trapezoid_xy

std.seq.trapezoid_xy · Level L2

Trapezoid rule over sample points x (any spacing, in order). Calls diff.

Σᵢ (xᵢ₊₁ − xᵢ)(yᵢ + yᵢ₊₁)/2

Signature

trapezoid_xy(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]diffdxSlicelaterSliceearlierAddpairMultiplystripsReduceSumtotal2.0Divideareaareaf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.trapezoid(y, x) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 37% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
78%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
86

Large ulp counts appear where a result is tiny next to the numbers it is computed from (after cancellation, for example), so one unit in the last place is tiny too; the absolute error is still inside the bound. Results within their own error of zero are not counted.

Identity

Calls
diff
Called by
—
sha256:3fe31ed77b8b984a3239ac7b8b73a889080378d378e6db5c3795ae3d2fe43dc7

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

Control handle

Symbol
Ω:std.seq.trapezoid_xy · Ω:trapezoid_xy
Pins
sha256:0943b4282107009177dd4bbd246732a9115be784853d91370f95bba7fb154d48this graph and the 1 it reaches through calls
Evidence
sha256:9836b24c66e2821608dbdd98393beae5b5ef57f9e9d43cc50cc430b111b5898cthe 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.