Average Error: 0.0 → 0.0
Time: 6.8s
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 r39094 = x;
        double r39095 = y;
        double r39096 = 1.0;
        double r39097 = r39095 - r39096;
        double r39098 = r39094 * r39097;
        double r39099 = 0.5;
        double r39100 = r39095 * r39099;
        double r39101 = r39098 - r39100;
        double r39102 = 0.918938533204673;
        double r39103 = r39101 + r39102;
        return r39103;
}
↓
double f(double x, double y) {
        double r39104 = x;
        double r39105 = y;
        double r39106 = r39104 * r39105;
        double r39107 = 1.0;
        double r39108 = -r39107;
        double r39109 = r39104 * r39108;
        double r39110 = r39106 + r39109;
        double r39111 = 0.5;
        double r39112 = r39105 * r39111;
        double r39113 = r39110 - r39112;
        double r39114 = 0.918938533204673;
        double r39115 = r39113 + r39114;
        return r39115;
}

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 2019304 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673003))