mvt_quadratic

std.elementwise.mvt_quadratic · Level L0

The mean value theorem for f(t) = A·t² + B·t + C on [a, b], a < b: the secant slope (f(b) − f(a))/(b − a), the midpoint c = (a + b)/2, which lies strictly inside, and f′(c) = 2A·c + B, which equals the secant slope: for a quadratic the midpoint is always a witness. When A = 0 every point of (a, b) is one; the witness need not be unique.

f′((a + b)/2) = (f(b) − f(a))/(b − a)

Signature

mvt_quadratic(A: f64[], B: f64[], C: f64[], a: f64[], b: f64[]) → f64[], f64[], 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the formulas in exact arithmetic in exact rational arithmetic, on all 40 test cases.
All 120 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:8e9cd65754c36ed9b682464808016927c3959a44a842129be7dcabc747394e7f

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.mvt_quadratic · Ω:mvt_quadratic
Pins: sha256:4f4fe29a6cd3189ad7064d5dc3a4c64497371b6c76ee80b08ac3e8f909129f81this graph alone
Evidence: sha256:9ded9ad07fe78752f677a650ebd740477abc12a2ea0973d2d9ab84e91bc1299cthe 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.