Average Error: 0.0 → 0.0
Time: 1.9s
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 r128737 = x;
        double r128738 = y;
        double r128739 = r128737 * r128738;
        double r128740 = z;
        double r128741 = t;
        double r128742 = r128740 * r128741;
        double r128743 = r128739 - r128742;
        return r128743;
}
↓
double f(double x, double y, double z, double t) {
        double r128744 = x;
        double r128745 = y;
        double r128746 = z;
        double r128747 = t;
        double r128748 = r128746 * r128747;
        double r128749 = -r128748;
        double r128750 = fma(r128744, r128745, r128749);
        return r128750;
}

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 2020035 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))