Average Error: 0.0 → 0.0
Time: 7.4s
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 r78622 = x;
        double r78623 = y;
        double r78624 = r78622 * r78623;
        double r78625 = z;
        double r78626 = t;
        double r78627 = r78625 * r78626;
        double r78628 = r78624 - r78627;
        return r78628;
}
↓
double f(double x, double y, double z, double t) {
        double r78629 = x;
        double r78630 = y;
        double r78631 = t;
        double r78632 = z;
        double r78633 = r78631 * r78632;
        double r78634 = -r78633;
        double r78635 = fma(r78629, r78630, r78634);
        return r78635;
}

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 2019325 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))