Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(x, y, z\right) \cdot y + t\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(x, y, z\right) \cdot y + t
double f(double x, double y, double z, double t) {
        double r119698 = x;
        double r119699 = y;
        double r119700 = r119698 * r119699;
        double r119701 = z;
        double r119702 = r119700 + r119701;
        double r119703 = r119702 * r119699;
        double r119704 = t;
        double r119705 = r119703 + r119704;
        return r119705;
}
↓
double f(double x, double y, double z, double t) {
        double r119706 = x;
        double r119707 = y;
        double r119708 = z;
        double r119709 = fma(r119706, r119707, r119708);
        double r119710 = r119709 * r119707;
        double r119711 = t;
        double r119712 = r119710 + r119711;
        return r119712;
}

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. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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))