reformulating

Reformulating is the process of expressing a concept, problem, or product in a new form or terms, often to clarify, adapt to constraints, or improve usefulness. It can involve restating wording, changing representation, or redesigning components.

In language, reformulation overlaps with paraphrase and reframing to preserve meaning while adjusting tone, complexity, or audience. In mathematics and computing, reformulating a problem or equation means changing variables, coordinates, or representation to simplify solution or analysis, such as converting nonlinear equations to a linear form or switching to dimensionless variables. In chemistry and product development, reformulation refers to altering formulas or ingredients to meet safety, regulatory, or cost requirements while preserving performance.

Methods include change of variables, normalization, dimensional analysis, surrogate modeling, and reformulating constraints. Problem reframing can reduce complexity or improve numerical stability; product reformulation can reduce hazards or environmental impact.

Risks include altering essential characteristics or misinterpreting the original intent; reformulation should document changes and preserve core objectives.

Example: Reformulating a drug's formulation to use a safer solvent; reformulating an economics problem by introducing a new variable representing aggregate demand to simplify analysis.