Average Error: 0.0 → 0.0
Time: 1.9s
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 r10002925 = x;
        double r10002926 = y;
        double r10002927 = r10002925 * r10002926;
        double r10002928 = z;
        double r10002929 = t;
        double r10002930 = r10002928 * r10002929;
        double r10002931 = r10002927 + r10002930;
        return r10002931;
}
↓
double f(double x, double y, double z, double t) {
        double r10002932 = x;
        double r10002933 = y;
        double r10002934 = z;
        double r10002935 = t;
        double r10002936 = r10002934 * r10002935;
        double r10002937 = fma(r10002932, r10002933, r10002936);
        return r10002937;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))