[WIP] Refactoring of the reformulation chain #447

Job	Run time
build (windows-latest, Debug, msys2 {0})	2m 46s
build (macos-latest, Debug, bash)	1m 11s
build (ubuntu-24.04-arm, Debug, bash)	44s
build (macos-15-intel, Debug, bash)	1m 51s
build (ubuntu-latest, Debug, bash)	50s
	7m 22s

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