Average Error: 0.0 → 0.0
Time: 1.2s
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 r115402 = x;
        double r115403 = y;
        double r115404 = r115402 * r115403;
        double r115405 = z;
        double r115406 = t;
        double r115407 = r115405 * r115406;
        double r115408 = r115404 - r115407;
        return r115408;
}
↓
double f(double x, double y, double z, double t) {
        double r115409 = x;
        double r115410 = y;
        double r115411 = z;
        double r115412 = t;
        double r115413 = r115411 * r115412;
        double r115414 = -r115413;
        double r115415 = fma(r115409, r115410, r115414);
        return r115415;
}

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 2020033 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))