Average Error: 0.0 → 0.0
Time: 6.5s
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 r4305253 = x;
        double r4305254 = y;
        double r4305255 = r4305253 * r4305254;
        double r4305256 = z;
        double r4305257 = t;
        double r4305258 = r4305256 * r4305257;
        double r4305259 = r4305255 - r4305258;
        return r4305259;
}
↓
double f(double x, double y, double z, double t) {
        double r4305260 = x;
        double r4305261 = y;
        double r4305262 = z;
        double r4305263 = t;
        double r4305264 = r4305262 * r4305263;
        double r4305265 = -r4305264;
        double r4305266 = fma(r4305260, r4305261, r4305265);
        return r4305266;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))