentclass{article}
\usepackage{amsmath} % For equation environment and mathematical symbols
\usepackage{booktabs} % For professional-looking tables (e.g., \toprule, \midrule, \bottomrule)
\use\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
(a+b+c)^3 &= a^3 + b^3 + c^3 \\
&\quad + 3a^2b + 3ab^2 + 3b^2c \\
&\quad + 3bc^2 + 3c\documentclass{article}
\usepackage{amsmath, amssymb}
\usepackage[most]{tcolorbox}
\begin{document}
\begin{tcolorbox}[colback=blue!10!white, colframe=blue!75!black, title=Definition, rounded corners\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
(a + b + c)^3 &= a^3 + 3a^2b + 3a^2c + 3ab^2 + 6abc + 3ac^2 + b^3 + 3b^2c + 3bc^2 + c^3 \\
&= a^3 + b^3 + \documentclass{article}
\begin{document}
\end{document}\documentclass{article}
\begin{document}
\end{document}\documentclass{article}
\begin{document}
\end{document}\documentclass{article}
\usepackage{amsmath}
\usepackage[most]{tcolorbox}
\tcbset{
defbox/.style={
colback=blue!10,
colframe=blue!75!black,
fonttitle=\bfseries,
rounded corners,
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsthm}
\begin{document}
\begin{theorem}
Let $(a_n)$ be a sequence such that
\[
\sum_{k=1}^\infty a_k < \infty.
\]
Then, the series
\[
\sum_{\documentclass{article}
\usepackage{amsmath, amsthm, amssymb}
\newtheorem{theorem}{Theorem}
\begin{document}
\begin{theorem}[Convergence of a Series]
The series defined by
\[
S = \sum_{n=1}^\infty \documentclass{article}
\usepackage{amsmath}
\usepackage[skins]{tcolorbox} % 'skins' loads necessary modules for rounded corners and enhanced features
\begin{document}
\section*{Mathematical Concept