全局转换与窗口本地转换的滚动窗口聚合性能差异探究

我观察到以下两种等价的滚动窗口聚合实现存在令人困惑的性能差异。原本以为采用全局转换的版本会比针对每个窗口转换的版本快很多，但实际上后者的速度几乎是前者的两倍。第二种写法实际上更便捷，因为聚合表达式完全包含在rolling代码块中，希望有人能解释这一现象。

import numpy as np
import pandas as pd
import polars as pl
import itertools
import time
from datetime import timedelta

rng = np.random.default_rng()
date = [t.date() for t in pd.date_range("2001-01-01", "2023-12-31", freq="B")]    
ids = [f"id_{i+1}" for i in range(1000)]
ids, date = zip(*itertools.product(ids, date))
values = np.expm1(0.01 * rng.normal(size=len(date)))

frame = pl.from_dict({"id": ids, "date": date, "value": values}).lazy()

# 全局转换版本
t0 = time.time()
frame.select(
    pl.col("id"),
    pl.col("date"),
    pl.col("value").log1p().alias("log_value")
).sort(
    by=["id", "date"]
).rolling(
    index_column="date", by="id", period=timedelta(days=30)
).agg(
    pl.col("log_value").sum()
).select(
    pl.col("id"),
    pl.col("date"),
    np.expm1(pl.col("log_value")).alias("result")
).collect()
t = time.time() - t0
print(f"Time for aggregation with frame global `log1p` and `expm1` is {t=:.3f}s.")
>>> Time for aggregation with frame global `log1p` and `expm1` is t=0.209s.

# 窗口本地转换版本
t0 = time.time()
frame.rolling(
    index_column="date", by="id", period=timedelta(days=30)
).agg(
    np.expm1(pl.col("value").log1p().sum())
).collect()
t = time.time() - t0
print(f"Time for aggregation with window local `log1p` and `expm1` is {t=:.3f}s.")
>>> Time for aggregation with window local `log1p` and `expm1` is t=0.119s.

内容的提问来源于stack exchange，提问作者Benjamin Trendelkamp-Schroer