median

std.stats.median · Level L2

The median: the 0.5-quantile, the mean of the two middle values when n is even. Calls quantile.

quantile(x, 1/2)

Signature

median(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]0.5quantilemmf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.median(x) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 8% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
100%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.50

Identity

Calls
quantile
Called by
madmad
sha256:cd3f61b683e0f1353aa56c7a0d8fa1ebcc1e49aff841961dd7f8ef946c472ad4

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