Average Error: 0.1 → 0.1
Time: 14.8s
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 r7000365 = x;
        double r7000366 = y;
        double r7000367 = r7000365 * r7000366;
        double r7000368 = z;
        double r7000369 = r7000367 + r7000368;
        double r7000370 = r7000369 * r7000366;
        double r7000371 = t;
        double r7000372 = r7000370 + r7000371;
        return r7000372;
}
↓
double f(double x, double y, double z, double t) {
        double r7000373 = y;
        double r7000374 = x;
        double r7000375 = z;
        double r7000376 = fma(r7000373, r7000374, r7000375);
        double r7000377 = t;
        double r7000378 = fma(r7000373, r7000376, r7000377);
        return r7000378;
}

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 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))