sample_variance

std.stats.sample_variance · Level L1

Sample variance, dividing by n − 1. The count comes from the Size primitive. Calls variance.

(1/(n − 1))·Σᵢ (xᵢ − x̄)²

Signature

sample_variance(x: f64[n]) → f64[]

Requires: n ≥ 2

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]1.0SizenvariancevSubtractnm1DividescaleMultiplys2s2f64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
  • Equal to the reference np.var(x, ddof=1) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 21% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
63%
bit-equal to the NumPy formula in float64
88%
largest error, in units in the last place
1.12

Identity

Calls
variance
Called by
—
sha256:7f4abf63a5108ab7a060143d773ab3896f6320759f432eb521d40465d099a7af

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.sample_variance · Ω:sample_variance
Pins
sha256:1fd650e8d0e1828b6421adfa7791f7e1cd4934941183589b3826efa9928c0071this graph and the 1 it reaches through calls
Evidence
sha256:a0ce661a89eef719e2c5dc82dfe3f26a3f21b37921c198a27ea4996fb31ad2d8the 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.