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BootstrapFewShot defines the behavior behind the "how" in few-shot example selection by differentiating examples and selecting those that meet the metric criteria as "passing examples" in the optimized prompt.
BootstrapInfer takes a next step in exploring the "why" by inducing learned rules from the selected few-shot examples and adding supplementary guidance within the optimized prompt. The optimizer explores various sets of complementary rules + fewshot example combinations, and outputs a final optimal prompt with the original DSPy program instruction, selected few-shot examples and additional natural language rules to guide the task.