> it's possible that the processor has facilities for bucketing the data such that results from such a dataset are the same or more accurate than the naive appr

> it's possible that the processor has facilities for bucketing the data such that results from such a dataset are the same or more accurate than the naive approach. It absolutely is not. Floating-point addition is completely defined (save for some of the bits in NaN results), and no CPU will start reordering your addition instructions in a way that changes the result. Even if it's an ordering that gives you better accuracy. Having SIMD do four (or more) of them in parallel does not change this.