horner

std.seq.horner · Level L2

Evaluate a polynomial at t by Horner's rule, coefficients from the highest degree down: a Scan of horner_step, keeping the last value.

p(t) = (…((c₀·t + c₁)·t + c₂)…)·t + cₙ₋₁

Signature

horner(c: f64[n], t: 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.

cf64[n]tf64[]0.0Scan·horner_steppartialSlicelastReshapeppf64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference np.polyval(c, t) in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 48% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
83%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
1.71

Identity

Calls
horner_step
Called by
—
sha256:b304d05ccf4578bc2bb1d3123385306c844fe3530724dc48ee2a624705dad050

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.horner · Ω:horner
Pins
sha256:17804286b9086c85fecde5064fca4ed221d1f20de7596bee7cdf7242b2f9e1c6this graph and the 1 it reaches through calls
Evidence
sha256:56beb7c0b4eaf346ddbf8d586efdce5ec589308ef9448f0d7b4e7c6d21f9d576the 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.