Interval union arithmetic redefines mathematical operations by allowing results as disjoint intervals, solving division-by-zero issues in standard interval arithmetic. The project, open-sourced in TypeScript, uses outward rounding over IEEE 754 floats to guarantee accuracy. For example, dividing 2 by [-2, 1] yields [-∞, -1] U [2, +∞], excluding undefined or infinite ranges.

This approach, detailed in a 2017 paper *Interval Unions*, enables closed arithmetic systems for non-continuous functions like tan(). The calculator handles complex expressions, such as [5, 10] U [15, 16] divided by [10, 100], producing [0.05, 1.6]. It also addresses floating-point precision by displaying results with full precision mode, showing values like 0.1 + 0.2 as [0.29999999999999993, 0.3000000000000001].

The tool supports operations like addition, subtraction, and exponentiation, with syntax allowing nested intervals (e.g., [0, [0, 100]]). Functions like sqrt() and log() adapt to interval inputs, while full precision mode ensures results contain true values despite rounding errors. A key innovation is its ability to represent uncertainty, such as 50 * (10 + [-1, 1]) yielding [450, 550].

Developers can use the dependency-free library for custom implementations. The project highlights the practicality of interval unions in engineering and scientific computing, offering a robust alternative to traditional methods. Primary keyword: interval union arithmetic. Secondary keywords: disjoint intervals, IEEE 754, open-source calculator, floating point precision.