Average Error: 0.0 → 0.0
Time: 4.3s
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 r11423918 = x;
        double r11423919 = y;
        double r11423920 = r11423918 * r11423919;
        double r11423921 = z;
        double r11423922 = t;
        double r11423923 = r11423921 * r11423922;
        double r11423924 = r11423920 - r11423923;
        return r11423924;
}
↓
double f(double x, double y, double z, double t) {
        double r11423925 = x;
        double r11423926 = y;
        double r11423927 = z;
        double r11423928 = t;
        double r11423929 = r11423927 * r11423928;
        double r11423930 = -r11423929;
        double r11423931 = fma(r11423925, r11423926, r11423930);
        return r11423931;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))