High memory usage when calculating variance?

[ts826848]

Checks

• I have checked that this issue has not already been reported.
• I have confirmed this bug exists on the latest version of Polars.

Reproducible example

import polars as pl
# ~7.6 GB in Task Manager
s = pl.repeat(1.5, 1_000_000_000, eager=True)
s.var() # Memory usage jumps to >15 GB before result returned

Log output

No log output?

Issue description

Potential culprit might be squared in

polars/crates/polars-core/src/chunked_array/ops/aggregate/var.rs

Lines 17 to 32 in 9384945

	fn var(&self, ddof: u8) -> Option<f64> {
	let n_values = self.len() - self.null_count();
	if n_values <= ddof as usize {
	return None;
	}
	let mean = self.mean()?;
	let squared: Float64Chunked = unary_elementwise_values(self, |value| {
	let tmp = value.to_f64().unwrap() - mean;
	tmp * tmp
	});
	squared
	.sum()
	.map(|sum| sum / (n_values as f64 - ddof as f64))
	}

I'm not a stats/numerical analysis expert so I'm not sure whether the extra allocation is strictly necessary for numerical stability/other reasons. It feels like it shouldn't be necessary though?

Looks like NumPy has a similar issue? numpy/numpy#13199 (var, std memory consumption)

Expected behavior

Expected memory usage to not jump when calculating the variance

Installed versions

--------Version info---------
Polars:              1.7.1
Index type:          UInt32
Platform:            Windows-11-10.0.22631-SP0
Python:              3.12.4 (tags/v3.12.4:8e8a4ba, Jun  6 2024, 19:30:16) [MSC v.1940 64 bit (AMD64)]

----Optional dependencies----
adbc_driver_manager  <not installed>
altair               <not installed>
cloudpickle          <not installed>
connectorx           <not installed>
deltalake            <not installed>
fastexcel            0.11.6
fsspec               <not installed>
gevent               <not installed>
great_tables         <not installed>
matplotlib           <not installed>
nest_asyncio         <not installed>
numpy                2.1.1
openpyxl             <not installed>
pandas               <not installed>
pyarrow              17.0.0
pydantic             <not installed>
pyiceberg            <not installed>
sqlalchemy           <not installed>
torch                <not installed>
xlsx2csv             <not installed>
xlsxwriter           3.2.0