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 r107828 = x;
        double r107829 = y;
        double r107830 = r107828 * r107829;
        double r107831 = z;
        double r107832 = t;
        double r107833 = r107831 * r107832;
        double r107834 = r107830 + r107833;
        return r107834;
}
↓
double f(double x, double y, double z, double t) {
        double r107835 = x;
        double r107836 = y;
        double r107837 = z;
        double r107838 = t;
        double r107839 = r107837 * r107838;
        double r107840 = fma(r107835, r107836, r107839);
        return r107840;
}

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 2020100 +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)))