Average Error: 0.1 → 0.1
Time: 9.7s
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 r135051 = x;
        double r135052 = y;
        double r135053 = r135051 * r135052;
        double r135054 = z;
        double r135055 = r135053 + r135054;
        double r135056 = r135055 * r135052;
        double r135057 = t;
        double r135058 = r135056 + r135057;
        return r135058;
}
↓
double f(double x, double y, double z, double t) {
        double r135059 = y;
        double r135060 = x;
        double r135061 = z;
        double r135062 = fma(r135059, r135060, r135061);
        double r135063 = t;
        double r135064 = fma(r135059, r135062, r135063);
        return r135064;
}

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 2019194 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))