Why am I getting this Arithmetic Overflow Error?

[woeful mesa]

This error appears to occur because I have too much content in my file. But when I searched it up, I only saw the error occurring for people doing calculations.

When the error comes, the PDF is just a blank white sheet of the same vertical height as if the content was there. But the content only appears when I remove the $$\dv{y}{x} = ... line.

[winged granite]

Because you're using standalone in the weirdest way possible, and defienitely not in the same it was designed to be used.

Note that the same overflow will happen if you were to insert lines of text thereafter Euler's method header

Also note, the code isn't fine, your line 388 is missing the closing $$

[woeful mesa]

• Even if im using standalone, why does it suddenly break after i add a line after Euler's Method?
• I prefer using standalaone because it avoids breaks between pages.
• thanks for catching the mistake, i fixed it

[winged granite]

It’s not the Euler method that magically gives rise to error, don’t read into it

In any case, the limitation seems to be coming from preview

try varwidth in lieu of preview

[lucid plume]

because the height of your page (or some quantity that depends on it) would exceed the maximum dimension allowed by TeX

which is around a few meters

[lucid plume]

it avoids breaks between pages
So you want your entire document to consist of one infinitely tall page? Why don't you use a webpage then?

[valid quarry]

why does TeX limit the dimensions?

[valid quarry]

if you mean using HTML- no
if you mean generating a site with LaTeX- can you show me?

[winged granite]

good question

don't know

[valid quarry]

btw leo whats the command to view another user's preamble

[winged granite]

you can't

it's reserved for preamble reviewers

[valid quarry]

what about through texit support?

[valid quarry]

can i request to view @woeful mesa's preamble

btw do you also see that account as "likely spammer"

[waxen folio]

TeX’s dimension limits trace back to its choice of a fixed‑point representation on 32‑bit hardware and conservative overflow protection in arithmetic. Internally, all lengths in TeX are stored as integral multiples of a “scaled point” (sp), with 1 pt = 65 536 sp, using a 32‑bit signed fixed‑point format (16 fractional bits) that Knuth implemented for efficiency and portability.

To avoid overflow during addition, TeX actually only expects 14 of the integer bits to be used, reserving the rest for sign and fractional precision.

[valid quarry]

overflow protection in arithmetic
but i'm not performing any arithmetic within my latex document

Internally, all lengths in TeX are stored as integral multiples of a “scaled point” (sp)
does this represent the quality of the vector graphic?

[waxen folio]

1. You aren't, but TeX does a lot of it under the hood.

2. Not directly. sp units affect precision, not visual resolution.

[valid quarry]

Not directly. sp units affect precision, not visual resolution.
is this regarding the rendering of the document, or the calculation of arithmetic?

[winged granite]

both

it's not you instructing TeX to do arithmetic, it's TeX doing internal arithmetic to figure out where to place what

[valid quarry]

leo can you view @woeful mesa's preamble

[waxen folio]

When you say "sp affects precision," it's about the arithmetic, not the rendering.

TeX does all of this math using integer arithmetic in units of sp. So precision here means how accurately TeX can represent and calculate lengths.

So even though TeX might compute something like:

\hspace{123.456789012345 pt}

and store it internally as an integer number of sp, that doesn't visually degrade anything, the final graphic remains sharp and scalable.

[valid quarry]

is it possible for me to reduce the precision

if the sp is really that many digits by default, is there any harm in removing a few digits?

how do i reduce sp?

[waxen folio]

Technically it is possible, but with caveats.

Since TeX uses fpa where 1 pt = 65536 sp, you're asking: "Can I make it, say, 1 pt = 1000 sp instead?" i.e., fewer fractional bits.

The answer is not within standard TeX. The 65536 sp/pt ratio is hardcoded into the TeX engine. It's not configurable at runtime, and it's deeply baked into how all dimensions, glue, and arithmetic work.

Although, you can simulate lower precision.

[valid quarry]

ok i see how this might be a problem. but i don't understand why the exact same content works in article but not standalone

[winged granite]

I still think you're mis-using, and maybe even abusing, the standalone package. According to the user guide of the standalone package, the main (sole?) purpose of the standalone package is to generate well-contained objects—often, but not exclusively, pictures—that can be saved as external files in a suitable file format for subsequent pasting into other documents, e.g., Word and PowerPoint files

[waxen folio]

Basically, standalone adds extra scaling and cropping logic, which can interfere with large dimensions or precision-sensitive code.

standalone.cls loads the preview package internally. It sets up a tight bounding box around your content. And yes, this includes measuring the exact size of the content, croppin the PDF to that size, and possibly applying scaling.

This process uses additional boxes, glue, and calculations, and TikZ picture bounding boxes are sometimes computed twice or offset.

It also often uses \vbox/\hbox wrappers with zero margins. These amplify rounding errors or trigger overflows if for example your TikZ picture is either very large (e.g., 1000000pt wide), infinitesimally small (e.g., 0.00001pt elements), or uses a lot of math or transformations (these include options like scale, rotate, etc.)

All that, and article just puts stuff on a normal page.

[valid quarry]

i already understand why i shouldnt be using standalone, but i dont understantd why i cant use `standalone

[waxen folio]

With article, you're less likely to hit arithmetic edge cases.

[valid quarry]

can theoretically infinite content be stored in an article

[winged granite]

No, there’s a hard limit

[valid quarry]

is there any document class that has no hard limit?

[winged granite]

it’s not the limit of the class. it’s of TeX itself

[waxen folio]

You can use standalone, but the issue is not a moral "shouldn't", it's that standalone can hit TeX's internal limits in cases where article doesn't, due to implementation details, especially in page size computation, bounding box measurement, and output drive interaction (pdflatex, luatex, etc.)

Now, look at this:

\setbox0=\hbox{<your content>}
\pdfpagewidth=\wd0
\pdfpageheight=\ht0+\dp0

This happens (indirectly) inside its code path via preview, unless you disable it.

Now suppose your content involves a TikZ drawing with very large dimensions (e.g., something like \draw (0,0) -- (100000pt,0);), or there's an internal dimension (like a \pgfmathsetlength result) that rounds to > \maxdimen (≈ 16383.99999pt). Then this will literally fail:

\pdfpagewidth=\wd0  % ← this right here may overflow

even though the drawing is visually fine, the engine can't store that page size.

[valid quarry]

so the tex will fail because the drawing simply doesnt fit on the standalone page?

whereas article class is able to change the page dimensions to accomodate more things?

[winged granite]

a page that stretches metres (standalone) vs multiple pages that are centimetres long (article)

[winged granite]

In any case, i'll consider this thread resolved