The Prospero Challenge, involving rendering an image from a mathematical formula, was explored using various optimization techniques.Most implementations followed Matt's Fidget closely but with additional optimizations.Prototyping was done in RPython before rewriting the program in C for better performance.The input program is a sequence of operations where variables are assigned once, and optimizations were applied to speed up execution.Quadtrees were used to simplify the formula by recursively evaluating in each quadrant based on range analysis.Peephole optimizations mainly focused on min and max operations, significantly reducing the number of operations executed.A 'demanded information' optimization was implemented to remove unnecessary operations by considering only the sign of the result.Testing included property-based tests to ensure the correctness of interval computations and random testing of optimizers.Further optimizations like dead code elimination and early return flags were explored to improve execution efficiency.Performance results showed improvements with the demanded information optimization in the C implementation.The C implementation outperformed the RPython version, showcasing the benefits of low-level optimizations.