Average Error: 0.0 → 0.0
Time: 20.5s
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 r90353 = x;
        double r90354 = y;
        double r90355 = r90353 * r90354;
        double r90356 = z;
        double r90357 = t;
        double r90358 = r90356 * r90357;
        double r90359 = r90355 - r90358;
        return r90359;
}
↓
double f(double x, double y, double z, double t) {
        double r90360 = x;
        double r90361 = y;
        double r90362 = t;
        double r90363 = z;
        double r90364 = r90362 * r90363;
        double r90365 = -r90364;
        double r90366 = fma(r90360, r90361, r90365);
        return r90366;
}

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 2019199 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))