poly_derivative_k

std.elementwise.poly_derivative_k · Level L3

The k-th derivative of a polynomial, coefficients highest degree first and the length kept: each coefficient of xᵈ is multiplied by the falling factorial d(d − 1)…(d − k + 1) and moved k places toward the constant term, and the k leading places become 0. Past the degree the derivative is 0. k = 1 is poly_derivative with a leading 0.

(xᵈ)⁽ᵏ⁾ = d(d − 1)⋯(d − k + 1)·x^{d−k}

Signature

poly_derivative_k(c: f64[n], k: i64[]) → 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.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference c[j]·perm(n − 1 − j, k), placed k positions later in exact rational arithmetic, on all 40 test cases.
All 165 float64 results inside the running error bound; the closest uses 7% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 9% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 0.50

Identity

Calls

permutations

Called by

—

sha256:72a58a0429aa307904bb92904e37c3f29baea0d0dd5fa96efad6daf6a18c8f39

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.poly_derivative_k · Ω:poly_derivative_k
Pins: sha256:152df88ea8e051867cc342ba976e0480ffe8a2151350880234b61e8ebb650cc4this graph and the 3 it reaches through calls
Evidence: sha256:c92b24ba0c65df20c3a6caf75ec60c7e0ef4f86bf9286ff171addbfc39763490the 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.