Average Error: 0.1 → 0.1
Time: 14.6s
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 r7326606 = x;
        double r7326607 = y;
        double r7326608 = r7326606 * r7326607;
        double r7326609 = z;
        double r7326610 = r7326608 + r7326609;
        double r7326611 = r7326610 * r7326607;
        double r7326612 = t;
        double r7326613 = r7326611 + r7326612;
        return r7326613;
}
↓
double f(double x, double y, double z, double t) {
        double r7326614 = y;
        double r7326615 = x;
        double r7326616 = z;
        double r7326617 = fma(r7326614, r7326615, r7326616);
        double r7326618 = t;
        double r7326619 = fma(r7326614, r7326617, r7326618);
        return r7326619;
}

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 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))