Average Error: 0.0 → 0.0
Time: 1.1s
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 r176895 = x;
        double r176896 = y;
        double r176897 = r176895 * r176896;
        double r176898 = z;
        double r176899 = t;
        double r176900 = r176898 * r176899;
        double r176901 = r176897 + r176900;
        return r176901;
}
↓
double f(double x, double y, double z, double t) {
        double r176902 = x;
        double r176903 = y;
        double r176904 = z;
        double r176905 = t;
        double r176906 = r176904 * r176905;
        double r176907 = fma(r176902, r176903, r176906);
        return r176907;
}

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 2019362 +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)))