Average Error: 0.0 → 0.0
Time: 5.4s
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 r1854457 = x;
        double r1854458 = y;
        double r1854459 = r1854457 * r1854458;
        double r1854460 = z;
        double r1854461 = t;
        double r1854462 = r1854460 * r1854461;
        double r1854463 = r1854459 - r1854462;
        return r1854463;
}
↓
double f(double x, double y, double z, double t) {
        double r1854464 = x;
        double r1854465 = y;
        double r1854466 = z;
        double r1854467 = t;
        double r1854468 = r1854466 * r1854467;
        double r1854469 = -r1854468;
        double r1854470 = fma(r1854464, r1854465, r1854469);
        return r1854470;
}

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 2019156 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))