quadratic_on_y

std.seq.quadratic_on_y · Level L2

The quadratic u(x, y) = c₀ + c₁x + c₂y + c₃x² + c₄xy + c₅y² restricted to the line y = y₀: a quadratic in x, coefficients highest degree first, (c₃, c₁ + c₄y₀, c₀ + c₂y₀ + c₅y₀²).

u(x, y₀) = c₃x² + (c₁ + c₄y₀)x + (c₀ + c₂y₀ + c₅y₀²)

Signature

quadratic_on_y(c: f64[6], y0: 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 [c3, c1 + c4*y0, c0 + c2*y0 + c5*y0²] in exact rational arithmetic, on all 40 test cases.
All 120 float64 results inside the running error bound; the closest uses 74% 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 74% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 93%
bit-equal to the NumPy formula in float64: 99%
largest error, in units in the last place: 6.76

Identity

Calls

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Called by

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sha256:95c53241dfb8eb228a37fad9db8d287b7533f7246e882621e50950a7113b3b86

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_y · Ω:quadratic_on_y
Pins: sha256:cdda0efbd75faf341fe4e7d2bfd32bd9ee1ec16087b258c4aab6e2525158ea90this graph alone
Evidence: sha256:18c25a3992ce923ab09c69e067a38efb9504da921aba411a91e529aa4ddcd54ethe 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.