Average Error: 0.0 → 0.0
Time: 1.3s
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 r117830 = x;
        double r117831 = y;
        double r117832 = r117830 * r117831;
        double r117833 = z;
        double r117834 = t;
        double r117835 = r117833 * r117834;
        double r117836 = r117832 + r117835;
        return r117836;
}
↓
double f(double x, double y, double z, double t) {
        double r117837 = x;
        double r117838 = y;
        double r117839 = z;
        double r117840 = t;
        double r117841 = r117839 * r117840;
        double r117842 = fma(r117837, r117838, r117841);
        return r117842;
}

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 2020034 +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)))