Average Error: 0.0 → 0.0
Time: 894.0ms
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 r101507 = x;
        double r101508 = y;
        double r101509 = r101507 * r101508;
        double r101510 = z;
        double r101511 = t;
        double r101512 = r101510 * r101511;
        double r101513 = r101509 - r101512;
        return r101513;
}
↓
double f(double x, double y, double z, double t) {
        double r101514 = x;
        double r101515 = y;
        double r101516 = z;
        double r101517 = t;
        double r101518 = r101516 * r101517;
        double r101519 = -r101518;
        double r101520 = fma(r101514, r101515, r101519);
        return r101520;
}

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 2019347 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))