Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(\left(x - 0.5\right) \cdot y - 1 \cdot x\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(\left(x - 0.5\right) \cdot y - 1 \cdot x\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r1586888 = x;
        double r1586889 = y;
        double r1586890 = 1.0;
        double r1586891 = r1586889 - r1586890;
        double r1586892 = r1586888 * r1586891;
        double r1586893 = 0.5;
        double r1586894 = r1586889 * r1586893;
        double r1586895 = r1586892 - r1586894;
        double r1586896 = 0.918938533204673;
        double r1586897 = r1586895 + r1586896;
        return r1586897;
}
↓
double f(double x, double y) {
        double r1586898 = x;
        double r1586899 = 0.5;
        double r1586900 = r1586898 - r1586899;
        double r1586901 = y;
        double r1586902 = r1586900 * r1586901;
        double r1586903 = 1.0;
        double r1586904 = r1586903 * r1586898;
        double r1586905 = r1586902 - r1586904;
        double r1586906 = 0.918938533204673;
        double r1586907 = r1586905 + r1586906;
        return r1586907;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

    \[\leadsto \left(\left(x - 0.5\right) \cdot y - 1 \cdot x\right) + 0.9189385332046730026078762421093415468931\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))