Average Error: 0.0 → 0.0
Time: 3.8s
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 r69506 = x;
        double r69507 = y;
        double r69508 = r69506 * r69507;
        double r69509 = z;
        double r69510 = t;
        double r69511 = r69509 * r69510;
        double r69512 = r69508 - r69511;
        return r69512;
}
↓
double f(double x, double y, double z, double t) {
        double r69513 = x;
        double r69514 = y;
        double r69515 = t;
        double r69516 = z;
        double r69517 = r69515 * r69516;
        double r69518 = -r69517;
        double r69519 = fma(r69513, r69514, r69518);
        return r69519;
}

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 2019303 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  :precision binary64
  (- (* x y) (* z t)))