Average Error: 0.1 → 0.1
Time: 14.7s
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 r5182258 = x;
        double r5182259 = y;
        double r5182260 = r5182258 * r5182259;
        double r5182261 = z;
        double r5182262 = r5182260 + r5182261;
        double r5182263 = r5182262 * r5182259;
        double r5182264 = t;
        double r5182265 = r5182263 + r5182264;
        return r5182265;
}
↓
double f(double x, double y, double z, double t) {
        double r5182266 = y;
        double r5182267 = x;
        double r5182268 = z;
        double r5182269 = fma(r5182266, r5182267, r5182268);
        double r5182270 = t;
        double r5182271 = fma(r5182266, r5182269, r5182270);
        return r5182271;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))