Average Error: 0.0 → 0.0
Time: 4.6s
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 r6167435 = x;
        double r6167436 = y;
        double r6167437 = r6167435 * r6167436;
        double r6167438 = z;
        double r6167439 = t;
        double r6167440 = r6167438 * r6167439;
        double r6167441 = r6167437 - r6167440;
        return r6167441;
}
↓
double f(double x, double y, double z, double t) {
        double r6167442 = x;
        double r6167443 = y;
        double r6167444 = z;
        double r6167445 = t;
        double r6167446 = r6167444 * r6167445;
        double r6167447 = -r6167446;
        double r6167448 = fma(r6167442, r6167443, r6167447);
        return r6167448;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))