Average Error: 0.0 → 0.0
Time: 1.9s
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 r107848 = x;
        double r107849 = y;
        double r107850 = r107848 * r107849;
        double r107851 = z;
        double r107852 = t;
        double r107853 = r107851 * r107852;
        double r107854 = r107850 - r107853;
        return r107854;
}
↓
double f(double x, double y, double z, double t) {
        double r107855 = x;
        double r107856 = y;
        double r107857 = z;
        double r107858 = t;
        double r107859 = r107857 * r107858;
        double r107860 = -r107859;
        double r107861 = fma(r107855, r107856, r107860);
        return r107861;
}

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 2020001 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))