Average Error: 0.1 → 0.1
Time: 20.5s
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 r6377836 = x;
        double r6377837 = y;
        double r6377838 = r6377836 * r6377837;
        double r6377839 = z;
        double r6377840 = r6377838 + r6377839;
        double r6377841 = r6377840 * r6377837;
        double r6377842 = t;
        double r6377843 = r6377841 + r6377842;
        return r6377843;
}
↓
double f(double x, double y, double z, double t) {
        double r6377844 = y;
        double r6377845 = x;
        double r6377846 = z;
        double r6377847 = fma(r6377844, r6377845, r6377846);
        double r6377848 = t;
        double r6377849 = fma(r6377844, r6377847, r6377848);
        return r6377849;
}

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 2019171 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))