quadratic_on_x

std.seq.quadratic_on_x · Level L2

The quadratic u(x, y) = c₀ + c₁x + c₂y + c₃x² + c₄xy + c₅y² restricted to the line x = x₀: a quadratic in y, coefficients highest degree first, (c₅, c₂ + c₄x₀, c₀ + c₁x₀ + c₃x₀²). Comparing them with the Dirichlet data on an edge, coefficient by coefficient, checks the boundary condition exactly.

u(x₀, y) = c₅y² + (c₂ + c₄x₀)y + (c₀ + c₁x₀ + c₃x₀²)

Signature

quadratic_on_x(c: f64[6], x0: f64[]) → f64[3]

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 [c5, c2 + c4*x0, c0 + c1*x0 + c3*x0²] in exact rational arithmetic, on all 40 test cases.
All 120 float64 results inside the running error bound; the closest uses 66% 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 71% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 90%
bit-equal to the NumPy formula in float64: 98%
largest error, in units in the last place: 3.44

Identity

Calls

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Called by

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sha256:11f6bc4b6ff942657bf6da43d167f2d6707edbd2420e5b7328b3542a1e3a1394

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.quadratic_on_x · Ω:quadratic_on_x
Pins: sha256:6d1450f2e02734cf48f1c43e7a8e67c18672cf73c226ca44985f9c55b84acf80this graph alone
Evidence: sha256:210b52b3c006582e7b210341ae6d7486b6c8a2906240f5539d5a7f4c3d5a9c4cthe 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.