mad

std.stats.mad · Level L2

Median absolute deviation, a robust spread: the median distance from the median. Calls median and abs.

median(|x − median(x)|)

Signature

mad(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]medianmSubtractdabsadmedianmadmadf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.median(np.abs(x - np.median(x))) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 14% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
95%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.72

Identity

Calls
absmedian
Called by
—
sha256:f206d24870e47046ef2148f30c4e607a25aa1fd8e89216792d7283dcabb66116

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.mad · Ω:mad
Pins
sha256:7b688690091be936a0e2067fb33f779e3436b786fa0f485a2a55deb6a39a7816this graph and the 3 it reaches through calls
Evidence
sha256:b5d7b91a55fd1801fe2b75f1d5cfc7b55285a54cd31a06a164fd9129d06c57bcthe 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.