Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931\right) - y \cdot 0.5\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931\right) - y \cdot 0.5
double f(double x, double y) {
        double r3424289 = x;
        double r3424290 = y;
        double r3424291 = 1.0;
        double r3424292 = r3424290 - r3424291;
        double r3424293 = r3424289 * r3424292;
        double r3424294 = 0.5;
        double r3424295 = r3424290 * r3424294;
        double r3424296 = r3424293 - r3424295;
        double r3424297 = 0.918938533204673;
        double r3424298 = r3424296 + r3424297;
        return r3424298;
}
↓
double f(double x, double y) {
        double r3424299 = y;
        double r3424300 = 1.0;
        double r3424301 = r3424299 - r3424300;
        double r3424302 = x;
        double r3424303 = 0.918938533204673;
        double r3424304 = fma(r3424301, r3424302, r3424303);
        double r3424305 = 0.5;
        double r3424306 = r3424299 * r3424305;
        double r3424307 = r3424304 - r3424306;
        return r3424307;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +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))