Average Error: 0.0 → 0.0
Time: 1.2s
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 r94329 = x;
        double r94330 = y;
        double r94331 = r94329 * r94330;
        double r94332 = z;
        double r94333 = t;
        double r94334 = r94332 * r94333;
        double r94335 = r94331 + r94334;
        return r94335;
}
↓
double f(double x, double y, double z, double t) {
        double r94336 = x;
        double r94337 = y;
        double r94338 = z;
        double r94339 = t;
        double r94340 = r94338 * r94339;
        double r94341 = fma(r94336, r94337, r94340);
        return r94341;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  :precision binary64
  (+ (* x y) (* z t)))