Julia vs Python

I gave a talk to economists (i.e., not professional programmers) about a Julia project we were working on. Julia is famous for its speed. It uses LLVM [1] as back-end for its JIT (Just In Time) compilation. As seeing is believing, here is an example algorithm which is used to compare performance between different languages and tools. This example was chosen as it is small, easy to explain, and easy to program while still showing meaningful time differences.

We have a square \([-1,+1]\times[-1,+1]\) and an inscribing circle with radius \(1\). See the dynamic figure below. Their areas are \(4\) and \(\pi\) respectively. The idea is to draw \(n\) points \[\begin{align}& x_i \sim U(-1,+1) \\ & y_i \sim U(-1,+1)\end{align}\]Let \(m\) be the number of points inside the circle, i.e. with \[x_i^2+y_i^2\lt 1\] Obviously, from the ratio of the areas, we have \[\frac{m}{n} \approx \frac{\pi}{4}\] It follows that an estimate of \(\pi\) is \[\hat{\pi}=4\frac{m}{n}\]

Simulation with n=1000

A Julia thingy

 In Julia, we can write 2x instead of 2*x. Not the most earth-shattering. But a bit special nonetheless.

The expression in the last cell is interpreted as a function call.