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108 lines
3.7 KiB
Python
108 lines
3.7 KiB
Python
"""Compute the power of a number."""
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from dataclasses import dataclass
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from decimal import Decimal
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from math import pow
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from random import Random
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from typing import Any, Optional
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from ..coaching import BaseCurriculum, RangeAttributeDefinition
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from ..factory import ProceduralDataset, register_dataset
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QUESTION_TEMPLATE = """Your task is to compute an exponentiation of a number.
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Compute {base}^{exponent}. Return your final answer correct to 3 significant figures.
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Provide your answer in scientific notation using 'e' notation (e.g., 1.23e+4).
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"""
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DATASET_NAME = "power_function"
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@dataclass
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class PowerFunctionConfig:
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"""Configuration for Power Function dataset generation"""
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min_base: float = -1e3 # Minimum base value
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max_base: float = 1e3 # Maximum base value
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min_exponent: int = 0 # Minimum exponent value
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max_exponent: int = 8 # Maximum exponent value
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size: int = 500 # Virtual dataset size
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seed: Optional[int] = None
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class PowerFunctionDataset(ProceduralDataset):
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"""Generates Power Function exercises with configurable difficulty"""
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def __init__(self, config: PowerFunctionConfig):
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super().__init__(config=config, seed=config.seed, size=config.size)
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def _format_sig_figs(self, x: Decimal, sig: int) -> Decimal:
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"""Format a Decimal to exactly 'sig' significant figures, keeping trailing zeros."""
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if x.is_zero():
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return "0." + "0" * (sig - 1)
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exp = x.adjusted()
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shift = sig - exp - 1
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rounded = x.quantize(Decimal("1e{}".format(-shift)))
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return Decimal(rounded)
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def score_answer(self, answer: Optional[str], entry: dict[str, Any]) -> float:
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"""Score the answer by checking if it matches the expected answer to 3 significant figures."""
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oracle_answer = entry["answer"]
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if answer is not None:
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try:
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user_answer = self._format_sig_figs(Decimal(answer), 3)
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oracle_answer = self._format_sig_figs(Decimal(oracle_answer), 3)
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# Check if they match to 3 significant figures
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if user_answer == oracle_answer:
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return 1.0
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else:
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return 0.01
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except Exception as e:
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return 0.01
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return 0.0
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def __getitem__(self, idx: int) -> dict:
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"""Generate a single Power Function question"""
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rng = Random(self.seed + idx)
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base = round(rng.uniform(self.config.min_base, self.config.max_base), 4)
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exponent = rng.randint(self.config.min_exponent, self.config.max_exponent)
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if rng.random() < 0.5:
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exponent = -exponent
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answer = pow(base, exponent)
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return {
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"question": QUESTION_TEMPLATE.format(base=base, exponent=exponent),
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"answer": str(answer),
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"metadata": {
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"source_dataset": DATASET_NAME,
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"source_index": idx,
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"base": base,
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"exponent": exponent,
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"solution": answer,
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"difficulty": {
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"exponent": (self.config.min_exponent, self.config.max_exponent),
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},
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},
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}
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class PowerFunctionCurriculum(BaseCurriculum):
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def __init__(self):
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super().__init__(PowerFunctionCurriculum.__name__, PowerFunctionConfig)
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self._define_attributes(
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RangeAttributeDefinition(
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name="exponent",
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levels=[2, 4, 6, 8, 10],
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lower_field_name="min_exponent",
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upper_field_name="max_exponent",
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),
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)
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register_dataset(DATASET_NAME, PowerFunctionDataset, PowerFunctionConfig, PowerFunctionCurriculum)
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