I wasn't aware of the GNU Octave project until I saw a post on Reddit that it had hit version 4.0.0. If you're not familiar with it either, here's a brief overview:
GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation.
So why is this exciting? Aside from a Windows installer for all you people too lazy to switch to GNU/Linux, it apparently finally got a GUI (kind of a must for "modern" software):
Octave 4.0 is a major new release with many new features, including a graphical user interface, support for classdef object-oriented programming, better compatibility with Matlab, and many new and improved functions.
You can also get the full list of user-visible changes here.
Share and enjoy!
Octave is basically trying to be like Wine - it's imitating MATLab including all of its faults, because that's what people are familiar with.
That doesn't make it the best, or even a good tool for the job. It's a good bridge to bring people from closed into open source tools.
If you want speed and performance, while retaining optimal usability, try Python. It's not a reimplementation of MATLab, but a massive improvement (namespaces! unit testing!) and it links into the same low-level libraries for math (BLAS/LAPACK). I've almost always been able to get NumPy code to run at equivalent or better speed to its MATLab counterparts. And when this isn't the case, it's easier to go from Python to Cython (C) than it is to rewrite everything in MATLab.
The tools are so much better in Python as well - the IPython/Jupyter project has a rich notebook including fun stuff like %profile and %debug which MATLab users can only dream about. The Python Package Index embarrasses MATLAB Central, with more tools which are actually robust and useful than anything available even for purchase through MathWorks. MATLab's machine learning is a toy compared to scikit-learn.
There are other options as well like Julia, which is faster than Python but has less of the support framework.