Average Error: 0.0 → 0.0
Time: 8.8s
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 r5256218 = x;
        double r5256219 = y;
        double r5256220 = r5256218 * r5256219;
        double r5256221 = z;
        double r5256222 = t;
        double r5256223 = r5256221 * r5256222;
        double r5256224 = r5256220 + r5256223;
        return r5256224;
}
↓
double f(double x, double y, double z, double t) {
        double r5256225 = x;
        double r5256226 = y;
        double r5256227 = z;
        double r5256228 = t;
        double r5256229 = r5256227 * r5256228;
        double r5256230 = fma(r5256225, r5256226, r5256229);
        return r5256230;
}

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 2019165 +o rules:numerics
(FPCore (x y z t)
  :name "Linear.V2:$cdot from linear-1.19.1.3, A"
  (+ (* x y) (* z t)))