Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y, x - 0.5, \mathsf{fma}\left(1, -x, 0.9189385332046730026078762421093415468931\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y, x - 0.5, \mathsf{fma}\left(1, -x, 0.9189385332046730026078762421093415468931\right)\right)
double f(double x, double y) {
        double r20894 = x;
        double r20895 = y;
        double r20896 = 1.0;
        double r20897 = r20895 - r20896;
        double r20898 = r20894 * r20897;
        double r20899 = 0.5;
        double r20900 = r20895 * r20899;
        double r20901 = r20898 - r20900;
        double r20902 = 0.918938533204673;
        double r20903 = r20901 + r20902;
        return r20903;
}
↓
double f(double x, double y) {
        double r20904 = y;
        double r20905 = x;
        double r20906 = 0.5;
        double r20907 = r20905 - r20906;
        double r20908 = 1.0;
        double r20909 = -r20905;
        double r20910 = 0.918938533204673;
        double r20911 = fma(r20908, r20909, r20910);
        double r20912 = fma(r20904, r20907, r20911);
        return r20912;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +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))