Average Error: 0.1 → 0.1
Time: 16.7s
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 r7217700 = x;
        double r7217701 = y;
        double r7217702 = r7217700 * r7217701;
        double r7217703 = z;
        double r7217704 = r7217702 + r7217703;
        double r7217705 = r7217704 * r7217701;
        double r7217706 = t;
        double r7217707 = r7217705 + r7217706;
        return r7217707;
}
↓
double f(double x, double y, double z, double t) {
        double r7217708 = y;
        double r7217709 = x;
        double r7217710 = z;
        double r7217711 = fma(r7217708, r7217709, r7217710);
        double r7217712 = t;
        double r7217713 = fma(r7217708, r7217711, r7217712);
        return r7217713;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))