Average Error: 0.0 → 0.0
Time: 2.5s
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 r174298 = x;
        double r174299 = y;
        double r174300 = r174298 * r174299;
        double r174301 = z;
        double r174302 = t;
        double r174303 = r174301 * r174302;
        double r174304 = r174300 - r174303;
        return r174304;
}
↓
double f(double x, double y, double z, double t) {
        double r174305 = x;
        double r174306 = y;
        double r174307 = z;
        double r174308 = t;
        double r174309 = r174307 * r174308;
        double r174310 = -r174309;
        double r174311 = fma(r174305, r174306, r174310);
        return r174311;
}

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 2020057 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))