Average Error: 0.1 → 0.1
Time: 6.9s
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 r7546967 = x;
        double r7546968 = y;
        double r7546969 = r7546967 * r7546968;
        double r7546970 = z;
        double r7546971 = r7546969 + r7546970;
        double r7546972 = r7546971 * r7546968;
        double r7546973 = t;
        double r7546974 = r7546972 + r7546973;
        return r7546974;
}
↓
double f(double x, double y, double z, double t) {
        double r7546975 = y;
        double r7546976 = x;
        double r7546977 = z;
        double r7546978 = fma(r7546975, r7546976, r7546977);
        double r7546979 = t;
        double r7546980 = fma(r7546975, r7546978, r7546979);
        return r7546980;
}

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 2019158 +o rules:numerics
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  (+ (* (+ (* x y) z) y) t))