pgfplots: Dimension too large with no obvious large numbers

Question

The following MWE results in the error Dimension too large. Changing the upper limit of the domain to a smaller value like 120 gets makes this error disappear.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
  \begin{axis} [
        domain=-20:150,
      ]
    \addplot+ {exp(-x*x)};
  \end{axis}
\end{tikzpicture}
\end{document}

But I cannot understand why. The largest number that should be involved in the calculation is 150^2, which is well in pgfplots' range (and in fact plotting x*x works just fine). My guess is that it has something to do with the implementation of exp that makes pgfplots try to compute exp(150^2) in the process of calculating exp(-150^2). However, the plot still appears just fine, so I'm not sure.

What is the reason for this error and how can I avoid it?

---

(Of course the real function I want to plot is a bit more complex, so just manually plotting y = 0 for x > 50 or something like that won't work. I need to solve/circumvent the underlying issue.)

Answer 1

• Not an answer.
• Just to make sure that there is no misunderstanding.
• I plotted your example in MS Excel (be aware that the decimal separator is a comma, German language setting).
• Is my screenshot in alignment with your expectations (or did I make a mistake)?

---

Update 1

• There is some kind of dependency on the version/compiler.
• Take the following code for example.

---

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
  \begin{axis} [
        domain = 120:130, % 120:121 works
        samples = 10,
      ]
    \addplot+ {exp(-x*x)};
  \end{axis}
\end{tikzpicture}
\end{document}

• TeXLive 2020, pdfLaTeX: Error
• TeXLive 2020, LuaLaTeX: Works
• TeXLive 2021, pdfLaTeX: Error
• TeXLive 2021, LuaLaTeX: Works
• TeXLive 2021, LuaLaTeX: Error when using \pgfplotsset{compat=1.10}!

Update 2

150^2 seems to work!

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\begin{document}
\begin{tikzpicture}
  \begin{axis} [
        domain = 140:150,
        samples = 10,
      ]
    \addplot+ {x^2};
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

As I commented above, sagetex is a good tool for more complicated mathematics. That's because it gives you access to a CAS and the Python programming language. Here is a quick sagetex implementation:

\documentclass[11pt,border=1mm]{standalone}
\usepackage{sagetex}
\usepackage[usenames,dvipsnames]{xcolor}
\usepackage{pgfplots}
\pgfplotsset{compat=1.16}
\begin{document}
\begin{sagesilent}
LowerX = -20
UpperX = 150
LowerY = -.1
UpperY = 1.1
step = .13
t = var('t')
g(x)= e^(-x^2)
x_coords = [t for t in srange(LowerX,UpperX,step)]
y_coords = [g(t).n(digits=6) for t in srange(LowerX,UpperX,step)]
output = r"\begin{tikzpicture}"
output += r"\begin{axis}[xmin=%f,xmax=%f,ymin= %f,ymax=%f,"%(LowerX,UpperX,LowerY, UpperY)
output += r"xlabel=$x$,ylabel=$y$,axis x line=middle,axis y line=middle,"
output += r"grid style=dashed]"
output += r"\addplot[thin, blue, unbounded coords=jump] coordinates {"
for i in range(0,len(x_coords)-1):
    if (y_coords[i])<LowerY or (y_coords[i])>UpperY:
        output += r"(%f , inf) "%(x_coords[i])
    else:
        output += r"(%f , %f) "%(x_coords[i],y_coords[i])
output += r"};"
output += r"\end{axis}"
output += r"\end{tikzpicture}"
\end{sagesilent}
\sagestr{output}
\end{document}

The output in Cocalc is below:

The sagetex package uses the Sage CAS. This is not part of the LaTeX distribution. The easiest way to get started is through a free Cocalc account.

Answer 3

When I understand your question right then the answer is: This type of question is quite common here on TeX.SX. Here one possible solution to circumvent the problem. For details have a look at the comments in the code.

Here a list of similar questions I have answered with some other possibilities to (most likely) circumvent the problem as well.

• https://tex.stackexchange.com/a/561246/95441
• https://tex.stackexchange.com/a/611646/95441
• https://tex.stackexchange.com/a/470199/95441

% used PGFPlots v1.18.1
\documentclass[border=5pt]{standalone}
\usepackage{pgfplots}
    \pgfplotsset{
        % When using `compat` level 1.11 or lower TeX will be used as
        % calculation engine. This includes not stating `compat` at all.
        % Stating a `compat` level 1.12 or higher *and* compiling/TeXing with
        % LuaLaTeX uses Lua as calculation engine (when the equation satisfies
        % some requirements)
        % --> using 1.11 results in a "Dimension too large" error
        % --> using 1.12 and compiling with LuaLaTeX works just fine
        compat=1.12,
    }
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        domain=-20:150,
    ]
        \addplot {exp(-x^2)};
    \end{axis}
\end{tikzpicture}
\end{document}