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Although user-defined functions (UDFs) are a popular way to augment SQL's declarative approach with procedural code, the mismatch between programming paradigms creates a fundamental optimization challenge. UDF inlining automatically removes all UDF calls by replacing them with equivalent SQL subqueries. Although inlining leaves queries entirely in SQL (resulting in large performance gains), we observe that inlining the entire UDF often leads to sub-optimal performance. A better approach is to analyze the UDF, deconstruct it into smaller pieces, and inline only the pieces that help query optimization. To achieve this, we propose UDF outlining, a technique to intentionally hide pieces of a UDF from the optimizer, resulting in simpler UDFs and significantly faster query plans. Our implementation (PRISM) demonstrates that UDF outlining improves performance over conventional inlining (on average 1.29× speedup for DuckDB and 298.73× for SQL Server) through a combination of more effective unnesting, improved data skipping, and by avoiding unnecessary joins.