Industry-grade database systems are expected to produce the same result if the same query is repeatedly run on the same input. However, the numerous sources of non-determinism in modern systems make reproducible results difficult to achieve. This is particularly true if floating-point numbers are involved, where the order of the operations affects the final result. As part of a larger effort to extend database engines with data representations more suitable for machine learning and scientific applications, in this paper we explore the problem of making relational GroupBy over floating-point formats bit-reproducible, i.e., ensuring any execution of the operator produces the same result up to every single bit. To that aim, we first propose a numeric data type that can be used as drop-in replacement for other number formats and is---unlike standard floating-point formats---associative. We use this data type to make state-of-the-art GroupBy operators reproducible, but this approach incurs a slowdown between 4x and 12x compared to the same operator using conventional database number formats. We thus explore how to modify existing GroupBy algorithms to make them bit-reproducible and efficient. By using vectorized summation on batches and carefully balancing batch size, cache footprint, and preprocessing costs, we are able to reduce the slowdown due to reproducibility to a factor between 1.9x and 2.4x of aggregation in isolation and to a mere 2.7% of end-to-end query performance even on aggregation-intensive queries in MonetDB. We thereby provide a solid basis for supporting more reproducible operations directly in relational engines. This document is an extended version of an article currently in print for the proceedings of ICDE'18 with the same title and by the same authors. The main additions are more implementation details and experiments.