Average Error: 0.0 → 0.0
Time: 3.8s
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 r113352 = x;
        double r113353 = y;
        double r113354 = r113352 * r113353;
        double r113355 = z;
        double r113356 = t;
        double r113357 = r113355 * r113356;
        double r113358 = r113354 - r113357;
        return r113358;
}
↓
double f(double x, double y, double z, double t) {
        double r113359 = x;
        double r113360 = y;
        double r113361 = t;
        double r113362 = z;
        double r113363 = r113361 * r113362;
        double r113364 = -r113363;
        double r113365 = fma(r113359, r113360, r113364);
        return r113365;
}

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 2019303 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))