Average Error: 0.0 → 0.0
Time: 3.7s
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 r85906 = x;
        double r85907 = y;
        double r85908 = r85906 * r85907;
        double r85909 = z;
        double r85910 = t;
        double r85911 = r85909 * r85910;
        double r85912 = r85908 + r85911;
        return r85912;
}
↓
double f(double x, double y, double z, double t) {
        double r85913 = x;
        double r85914 = y;
        double r85915 = z;
        double r85916 = t;
        double r85917 = r85915 * r85916;
        double r85918 = fma(r85913, r85914, r85917);
        return r85918;
}

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 2019323 +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)))