Average Error: 0.0 → 0.0
Time: 14.4s
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 r6471865 = x;
        double r6471866 = y;
        double r6471867 = r6471865 * r6471866;
        double r6471868 = z;
        double r6471869 = t;
        double r6471870 = r6471868 * r6471869;
        double r6471871 = r6471867 - r6471870;
        return r6471871;
}
↓
double f(double x, double y, double z, double t) {
        double r6471872 = x;
        double r6471873 = y;
        double r6471874 = z;
        double r6471875 = t;
        double r6471876 = r6471874 * r6471875;
        double r6471877 = -r6471876;
        double r6471878 = fma(r6471872, r6471873, r6471877);
        return r6471878;
}

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 2019192 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))