Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[x \cdot y + z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, z \cdot t\right)\]
x \cdot y + z \cdot t
↓
\mathsf{fma}\left(x, y, z \cdot t\right)
double f(double x, double y, double z, double t) {
        double r108914 = x;
        double r108915 = y;
        double r108916 = r108914 * r108915;
        double r108917 = z;
        double r108918 = t;
        double r108919 = r108917 * r108918;
        double r108920 = r108916 + r108919;
        return r108920;
}
↓
double f(double x, double y, double z, double t) {
        double r108921 = x;
        double r108922 = y;
        double r108923 = z;
        double r108924 = t;
        double r108925 = r108923 * r108924;
        double r108926 = fma(r108921, r108922, r108925);
        return r108926;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.0

    \[x \cdot y + z \cdot t\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))