Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r1900865 = x;
        double r1900866 = y;
        double r1900867 = 1.0;
        double r1900868 = r1900866 - r1900867;
        double r1900869 = r1900865 * r1900868;
        double r1900870 = 0.5;
        double r1900871 = r1900866 * r1900870;
        double r1900872 = r1900869 - r1900871;
        double r1900873 = 0.918938533204673;
        double r1900874 = r1900872 + r1900873;
        return r1900874;
}
↓
double f(double x, double y) {
        double r1900875 = x;
        double r1900876 = y;
        double r1900877 = 1.0;
        double r1900878 = r1900876 - r1900877;
        double r1900879 = 0.918938533204673;
        double r1900880 = 0.5;
        double r1900881 = r1900880 * r1900876;
        double r1900882 = r1900879 - r1900881;
        double r1900883 = fma(r1900875, r1900878, r1900882);
        return r1900883;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))