Can you explain me how Profile-guided optimization works and why it works?
Profile-guided optimization (PGO) is a technique used in computer software engineering to optimize the performance of a binary executable by using profiling information. The basic idea behind PGO is to collect information about how a program is executed at runtime, and then use this information to optimize the program's binary code.

PGO works by executing the program several times, with each run collecting information about which sections of code are executed most frequently and which are executed less frequently. This information is then used to guide the optimization process. For example, the compiler can use this information to better optimize the frequently executed sections of code, by reducing the number of instructions and improving the cache usage.

The reason PGO works is that it allows the compiler to make informed decisions about how to optimize the code. Without profiling information, the compiler has to make decisions about code optimization based on heuristics and general assumptions about how programs run. But these assumptions may not always be accurate, especially for complex and large applications. With PGO, the compiler can make optimization decisions based on real-world information about how the program is actually being executed.

PGO is particularly useful for improving the performance of applications that are performance-critical, such as video games, scientific simulations, and financial applications. By using PGO, developers can achieve substantial performance improvements with relatively low effort, as the optimization process is fully automated.