Higher-order Spark SQL functions primarily optimize performance by:

Higher-order Spark SQL functions enhance performance by both simplifying complex queries and reducing the amount of filtered data.

Firstly, these functions enable users to encapsulate intricate logic, allowing queries to be expressed more succinctly and understandably. This simplification not only makes it easier for data analysts and engineers to write and maintain their SQL queries but also helps the Spark engine optimize the execution plan. A more straightforward query can lead to more efficient resource allocation and processing.

Secondly, higher-order functions can help minimize the volume of data processed by allowing for more precise filtering and transformation of data within the query. By performing more operations at a higher abstraction level, these functions can work directly on data collections, thus enabling Spark to push down filters and other operations closer to the data source before the data is ingested into memory. This results in less data being loaded and processed, which can significantly enhance query performance.

In summary, the combination of simplifying complex queries and effectively reducing the amount of data to be filtered leads to the superior performance optimizations associated with higher-order Spark SQL functions.