Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[x \cdot y - z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, -t \cdot z\right)\]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(x, y, -t \cdot z\right)
double f(double x, double y, double z, double t) {
        double r102711 = x;
        double r102712 = y;
        double r102713 = r102711 * r102712;
        double r102714 = z;
        double r102715 = t;
        double r102716 = r102714 * r102715;
        double r102717 = r102713 - r102716;
        return r102717;
}
↓
double f(double x, double y, double z, double t) {
        double r102718 = x;
        double r102719 = y;
        double r102720 = t;
        double r102721 = z;
        double r102722 = r102720 * r102721;
        double r102723 = -r102722;
        double r102724 = fma(r102718, r102719, r102723);
        return r102724;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))