Average Error: 0.0 → 0.0
Time: 8.5s
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 r40764 = x;
        double r40765 = y;
        double r40766 = 1.0;
        double r40767 = r40765 - r40766;
        double r40768 = r40764 * r40767;
        double r40769 = 0.5;
        double r40770 = r40765 * r40769;
        double r40771 = r40768 - r40770;
        double r40772 = 0.918938533204673;
        double r40773 = r40771 + r40772;
        return r40773;
}
↓
double f(double x, double y) {
        double r40774 = y;
        double r40775 = 1.0;
        double r40776 = r40774 - r40775;
        double r40777 = x;
        double r40778 = 0.5;
        double r40779 = -r40774;
        double r40780 = 0.918938533204673;
        double r40781 = fma(r40778, r40779, r40780);
        double r40782 = fma(r40776, r40777, r40781);
        return r40782;
}

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 2019303 +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))