The field of numerical computations is moving towards developing more accurate and efficient algorithms for floating-point arithmetic and geometric calculations. Researchers are exploring innovative methods to detect and repair floating-point errors, which can have severe consequences in critical domains. New approaches, such as using original-precision arithmetic and mathematical guidance, are being proposed to address the limitations of existing methods. Additionally, there is a growing interest in mechanizing error arithmetic and developing certified rounding error bounds. These advancements have the potential to improve the accuracy and reliability of numerical computations in various fields. Noteworthy papers include: Fast and Accurate Intersections on a Sphere, which introduces a fast and high-precision algorithm for calculating intersections on a sphere. OFP-Repair, which proposes a novel method for repairing floating-point errors via original-precision arithmetic. A Mathematics-Guided Approach to Floating-Point Error Detection, which presents a highly effective and efficient method for detecting error-inducing inputs. Mechanizing Olver's Error Arithmetic, which formalizes the fundamental properties of a rounding error model for floating-point arithmetic. Fast Trigonometric Functions using the RLIBM Approach, which describes the development of polynomial approximations for trigonometric functions that produce correctly rounded results.