Average Error: 0.0 → 0.0
Time: 2.0s
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 r116438 = x;
        double r116439 = y;
        double r116440 = r116438 * r116439;
        double r116441 = z;
        double r116442 = t;
        double r116443 = r116441 * r116442;
        double r116444 = r116440 - r116443;
        return r116444;
}
↓
double f(double x, double y, double z, double t) {
        double r116445 = x;
        double r116446 = y;
        double r116447 = z;
        double r116448 = t;
        double r116449 = r116447 * r116448;
        double r116450 = -r116449;
        double r116451 = fma(r116445, r116446, r116450);
        return r116451;
}

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 2020081 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))