Average Error: 0.1 → 0.1
Time: 14.3s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)
double f(double x, double y, double z, double t) {
        double r133892 = x;
        double r133893 = y;
        double r133894 = r133892 * r133893;
        double r133895 = z;
        double r133896 = r133894 + r133895;
        double r133897 = r133896 * r133893;
        double r133898 = t;
        double r133899 = r133897 + r133898;
        return r133899;
}
↓
double f(double x, double y, double z, double t) {
        double r133900 = y;
        double r133901 = x;
        double r133902 = z;
        double r133903 = fma(r133900, r133901, r133902);
        double r133904 = t;
        double r133905 = fma(r133900, r133903, r133904);
        return r133905;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))