Average Error: 0.0 → 0.0
Time: 2.4s
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 r100247 = x;
        double r100248 = y;
        double r100249 = r100247 * r100248;
        double r100250 = z;
        double r100251 = t;
        double r100252 = r100250 * r100251;
        double r100253 = r100249 - r100252;
        return r100253;
}
↓
double f(double x, double y, double z, double t) {
        double r100254 = x;
        double r100255 = y;
        double r100256 = z;
        double r100257 = t;
        double r100258 = r100256 * r100257;
        double r100259 = -r100258;
        double r100260 = fma(r100254, r100255, r100259);
        return r100260;
}

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 2020020 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))