Average Error: 0.0 → 0.0
Time: 2.0s
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 r105256 = x;
        double r105257 = y;
        double r105258 = r105256 * r105257;
        double r105259 = z;
        double r105260 = t;
        double r105261 = r105259 * r105260;
        double r105262 = r105258 - r105261;
        return r105262;
}
↓
double f(double x, double y, double z, double t) {
        double r105263 = x;
        double r105264 = y;
        double r105265 = z;
        double r105266 = t;
        double r105267 = r105265 * r105266;
        double r105268 = -r105267;
        double r105269 = fma(r105263, r105264, r105268);
        return r105269;
}

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 2020002 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))