# Fast computation of quadrupole and hexadecapole approximations in microlensing with a single point-source evaluation

## TL;DR

This paper introduces a faster method for computing quadrupole and hexadecapole approximations in gravitational microlensing, significantly reducing computation time and enabling more efficient analysis of large datasets.

## Contribution

It presents an optimized computational approach that accelerates quadrupole and hexadecapole calculations, making microlensing modeling more efficient and accessible.

## Key findings

- Quadrupole approximation is about twice as slow as point-source evaluation.
- Hexadecapole approximation is approximately four times faster than previous methods.
- Open-source Python routines are provided for practical use.

## Abstract

The exoplanet detection rate from gravitational microlensing has grown significantly in recent years thanks to a great enhancement of resources and improved observational strategy. Current observatories include ground-based wide-field and/or robotic world-wide networks of telescopes, as well as space-based observatories such as satellites Spitzer or Kepler/K2. This results in a large quantity of data to be processed and analyzed, which is a challenge for modeling codes because of the complexity of the parameter space to be explored, and the intensive computations required to evaluate the models. In this work, I present a method that allows to compute the quadrupole and hexadecapole approximation of the finite-source magnification with more efficiency that previously available codes, with routines about x6 and x4 faster respectively. The quadrupole takes just about twice the time of a point-source evaluation, which advocates for generalizing its use to large portion of the light curves. The corresponding routines are available as open-source python codes.