Average Error: 0.0 → 0.0
Time: 1.3s
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 r60652 = x;
        double r60653 = y;
        double r60654 = 1.0;
        double r60655 = r60653 - r60654;
        double r60656 = r60652 * r60655;
        double r60657 = 0.5;
        double r60658 = r60653 * r60657;
        double r60659 = r60656 - r60658;
        double r60660 = 0.918938533204673;
        double r60661 = r60659 + r60660;
        return r60661;
}
↓
double f(double x, double y) {
        double r60662 = x;
        double r60663 = y;
        double r60664 = r60662 * r60663;
        double r60665 = 1.0;
        double r60666 = -r60665;
        double r60667 = r60662 * r60666;
        double r60668 = r60664 + r60667;
        double r60669 = 0.5;
        double r60670 = r60663 * r60669;
        double r60671 = r60668 - r60670;
        double r60672 = 0.918938533204673;
        double r60673 = r60671 + r60672;
        return r60673;
}

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 2019346 
(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))