Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[x \cdot y - z \cdot t\]
↓
\[\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)\]
x \cdot y - z \cdot t
↓
\mathsf{fma}\left(x, y, \left(-t\right) \cdot z\right)
double f(double x, double y, double z, double t) {
        double r88134 = x;
        double r88135 = y;
        double r88136 = r88134 * r88135;
        double r88137 = z;
        double r88138 = t;
        double r88139 = r88137 * r88138;
        double r88140 = r88136 - r88139;
        return r88140;
}
↓
double f(double x, double y, double z, double t) {
        double r88141 = x;
        double r88142 = y;
        double r88143 = t;
        double r88144 = -r88143;
        double r88145 = z;
        double r88146 = r88144 * r88145;
        double r88147 = fma(r88141, r88142, r88146);
        return r88147;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))