Average Error: 0.0 → 0.0
Time: 4.3s
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 r4972260 = x;
        double r4972261 = y;
        double r4972262 = r4972260 * r4972261;
        double r4972263 = z;
        double r4972264 = t;
        double r4972265 = r4972263 * r4972264;
        double r4972266 = r4972262 - r4972265;
        return r4972266;
}
↓
double f(double x, double y, double z, double t) {
        double r4972267 = x;
        double r4972268 = y;
        double r4972269 = z;
        double r4972270 = t;
        double r4972271 = r4972269 * r4972270;
        double r4972272 = -r4972271;
        double r4972273 = fma(r4972267, r4972268, r4972272);
        return r4972273;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))