Average Error: 0.0 → 0.0
Time: 13.0s
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 r14212488 = x;
        double r14212489 = y;
        double r14212490 = r14212488 * r14212489;
        double r14212491 = z;
        double r14212492 = t;
        double r14212493 = r14212491 * r14212492;
        double r14212494 = r14212490 - r14212493;
        return r14212494;
}
↓
double f(double x, double y, double z, double t) {
        double r14212495 = x;
        double r14212496 = y;
        double r14212497 = z;
        double r14212498 = t;
        double r14212499 = r14212497 * r14212498;
        double r14212500 = -r14212499;
        double r14212501 = fma(r14212495, r14212496, r14212500);
        return r14212501;
}

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 2019173 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V3:cross from linear-1.19.1.3"
  (- (* x y) (* z t)))