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 r5201188 = x;
        double r5201189 = y;
        double r5201190 = r5201188 * r5201189;
        double r5201191 = z;
        double r5201192 = t;
        double r5201193 = r5201191 * r5201192;
        double r5201194 = r5201190 - r5201193;
        return r5201194;
}
↓
double f(double x, double y, double z, double t) {
        double r5201195 = x;
        double r5201196 = y;
        double r5201197 = z;
        double r5201198 = t;
        double r5201199 = r5201197 * r5201198;
        double r5201200 = -r5201199;
        double r5201201 = fma(r5201195, r5201196, r5201200);
        return r5201201;
}

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 2019172 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))