zscore

std.stats.zscore · Level L1

Standard scores: each element's distance from the mean, in standard deviations. Calls std.

(xᵢ − x̄) / σ

Signature

zscore(x: f64[n]) → f64[n]

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]MeanmustdsSubtractdDividezzf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size with n ≥ 2.
  • Agrees with the reference (x - x.mean()) / x.std() to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 191 float64 results inside the running error bound; the closest uses 20% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
60%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
44

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
std
Called by
—
sha256:b0b89d5d97a1925ce1c5e581897ebbd69f541b4e08e8c702ac0a8408331e80a5

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.zscore · Ω:zscore
Pins
sha256:8e16fa53dcbd07cf39249b339d0914449ce5ae5b965e45edb6e29c2f36351b28this graph and the 2 it reaches through calls
Evidence
sha256:72ac10e8eb79e430554e89c07a28e70618b650aab525af900ee3587c162d4033the 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.