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 r47302 = x;
        double r47303 = y;
        double r47304 = 1.0;
        double r47305 = r47303 - r47304;
        double r47306 = r47302 * r47305;
        double r47307 = 0.5;
        double r47308 = r47303 * r47307;
        double r47309 = r47306 - r47308;
        double r47310 = 0.918938533204673;
        double r47311 = r47309 + r47310;
        return r47311;
}
↓
double f(double x, double y) {
        double r47312 = y;
        double r47313 = 1.0;
        double r47314 = r47312 - r47313;
        double r47315 = x;
        double r47316 = 0.5;
        double r47317 = -r47312;
        double r47318 = 0.918938533204673;
        double r47319 = fma(r47316, r47317, r47318);
        double r47320 = fma(r47314, r47315, r47319);
        return r47320;
}

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 2019323 +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)) 0.918938533204673))