Average Error: 0.0 → 0.0
Time: 4.1s
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 r6136056 = x;
        double r6136057 = y;
        double r6136058 = r6136056 * r6136057;
        double r6136059 = z;
        double r6136060 = t;
        double r6136061 = r6136059 * r6136060;
        double r6136062 = r6136058 + r6136061;
        return r6136062;
}
↓
double f(double x, double y, double z, double t) {
        double r6136063 = x;
        double r6136064 = y;
        double r6136065 = z;
        double r6136066 = t;
        double r6136067 = r6136065 * r6136066;
        double r6136068 = fma(r6136063, r6136064, r6136067);
        return r6136068;
}

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 2019158 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))