Average Error: 0.0 → 0.0
Time: 7.0s
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 r4887765 = x;
        double r4887766 = y;
        double r4887767 = r4887765 * r4887766;
        double r4887768 = z;
        double r4887769 = t;
        double r4887770 = r4887768 * r4887769;
        double r4887771 = r4887767 - r4887770;
        return r4887771;
}
↓
double f(double x, double y, double z, double t) {
        double r4887772 = x;
        double r4887773 = y;
        double r4887774 = z;
        double r4887775 = t;
        double r4887776 = r4887774 * r4887775;
        double r4887777 = -r4887776;
        double r4887778 = fma(r4887772, r4887773, r4887777);
        return r4887778;
}

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 2019162 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))