"Batched affine" short-Weierstrass elliptic-curve additions
The affine addition formula for short Weierstrass curves is usually given by
$$
\begin{align}
\lambda &amp;= \frac{y_2 - y_1}{x_2 - x_1} \\
x_3 &amp;= \lambda^2 - x_1 - x_2 \\
y_3 &amp;= \lambda(x_1 - x_3) - y_1 \\
\end{align}.
$$
This gives us 1 inversion, 2 multiplications, 1 squaring, and a few field additions.
The trick here, when adding many points in parallel, is to use the so-called Montgomery trick (thus called because it was popularized in Montgomery's 1987 paper), which trades $n$ inversions by $3n$ multiplications and a single field inversion.
Here follows a simple description of the algorithm from Modern Computer Arithmetic:

So in reality you are still performing an inverse, but it is amortized among many simultaneous additions; for large enough numbers its cost becomes negligible.