dist

std.geometry.dist · Level L1

Euclidean distance between two points. Calls sqdist.

‖x − y‖

Signature

dist(x: f64[n], y: 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]yf64[n]sqdistsqSqrtssf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Agrees with the reference np.linalg.norm(x - y) to 80 digits (100-digit arithmetic), on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 60% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
88%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.92

Identity

Calls
sqdist
Called by
—
sha256:2c09489fe10ca7859d0e5731c78e7c1a25a0830df9446fea12483d7c9a6a041b

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

Control handle

Symbol
Ω:std.geometry.dist · Ω:dist
Pins
sha256:fa90879bb8a49c77f170380b509c7596ee330d8cdca34ff34aff4edce4b42ce1this graph and the 3 it reaches through calls
Evidence
sha256:80fe7a2396bcea546dc9dfc91853e11036412d8c1eb16548f37c82e95605f880the 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.