Average Error: 0.0 → 0.0
Time: 3.2s
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 r116475 = x;
        double r116476 = y;
        double r116477 = r116475 * r116476;
        double r116478 = z;
        double r116479 = t;
        double r116480 = r116478 * r116479;
        double r116481 = r116477 - r116480;
        return r116481;
}
↓
double f(double x, double y, double z, double t) {
        double r116482 = x;
        double r116483 = y;
        double r116484 = z;
        double r116485 = t;
        double r116486 = r116484 * r116485;
        double r116487 = -r116486;
        double r116488 = fma(r116482, r116483, r116487);
        return r116488;
}

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 2020047 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))