Average Error: 0.0 → 0.0
Time: 7.0s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.9189385332046730026078762421093415468931\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.9189385332046730026078762421093415468931\right)\right)
double f(double x, double y) {
        double r27859 = x;
        double r27860 = y;
        double r27861 = 1.0;
        double r27862 = r27860 - r27861;
        double r27863 = r27859 * r27862;
        double r27864 = 0.5;
        double r27865 = r27860 * r27864;
        double r27866 = r27863 - r27865;
        double r27867 = 0.918938533204673;
        double r27868 = r27866 + r27867;
        return r27868;
}
↓
double f(double x, double y) {
        double r27869 = y;
        double r27870 = 1.0;
        double r27871 = r27869 - r27870;
        double r27872 = x;
        double r27873 = 0.5;
        double r27874 = -r27869;
        double r27875 = 0.918938533204673;
        double r27876 = fma(r27873, r27874, r27875);
        double r27877 = fma(r27871, r27872, r27876);
        return r27877;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673003))