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Explore two powerful algorithms used in modern optimizing compilers in this comprehensive conference talk from CppNow 2021. Delve into the foundations of compiler construction as Gábor Horváth, a seasoned compiler developer and researcher, presents chains of recurrences and value numbering. Gain insights into the theory, basic math, and implementations of these algorithms in popular compilers, with numerous examples provided. Learn how these elegant solutions find optimization opportunities in programs and develop an intuition about modern compiler capabilities. Discover the potential applications of these algorithms and get pointers on implementing them yourself, all while requiring only high school math knowledge.