Average Error: 0.0 → 0.0
Time: 1.3s
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 r93908 = x;
        double r93909 = y;
        double r93910 = r93908 * r93909;
        double r93911 = z;
        double r93912 = t;
        double r93913 = r93911 * r93912;
        double r93914 = r93910 + r93913;
        return r93914;
}
↓
double f(double x, double y, double z, double t) {
        double r93915 = x;
        double r93916 = y;
        double r93917 = z;
        double r93918 = t;
        double r93919 = r93917 * r93918;
        double r93920 = fma(r93915, r93916, r93919);
        return r93920;
}

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 2019304 +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)))