Average Error: 0.0 → 0.0
Time: 5.3s
Precision: 64
\[x \cdot y - z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, -t \cdot z\right)\]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(x, y, -t \cdot z\right)
double f(double x, double y, double z, double t) {
        double r135458 = x;
        double r135459 = y;
        double r135460 = r135458 * r135459;
        double r135461 = z;
        double r135462 = t;
        double r135463 = r135461 * r135462;
        double r135464 = r135460 - r135463;
        return r135464;
}
↓
double f(double x, double y, double z, double t) {
        double r135465 = x;
        double r135466 = y;
        double r135467 = t;
        double r135468 = z;
        double r135469 = r135467 * r135468;
        double r135470 = -r135469;
        double r135471 = fma(r135465, r135466, r135470);
        return r135471;
}

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. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-t \cdot z}\right)\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, -t \cdot z\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))