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 r118899 = x;
        double r118900 = y;
        double r118901 = r118899 * r118900;
        double r118902 = z;
        double r118903 = t;
        double r118904 = r118902 * r118903;
        double r118905 = r118901 - r118904;
        return r118905;
}
↓
double f(double x, double y, double z, double t) {
        double r118906 = x;
        double r118907 = y;
        double r118908 = z;
        double r118909 = t;
        double r118910 = r118908 * r118909;
        double r118911 = -r118910;
        double r118912 = fma(r118906, r118907, r118911);
        return r118912;
}

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. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, -z \cdot t\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, -z \cdot t\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))