Average Error: 0.0 → 0.0
Time: 4.1s
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 r2284880 = x;
        double r2284881 = y;
        double r2284882 = r2284880 * r2284881;
        double r2284883 = z;
        double r2284884 = t;
        double r2284885 = r2284883 * r2284884;
        double r2284886 = r2284882 - r2284885;
        return r2284886;
}
↓
double f(double x, double y, double z, double t) {
        double r2284887 = x;
        double r2284888 = y;
        double r2284889 = z;
        double r2284890 = t;
        double r2284891 = r2284889 * r2284890;
        double r2284892 = -r2284891;
        double r2284893 = fma(r2284887, r2284888, r2284892);
        return r2284893;
}

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 2019158 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))