Useful applications of correctly-rounded operators of the form ab + cd + e

We show that the availability of fused arithmetic operators that evaluate expressions of the form ab + cd (FD2 instruction) or ab + cd + e (FD2A instruction) in floating-point arithmetic with one final rounding only would significantly facilitate many calculations that are hard to perform with high accuracy at small cost using only the traditional operations +, −, ×, ÷, √, and fused multiply-add (FMA).