Average Error: 0.0 → 0.0
Time: 1.9s
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 r8197943 = x;
        double r8197944 = y;
        double r8197945 = r8197943 * r8197944;
        double r8197946 = z;
        double r8197947 = t;
        double r8197948 = r8197946 * r8197947;
        double r8197949 = r8197945 + r8197948;
        return r8197949;
}
↓
double f(double x, double y, double z, double t) {
        double r8197950 = x;
        double r8197951 = y;
        double r8197952 = z;
        double r8197953 = t;
        double r8197954 = r8197952 * r8197953;
        double r8197955 = fma(r8197950, r8197951, r8197954);
        return r8197955;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))