variance

std.stats.variance · Level L0

Population variance, two-pass: the mean first, then the mean squared deviation.

(1/n)·Σᵢ (xᵢ − x̄)²

Signature

variance(x: f64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks a call to another library function; select it to open that function.

xf64[n]MeanmuSubtractdMultiplyddMeanvvf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.var(x) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 19% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
73%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.34

Identity

Calls
—
Called by
—
sha256:3d2fc93518e17c2554f8eec5a39f13028bc1fcc5b5f0d7e5f5685b0f2cba78a2

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.