Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r522823 = x;
        double r522824 = y;
        double r522825 = 1.0;
        double r522826 = r522824 - r522825;
        double r522827 = r522823 * r522826;
        double r522828 = 0.5;
        double r522829 = r522824 * r522828;
        double r522830 = r522827 - r522829;
        double r522831 = 0.918938533204673;
        double r522832 = r522830 + r522831;
        return r522832;
}
↓
double f(double x, double y) {
        double r522833 = y;
        double r522834 = 1.0;
        double r522835 = r522833 - r522834;
        double r522836 = x;
        double r522837 = 0.918938533204673;
        double r522838 = 0.5;
        double r522839 = r522838 * r522833;
        double r522840 = r522837 - r522839;
        double r522841 = fma(r522835, r522836, r522840);
        return r522841;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 +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))