Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[x \cdot y - z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, -t \cdot z\right)\]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(x, y, -t \cdot z\right)
double f(double x, double y, double z, double t) {
        double r107524 = x;
        double r107525 = y;
        double r107526 = r107524 * r107525;
        double r107527 = z;
        double r107528 = t;
        double r107529 = r107527 * r107528;
        double r107530 = r107526 - r107529;
        return r107530;
}
↓
double f(double x, double y, double z, double t) {
        double r107531 = x;
        double r107532 = y;
        double r107533 = t;
        double r107534 = z;
        double r107535 = r107533 * r107534;
        double r107536 = -r107535;
        double r107537 = fma(r107531, r107532, r107536);
        return r107537;
}

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. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{-t \cdot z}\right)\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, -t \cdot z\right)\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))