Average Error: 0.1 → 0.1
Time: 16.5s
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 r5813642 = x;
        double r5813643 = y;
        double r5813644 = r5813642 * r5813643;
        double r5813645 = z;
        double r5813646 = r5813644 + r5813645;
        double r5813647 = r5813646 * r5813643;
        double r5813648 = t;
        double r5813649 = r5813647 + r5813648;
        return r5813649;
}
↓
double f(double x, double y, double z, double t) {
        double r5813650 = y;
        double r5813651 = x;
        double r5813652 = z;
        double r5813653 = fma(r5813650, r5813651, r5813652);
        double r5813654 = t;
        double r5813655 = fma(r5813650, r5813653, r5813654);
        return r5813655;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))