Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)
double f(double x, double y, double z, double t) {
        double r188804 = x;
        double r188805 = y;
        double r188806 = r188804 * r188805;
        double r188807 = z;
        double r188808 = r188806 + r188807;
        double r188809 = r188808 * r188805;
        double r188810 = t;
        double r188811 = r188809 + r188810;
        return r188811;
}
↓
double f(double x, double y, double z, double t) {
        double r188812 = x;
        double r188813 = y;
        double r188814 = z;
        double r188815 = fma(r188812, r188813, r188814);
        double r188816 = t;
        double r188817 = fma(r188815, r188813, r188816);
        return r188817;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))