Average Error: 0.0 → 0.0
Time: 36.7s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(x \cdot y + \left(x \cdot \left(-1\right) - 0.5 \cdot y\right)\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(x \cdot y + \left(x \cdot \left(-1\right) - 0.5 \cdot y\right)\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r43638 = x;
        double r43639 = y;
        double r43640 = 1.0;
        double r43641 = r43639 - r43640;
        double r43642 = r43638 * r43641;
        double r43643 = 0.5;
        double r43644 = r43639 * r43643;
        double r43645 = r43642 - r43644;
        double r43646 = 0.918938533204673;
        double r43647 = r43645 + r43646;
        return r43647;
}
↓
double f(double x, double y) {
        double r43648 = x;
        double r43649 = y;
        double r43650 = r43648 * r43649;
        double r43651 = 1.0;
        double r43652 = -r43651;
        double r43653 = r43648 * r43652;
        double r43654 = 0.5;
        double r43655 = r43654 * r43649;
        double r43656 = r43653 - r43655;
        double r43657 = r43650 + r43656;
        double r43658 = 0.918938533204673;
        double r43659 = r43657 + r43658;
        return r43659;
}

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. Applied associate--l+0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019202 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1)) (* y 0.5)) 0.918938533204673003))