iqr

std.stats.iqr · Level L2

Interquartile range: the 0.75-quantile minus the 0.25-quantile. Calls quantile twice.

Q(3/4) − Q(1/4)

Signature

iqr(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.

0.75xf64[n]0.25quantileupperquantilelowerSubtractrrf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.quantile(x, 0.75) - np.quantile(x, 0.25) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 32% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
85%
bit-equal to the NumPy formula in float64
88%
largest error, in units in the last place
2.00

Identity

Calls
quantile
Called by
—
sha256:9522834d21069a63b253cc4d6df6435fc3ae20929fdaeb0ef062f35561798d71

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.iqr · Ω:iqr
Pins
sha256:0643d1f601cb79b35c7f4d92ecf46b3ccd50d15cb45215353be7cc5797d3aa82this graph and the 1 it reaches through calls
Evidence
sha256:17494d2d873db0c66194e46b655601ffdc8daca909501925cd0e35cd3adf942athe 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.