Average Error: 0.0 → 0.0
Time: 7.7s
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 r59500 = x;
        double r59501 = y;
        double r59502 = r59500 * r59501;
        double r59503 = z;
        double r59504 = t;
        double r59505 = r59503 * r59504;
        double r59506 = r59502 - r59505;
        return r59506;
}
↓
double f(double x, double y, double z, double t) {
        double r59507 = x;
        double r59508 = y;
        double r59509 = t;
        double r59510 = z;
        double r59511 = r59509 * r59510;
        double r59512 = -r59511;
        double r59513 = fma(r59507, r59508, r59512);
        return r59513;
}

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 2019322 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))