cube

std.elementwise.cube · Level L0

Elementwise cube.

x³

Signature

cube(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]MultiplysqMultiplyyyf64[n]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference x ** 3 in exact rational arithmetic, on all 40 test cases.
  • All 160 float64 results inside the running error bound; the closest uses 62% 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
86%
largest error, in units in the last place
1.15

Identity

Calls
—
Called by
gelu_tanh
sha256:60e33906180fa9499323ae4dd05bf33a89b54a1c3887922934e64e4948fcb66f

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

Control handle

Symbol
Ω:std.elementwise.cube · Ω:cube
Pins
sha256:fb96bc27b7368c62b590e697e907175fcbf7200a6458d61190bddbee79f02264this graph alone
Evidence
sha256:83462e736747c3ff7e6b05f1e15870a402e6cacb8d69597177288dd33dedd7b9the 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.