How does pipelining make computer calculations faster?

In the context of numerical analysis and computer architecture, pipelining is a technique that increases computational speed by overlapping the execution of multiple instructions.1

Rather than processing instructions serially—where one must finish entirely before the next begins—pipelining allows the central processing unit (CPU) to work on several instructions simultaneously at different stages of the "fetch-decode-execute" cycle. For example, while one instruction is being executed, another can be decoding, and a third can be fetched from memory.2

If each phase of the cycle requires the same amount of time, a new instruction can enter the pipeline at every phase. This allows the computer to complete multiple instructions in the time it would otherwise take to complete just one, significantly improving throughput. While pipelining is a powerful method for accelerating numerical analysis tasks, its efficiency can be affected by branch instructions or dependencies between operations, which require sophisticated circuits to manage and rearrange instructions for optimal parallel execution.2