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In programming, readability is a pivotal factor that determines how easily developers can understand and work with the code. When you use named constants, you improve the clarity of your code significantly. Instead of seeing a number like 25 scattered throughout your code, you might see something like max_students, which instantly tells you what the number represents.
This descriptive nature of named constants ensures that anyone reading the code does not have to dive into the nitty-gritty details to comprehend a value's purpose. This improves not just immediate understanding but also long-term maintenance. If a particular value needs to be changed later, you can simply update the named constant in one place, avoiding the hassle of locating everywhere the magic number is used.
In summary, better readability allows developers to more easily update, debug, and expand upon existing code with confidence.

Magic numbers refer to numerical values that appear in code without explanation. These numbers can be a source of confusion and errors, since they don't convey the purpose they serve in the program. By replacing magic numbers with named constants, you eliminate ambiguity and enhance readability.
Consider this snippet: `if (tickets_sold > 100)`, versus `if (tickets_sold > MAX_TICKETS)`. The second is straightforward and reduces the mental burden on developers, as the purpose of 'MAX_TICKETS' is evident.
Using named constants ensures that these context-free numbers are identified with a meaningful name. This makes the code more self-documenting, thus easing debugging and reducing the likelihood of mistakes that could arise from incorrect value duplication.

Compiler optimization is an advanced concept where the compiler enhances the efficiency of the code during the compilation process. One benefit of using named constants is the opportunity for more efficient computation.
When constants are clearly defined, they provide the compiler with fixed values to work with, allowing it to perform optimizations such as loop unrolling and constant folding. These enhancements can lead to faster execution times and reduced resource consumption, which are critical in performance-intensive applications.
Manipulating named constants as fixed values can lead to substantial optimization opportunities that would be unavailable with variables. Ultimately, leveraging named constants aids in producing high-performance, efficient programs, and takes full advantage of the compiler's ability to streamline computation.