Average Error: 0.1 → 0.1
Time: 6.1s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(x \cdot y + z, y, t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(x \cdot y + z, y, t\right)
double f(double x, double y, double z, double t) {
        double r738 = x;
        double r739 = y;
        double r740 = r738 * r739;
        double r741 = z;
        double r742 = r740 + r741;
        double r743 = r742 * r739;
        double r744 = t;
        double r745 = r743 + r744;
        return r745;
}
↓
double f(double x, double y, double z, double t) {
        double r746 = x;
        double r747 = y;
        double r748 = r746 * r747;
        double r749 = z;
        double r750 = r748 + r749;
        double r751 = t;
        double r752 = fma(r750, r747, r751);
        return r752;
}

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. Using strategy rm

  3. Applied fma-def0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))