Average Error: 0.0 → 0.0
Time: 4.4s
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 r4174612 = x;
        double r4174613 = y;
        double r4174614 = r4174612 * r4174613;
        double r4174615 = z;
        double r4174616 = t;
        double r4174617 = r4174615 * r4174616;
        double r4174618 = r4174614 - r4174617;
        return r4174618;
}
↓
double f(double x, double y, double z, double t) {
        double r4174619 = x;
        double r4174620 = y;
        double r4174621 = z;
        double r4174622 = t;
        double r4174623 = r4174621 * r4174622;
        double r4174624 = -r4174623;
        double r4174625 = fma(r4174619, r4174620, r4174624);
        return r4174625;
}

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 2019169 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))