Average Error: 0.0 → 0.0
Time: 6.8s
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 r4284542 = x;
        double r4284543 = y;
        double r4284544 = r4284542 * r4284543;
        double r4284545 = z;
        double r4284546 = t;
        double r4284547 = r4284545 * r4284546;
        double r4284548 = r4284544 - r4284547;
        return r4284548;
}
↓
double f(double x, double y, double z, double t) {
        double r4284549 = x;
        double r4284550 = y;
        double r4284551 = z;
        double r4284552 = t;
        double r4284553 = r4284551 * r4284552;
        double r4284554 = -r4284553;
        double r4284555 = fma(r4284549, r4284550, r4284554);
        return r4284555;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))