Average Error: 0.0 → 0.0
Time: 11.1s
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 r110882 = x;
        double r110883 = y;
        double r110884 = r110882 * r110883;
        double r110885 = z;
        double r110886 = t;
        double r110887 = r110885 * r110886;
        double r110888 = r110884 - r110887;
        return r110888;
}
↓
double f(double x, double y, double z, double t) {
        double r110889 = x;
        double r110890 = y;
        double r110891 = t;
        double r110892 = z;
        double r110893 = r110891 * r110892;
        double r110894 = -r110893;
        double r110895 = fma(r110889, r110890, r110894);
        return r110895;
}

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 2019306 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))