Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r47053 = x;
        double r47054 = y;
        double r47055 = 1.0;
        double r47056 = r47054 - r47055;
        double r47057 = r47053 * r47056;
        double r47058 = 0.5;
        double r47059 = r47054 * r47058;
        double r47060 = r47057 - r47059;
        double r47061 = 0.918938533204673;
        double r47062 = r47060 + r47061;
        return r47062;
}
↓
double f(double x, double y) {
        double r47063 = x;
        double r47064 = y;
        double r47065 = r47063 * r47064;
        double r47066 = 1.0;
        double r47067 = -r47066;
        double r47068 = r47063 * r47067;
        double r47069 = r47065 + r47068;
        double r47070 = 0.5;
        double r47071 = r47064 * r47070;
        double r47072 = r47069 - r47071;
        double r47073 = 0.918938533204673;
        double r47074 = r47072 + r47073;
        return r47074;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 +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))