horner_step

std.seq.horner_step · Level L0

One step of Horner's rule: multiply by t, add the next coefficient. The body that horner scans.

a′ = a·t + c

Signature

horner_step(acc: f64[], c: f64[], 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.

accf64[]tf64[]cf64[]MultiplyscaledAddacc2acc2f64[]
  • input
  • operation
  • constant
  • call
  • output

Verification

  • Signature proven by NOVA’s shape solver, for every size.
  • Equal to the reference acc * t + c in exact rational arithmetic, on all 40 test cases.
  • All 40 float64 results inside the running error bound; the closest uses 77% of it.
  • Interpreter and NumPy backend return bit-identical results.
Accuracy in detail
correctly rounded (the float64 nearest the exact value)
85%
bit-equal to the NumPy formula in float64
100%
largest error, in units in the last place
0.94

Identity

Calls
—
Called by
horner
sha256:2acf277e6801ea8ef41fbb6135b81b685ff8ad114e681cc4e7bc806377fb9743

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.