Average Error: 0.0 → 0.0
Time: 708.0ms
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 r80420 = x;
        double r80421 = y;
        double r80422 = r80420 * r80421;
        double r80423 = z;
        double r80424 = t;
        double r80425 = r80423 * r80424;
        double r80426 = r80422 + r80425;
        return r80426;
}
↓
double f(double x, double y, double z, double t) {
        double r80427 = x;
        double r80428 = y;
        double r80429 = z;
        double r80430 = t;
        double r80431 = r80429 * r80430;
        double r80432 = fma(r80427, r80428, r80431);
        return r80432;
}

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 2019354 +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)))