Average Error: 0.1 → 0.1
Time: 19.0s
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 r6966098 = x;
        double r6966099 = y;
        double r6966100 = r6966098 * r6966099;
        double r6966101 = z;
        double r6966102 = r6966100 + r6966101;
        double r6966103 = r6966102 * r6966099;
        double r6966104 = t;
        double r6966105 = r6966103 + r6966104;
        return r6966105;
}
↓
double f(double x, double y, double z, double t) {
        double r6966106 = y;
        double r6966107 = x;
        double r6966108 = z;
        double r6966109 = fma(r6966106, r6966107, r6966108);
        double r6966110 = t;
        double r6966111 = fma(r6966106, r6966109, r6966110);
        return r6966111;
}

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 2019179 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))