trapezoid

std.seq.trapezoid · Level L2

Trapezoid rule with unit spacing: the area under the samples y.

Σᵢ (yᵢ + yᵢ₊₁)/2

Signature

trapezoid(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.

yf64[n]SlicelaterSliceearlierAddpairReduceSumtotal2.0Divideareaareaf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.trapezoid(y) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 25% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
90%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.08

Identity

Calls
—
Called by
—
sha256:50afb73dd8323f9ad050eab503a108a8348228dd65aea5280a9d6da6ebeb2d02

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 · Ω:trapezoid
Pins
sha256:9c8ab44ac0fd7fc6a32ae4f185d1c247ad8e597334132dc7cb1172f24fc17340this graph alone
Evidence
sha256:f938e24ab5d86c9344f3e6ab5f3158ab631488dde53018f8b86800f558778b55the 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.