Average Error: 0.0 → 0.0
Time: 4.5s
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 r4506160 = x;
        double r4506161 = y;
        double r4506162 = r4506160 * r4506161;
        double r4506163 = z;
        double r4506164 = t;
        double r4506165 = r4506163 * r4506164;
        double r4506166 = r4506162 + r4506165;
        return r4506166;
}
↓
double f(double x, double y, double z, double t) {
        double r4506167 = x;
        double r4506168 = y;
        double r4506169 = z;
        double r4506170 = t;
        double r4506171 = r4506169 * r4506170;
        double r4506172 = fma(r4506167, r4506168, r4506171);
        return r4506172;
}

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 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))