Average Error: 0.0 → 0.0
Time: 1.0s
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 r118843 = x;
        double r118844 = y;
        double r118845 = r118843 * r118844;
        double r118846 = z;
        double r118847 = t;
        double r118848 = r118846 * r118847;
        double r118849 = r118845 - r118848;
        return r118849;
}
↓
double f(double x, double y, double z, double t) {
        double r118850 = x;
        double r118851 = y;
        double r118852 = z;
        double r118853 = t;
        double r118854 = r118852 * r118853;
        double r118855 = -r118854;
        double r118856 = fma(r118850, r118851, r118855);
        return r118856;
}

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 2020021 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))