Average Error: 0.0 → 0.0
Time: 1.0s
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 r121519 = x;
        double r121520 = y;
        double r121521 = r121519 * r121520;
        double r121522 = z;
        double r121523 = t;
        double r121524 = r121522 * r121523;
        double r121525 = r121521 + r121524;
        return r121525;
}
↓
double f(double x, double y, double z, double t) {
        double r121526 = x;
        double r121527 = y;
        double r121528 = z;
        double r121529 = t;
        double r121530 = r121528 * r121529;
        double r121531 = fma(r121526, r121527, r121530);
        return r121531;
}

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 2020036 +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)))