cummean

std.seq.cummean · Level L2

Running mean: element i is the mean of x₀ … xᵢ. The counts 1, 2, … come from Iota.

mᵢ = (Σⱼ≤ᵢ xⱼ) / (i + 1)

Signature

cummean(x: f64[n]) → f64[n]

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]CumSumsIotai1.0AddcountDividemmf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.cumsum(x) / np.arange(1, len(x) + 1) in exact rational arithmetic, on all 40 test cases.
  • All 155 float64 results inside the running error bound; the closest uses 50% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
86%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
5.00

Identity

Calls
—
Called by
—
sha256:6536b23796e3d5a76cf250ca2fe90b1fabe227191da6f07d4e1287c2b0629f5d

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

Control handle

Symbol
Ω:std.seq.cummean · Ω:cummean
Pins
sha256:f03568b6b1a3180ef30aae7c4baa11dac894e7a67ff9ba3a13467da868b13c53this graph alone
Evidence
sha256:b9c3d4a38ce1ebb2e8dc125a3037b40575ced19557018dbc70d22d055f80d4c4the 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.