Average Error: 0.0 → 0.0
Time: 7.4s
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 r91035 = x;
        double r91036 = y;
        double r91037 = r91035 * r91036;
        double r91038 = z;
        double r91039 = t;
        double r91040 = r91038 * r91039;
        double r91041 = r91037 - r91040;
        return r91041;
}
↓
double f(double x, double y, double z, double t) {
        double r91042 = x;
        double r91043 = y;
        double r91044 = t;
        double r91045 = z;
        double r91046 = r91044 * r91045;
        double r91047 = -r91046;
        double r91048 = fma(r91042, r91043, r91047);
        return r91048;
}

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)))