Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
\[\left(x \cdot y + z\right) \cdot y + t\]
↓
\[\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)\]
\left(x \cdot y + z\right) \cdot y + t
↓
\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)
double f(double x, double y, double z, double t) {
        double r6843361 = x;
        double r6843362 = y;
        double r6843363 = r6843361 * r6843362;
        double r6843364 = z;
        double r6843365 = r6843363 + r6843364;
        double r6843366 = r6843365 * r6843362;
        double r6843367 = t;
        double r6843368 = r6843366 + r6843367;
        return r6843368;
}
↓
double f(double x, double y, double z, double t) {
        double r6843369 = y;
        double r6843370 = x;
        double r6843371 = z;
        double r6843372 = fma(r6843369, r6843370, r6843371);
        double r6843373 = t;
        double r6843374 = fma(r6843369, r6843372, r6843373);
        return r6843374;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y + z\right) \cdot y + t\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), t\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))