Average Error: 0.0 → 0.0
Time: 1.5s
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 r5739062 = x;
        double r5739063 = y;
        double r5739064 = r5739062 * r5739063;
        double r5739065 = z;
        double r5739066 = t;
        double r5739067 = r5739065 * r5739066;
        double r5739068 = r5739064 + r5739067;
        return r5739068;
}
↓
double f(double x, double y, double z, double t) {
        double r5739069 = x;
        double r5739070 = y;
        double r5739071 = z;
        double r5739072 = t;
        double r5739073 = r5739071 * r5739072;
        double r5739074 = fma(r5739069, r5739070, r5739073);
        return r5739074;
}

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 2019164 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))