Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.9189385332046730026078762421093415468931\right)\right)\]
\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 r53249 = x;
        double r53250 = y;
        double r53251 = 1.0;
        double r53252 = r53250 - r53251;
        double r53253 = r53249 * r53252;
        double r53254 = 0.5;
        double r53255 = r53250 * r53254;
        double r53256 = r53253 - r53255;
        double r53257 = 0.918938533204673;
        double r53258 = r53256 + r53257;
        return r53258;
}
↓
double f(double x, double y) {
        double r53259 = y;
        double r53260 = 1.0;
        double r53261 = r53259 - r53260;
        double r53262 = x;
        double r53263 = 0.5;
        double r53264 = -r53259;
        double r53265 = 0.918938533204673;
        double r53266 = fma(r53263, r53264, r53265);
        double r53267 = fma(r53261, r53262, r53266);
        return r53267;
}

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 2019235 +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))