Average Error: 0.1 → 0.1
Time: 21.6s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)
double f(double x, double y, double z, double t) {
        double r106574 = x;
        double r106575 = y;
        double r106576 = r106574 * r106575;
        double r106577 = z;
        double r106578 = r106576 + r106577;
        double r106579 = r106578 * r106575;
        double r106580 = t;
        double r106581 = r106579 + r106580;
        return r106581;
}
↓
double f(double x, double y, double z, double t) {
        double r106582 = x;
        double r106583 = y;
        double r106584 = z;
        double r106585 = fma(r106582, r106583, r106584);
        double r106586 = t;
        double r106587 = fma(r106585, r106583, r106586);
        return r106587;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y + z\right) \cdot y + t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))