Average Error: 0.1 → 0.1
Time: 15.0s
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 r9569688 = x;
        double r9569689 = y;
        double r9569690 = r9569688 * r9569689;
        double r9569691 = z;
        double r9569692 = r9569690 + r9569691;
        double r9569693 = r9569692 * r9569689;
        double r9569694 = t;
        double r9569695 = r9569693 + r9569694;
        return r9569695;
}
↓
double f(double x, double y, double z, double t) {
        double r9569696 = y;
        double r9569697 = x;
        double r9569698 = z;
        double r9569699 = fma(r9569696, r9569697, r9569698);
        double r9569700 = t;
        double r9569701 = fma(r9569696, r9569699, r9569700);
        return r9569701;
}

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 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))