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What magical feature of an IDE "allows you more freedom to explore ideas and experiment faster"?Refactoring.
Code completion/validation/formatting (make fewer errors, and reformat external code to suit you).
GUI design (a lot of times you will have to make GUIs, no point in avoiding it).
Code analysis (on-the-fly code analysis and error-detection (syntax, compile, and run-time) = less creep-in errors, easier to spot errors earlier, and less compiles = more productivity).
Performance bottleneck detection.
Testing made easier (simpler an faster to build and do unit/integration/etc. tests)
Framework/Design-Pattern skeletons (got an idea, think pattern X may help, try it out quickly = make a good/bad decision faster).
Teamwork features (version control, changelist management, build management etc. made easier).
Etc. Etc.
Who said anything about more LOC being the/a measure of productivity?