rehype-katex@7.0.1 · lil2 family · @itslil/lil2-rehype-katex

rehype-katex,
flat.

Every math element rendered by KaTeX, and KaTeX’s HTML read into the flat hast arena: tag ids, property ids and value kinds generated from property-information.

npm install @itslil/lil2-rehype-katex

Playground GitHub ↗

lil2 browser build versus minified upstream · Brotli-11 26.0%smaller

26,829 B upstream (Terser) → 19,848 B lil2

24.6% smallergzip-9 objective build

34.0% smallerraw objective build

0.77× the timeof upstream’s per call, Chromium 151.0.7922.34 (geometric mean)

3/3size cells smaller

Raw, gzip and Brotli each use a separate LilScript compilation targeting that objective; upstream is the smallest of Terser, esbuild and Oxc on the same API bundled for the browser.

A chat app · Playwright · phone CPUs

Streaming chats,
2.5× less CPU.

react-markdown 10.1.0 + remark-gfm, remark-math, rehype-katex → lil2 /full; main-thread time, Chromium 151
	short chat (5 replies)	average chat (20 replies)	long chat (60 replies)
CPU while the replies stream, mid-tier phone (4×)	7.1 s → 3.2 s 2.2×	29.1 s → 11.5 s 2.5×	1.3 min → 31.0 s 2.5×
CPU while the replies stream, low-end phone (6×)	11.2 s → 4.7 s 2.4×	45.9 s → 17.7 s 2.6×	2.0 min → 47.4 s 2.5×
CPU while the replies stream, this machine	1.6 s → 0.8 s 2.1×	6.8 s → 2.7 s 2.5×	17.6 s → 7.0 s 2.5×
updates slower than a frame (16.7 ms), low-end phone (6×)	125 → 6 of 1,053	671 → 6 of 4,615	1,318 → 67 of 12,897
opening the saved chat, low-end phone (6×)	417 ms → 317 ms 1.3×	843 ms → 519 ms 1.6×	1.77 s → 960 ms 1.8×

Measured through lil2-react-markdown, which this package is a layer of. LLM-style replies (lists, code, tables, math; about 2.5 KB each) streamed a few tokens at a time and rendered by React, finished messages memoized. Chrome's CPU throttling stands in for phones (4×: Lighthouse's mid-tier mobile; 6×: DevTools' low-end mobile); median of 2 runs, libraries alternating, fresh tab each. Every streamed update renders the same DOM as react-markdown (test/chat.test.mjs, Chromium and Firefox). Reproduce: npm run bench:chat.

lil2-micromark ✦ lil2-mdast-util-from-markdown ✦ lil2-mdast-util-to-hast ✦ lil2-remark-gfm ✦ lil2-remark-math ✦ lil2-rehype-katex ✦ lil2-remark-breaks ✦ lil2-react-markdown ✦ lil2-react-markdown + gfm ✦ lil2-react-markdown + gfm, math, KaTeX, breaks ✦ lil2-micromark ✦ lil2-mdast-util-from-markdown ✦ lil2-mdast-util-to-hast ✦ lil2-remark-gfm ✦ lil2-remark-math ✦ lil2-rehype-katex ✦ lil2-remark-breaks ✦ lil2-react-markdown ✦ lil2-react-markdown + gfm ✦ lil2-react-markdown + gfm, math, KaTeX, breaks

The lil2 family

This package,
then the stack.

Every layer of the react-markdown stack, rewritten bottom to top with ints for every id and enum and flat arrays for every tree. Each tab is one package: its size against minified upstream for each objective, its speed in real browsers, and the checks that its output equals upstream’s.

lil2-rehype-katex

Every math element rendered by KaTeX, and KaTeX’s HTML read into the flat hast arena: tag ids, property ids and value kinds generated from property-information.

GitHub ↗page ↗comparison.json ↗

Rewritesrehype-katex@7.0.1 APImarkdownToHast(value, katexOptions) → hast columns BehaviourSame hast as upstream under eight KaTeX setting sets on 182 formulas as text, display and fenced math, in Node (tokenizer) and in Chromium and Firefox (the document parses). Cells3 of 3 smaller

Both builds, in this page

Live
lab.

Left is markdown. Right is lil2-react-markdown/full rendering it as you type. Race times upstream rehype-katex against lil2 on the current text, both loaded here.

# Notes on Fourier analysis

The Fourier transform of an integrable function $f$ is
$\hat f(\xi) = \int_{-\infty}^{\infty} f(x)\, e^{-2\pi i x \xi}\, dx$, and when
$\hat f$ is integrable too the inversion formula holds:

$$
f(x) = \int_{-\infty}^{\infty} \hat f(\xi)\, e^{2\pi i x \xi}\, d\xi .
$$

## Plancherel

For $f \in L^1 \cap L^2$ we have $\|f\|_2 = \|\hat f\|_2$, so the transform
extends to a unitary map on $L^2(\mathbb{R})$.

$$
\int_{\mathbb{R}} |f(x)|^2 \, dx = \int_{\mathbb{R}} |\hat f(\xi)|^2 \, d\xi
$$

## Convolution

If $h = f * g$ with $(f * g)(x) = \int f(y) g(x - y)\, dy$, then
$\hat h = \hat f \cdot \hat g$. The Gaussian $g(x) = e^{-\pi x^2}$ is its own
transform, $\hat g = g$.

| Function | Transform |
| --- | --- |
| $e^{-\pi x^2}$ | $e^{-\pi \xi^2}$ |
| $\mathbf{1}_{[-1/2, 1/2]}(x)$ | $\operatorname{sinc}(\xi) = \frac{\sin \pi \xi}{\pi \xi}$ |
| $f(x - a)$ | $e^{-2\pi i a \xi} \hat f(\xi)$ |
| $f'(x)$ | $2\pi i \xi\, \hat f(\xi)$ |

## Poisson summation

For a Schwartz function $f$:

$$
\sum_{n \in \mathbb{Z}} f(n) = \sum_{k \in \mathbb{Z}} \hat f(k)
$$

Applied to $f(x) = e^{-\pi t x^2}$ this gives the theta identity
$\theta(t) = t^{-1/2}\, \theta(1/t)$ where $\theta(t) = \sum_n e^{-\pi n^2 t}$.

## A matrix

$$
\begin{pmatrix} a & b \\ c & d \end{pmatrix}^{-1}
= \frac{1}{ad - bc} \begin{pmatrix} d & -b \\ -c & a \end{pmatrix},
\qquad ad - bc \neq 0 .
$$

- [x] inversion
- [x] Plancherel
- [ ] uncertainty principle: $\Delta x\, \Delta \xi \ge \frac{1}{4\pi}$

The output is rendered by the shipped browser build; the race runs each side for 400 ms after a warm-up.

Browser build · minified upstream

Three objectives.
Measured separately.

Raw69,460 B

34% smaller than original

Terser · 105,268 B

gzip-922,895 B

24.6% smaller than original

Terser · 30,350 B

Brotli-1119,848 B

26% smaller than original

Terser · 26,829 B

Current LilScript versus minified original
Compiler objective	LilScript	Original minified	Original minifier	Difference
Raw	69,460 B	105,268 B	Terser	34% smaller
gzip-9	22,895 B	30,350 B	Terser	24.6% smaller
Brotli-11	19,848 B	26,829 B	Terser	26% smaller

Each LilScript row comes from a separate compilation targeting that row’s objective. Raw is uncompressed JavaScript; gzip uses level 9; Brotli uses quality 11 and window 22. For each metric, the original is the smallest result among the minifiers below. No JavaScript minifier runs after LilScript.

Every artifact, measured with all three codecs

Artifact	Raw	gzip-9	Brotli-11
LilScript · Raw objective	69,460 B	24,113 B	20,898 B
LilScript · gzip-9 objective	72,831 B	22,895 B	19,821 B
LilScript · Brotli-11 objective	73,031 B	22,915 B	19,848 B
Original · Terser 5.51.2	105,268 B	30,350 B	26,829 B
Original · esbuild 0.28.1	107,551 B	32,257 B	28,619 B
Original · Oxc vite 8.2.1	105,338 B	30,796 B	27,390 B

Browser builds on both sides: lil2’s `browser` condition and upstream bundled by esbuild 0.28.1 with the browser condition (`export {fromMarkdown} from 'mdast-util-from-markdown'; export {math} from 'micromark-extension-math'; export {mathFromMarkdown} from 'mdast-util-math'; export {toHast} from 'mdast-util-to-hast'; export {default as rehypeKatex} from 'rehype-katex'`). Upstream: rehype-katex@7.0.1. External dependencies excluded from sizes: katex. CSS, fonts, type declarations and source maps are outside these JavaScript sizes.

Measurements, hashes and settings ↗ · Commands and build receipts ↗

Real browsers · identical output first

Speed.

Chromium 151.0.7922.34 · median per call, identical output checked first
Document	Upstream	lil2	Time
math	10.100 ms	7.800 ms	0.77×
load (import)	29.0 ms	23.1 ms	0.80×
first call, cold	41.0 ms	40.4 ms	0.99×

Firefox 153.0 · median per call, identical output checked first
Document	Upstream	lil2	Time
math	14.000 ms	12.000 ms	0.86×
load (import)	47.0 ms	42.0 ms	0.89×
first call, cold	48.0 ms	44.0 ms	0.92×

Playwright, one fresh browser context per lane; lanes interleave and alternate order every round. Upstream is the same API bundled from npm for the browser; lil2 is the shipped browser build. Load is the module import after the file is fetched; first call is the first document, cold.

Same machine · sequential builds

Build time.

Build wall time on the same machine
Output objective	LilScript compilation	Original bundling + minification	Original minifier
Raw	18.13 s	0.813 s	Terser
gzip-9	18.13 s	0.813 s	Terser
Brotli-11	6.03 s	0.813 s	Terser

One fresh output build per objective and minifier, run sequentially. LilScript compilation includes optimization and objective scoring with persistent caches disabled and one worker. Original time includes Node startup, esbuild bundling of installed upstream ESM, and the named minifier. It excludes building the upstream package from its original TypeScript sources. Dependency installation, tests and final file compression are excluded on both sides. These are observations on a shared machine, not a build-speed guarantee.

AMD EPYC 7763 64-Core Processor · 8 logical CPUs · 15.6 GiB RAM · Linux 7.0.0-1014-azure · Node v20.19.0. Measured 2026-10-04. Exact commands and compiler identity ↗

Install

Typed, flat,
same output.

npm install @itslil/lil2-rehype-katex

rehype-katex,flat.

Streaming chats,2.5× less CPU.

This package,then the stack.