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 another library function this one runs — called once, or by Scan once per element; 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

sha256:3d2fc93518e17c2554f8eec5a39f13028bc1fcc5b5f0d7e5f5685b0f2cba78a2

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

Control handle

Symbol
Ω:std.stats.variance · Ω:variance
Pins
sha256:a831628abec3897cac3dd143037c99df165eb3a0b87eb29a58b82473eb854c4athis graph alone
Evidence
sha256:4776cbf33ac5322dd6c7881497eb73481d0c929a5bfb7752115842d45cfa5fa8the hash of its verification record
Needs
no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.