Average Error: 0.1 → 0.1
Time: 14.9s
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 r112002 = x;
        double r112003 = y;
        double r112004 = r112002 * r112003;
        double r112005 = z;
        double r112006 = r112004 + r112005;
        double r112007 = r112006 * r112003;
        double r112008 = t;
        double r112009 = r112007 + r112008;
        return r112009;
}
↓
double f(double x, double y, double z, double t) {
        double r112010 = y;
        double r112011 = x;
        double r112012 = z;
        double r112013 = fma(r112010, r112011, r112012);
        double r112014 = t;
        double r112015 = fma(r112010, r112013, r112014);
        return r112015;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))