Average Error: 0.0 → 0.0
Time: 2.8s
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 r77073 = x;
        double r77074 = y;
        double r77075 = r77073 * r77074;
        double r77076 = z;
        double r77077 = t;
        double r77078 = r77076 * r77077;
        double r77079 = r77075 - r77078;
        return r77079;
}
↓
double f(double x, double y, double z, double t) {
        double r77080 = x;
        double r77081 = y;
        double r77082 = z;
        double r77083 = t;
        double r77084 = r77082 * r77083;
        double r77085 = -r77084;
        double r77086 = fma(r77080, r77081, r77085);
        return r77086;
}

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 2020034 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))