Reliable computations for high-assurance systems: A couple of ideas for your project:
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The first thing to do in this team is that Jorge should give the other members of the team a tutorial about interval computations, so that all of you understand the mechanisms that you will have to deal with all project long. 

You have to make sure that you clearly understand the meaning of accuracy, consistency, reliability. I would suggest that you submit these definitions to me in a scheduled meeting with the whole team and we go over your answers together.

When you understand what the problem is, you should read a paper of mine, about Horner's rule for Interval Evaluation Revisited. This will give you an idea of what can be done to improve the efficiency of interval evaluation (in terms of the width of the resulting interval). 

In the meantime, you should explore the potential interval libraries that you may want to use. It would be a good idea to describe a couple of interesting interval libraries (interesting for the purpose of your project) in the tutorial that is due by the end of week 4 of the project.

Once you reach a good understanding of the problem and you master a library, you should propose a plan of action: what is your proposal to improve interval evaluation? or at least to assess the performance of several proposed interval evaluations? how do you plan to implement it? etc.

You should also consider revising your timeline in the light of the above advises. Don't forget that you have to define milestones at which points you will have to release deliverables. The graduate student of the team should be in charge of making sure that other members will turn their work on time.

I also recommend that you visit the website maintained by Vladik Kreinovich on interval computations, and that you read the book of Luc Jaulin about Interval Analysis (probably available at the library).