Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(y \cdot x + 0.9189385332046730026078762421093415468931\right) - \left(1 \cdot x + 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(y \cdot x + 0.9189385332046730026078762421093415468931\right) - \left(1 \cdot x + 0.5 \cdot y\right)
double f(double x, double y) {
        double r32680 = x;
        double r32681 = y;
        double r32682 = 1.0;
        double r32683 = r32681 - r32682;
        double r32684 = r32680 * r32683;
        double r32685 = 0.5;
        double r32686 = r32681 * r32685;
        double r32687 = r32684 - r32686;
        double r32688 = 0.918938533204673;
        double r32689 = r32687 + r32688;
        return r32689;
}
↓
double f(double x, double y) {
        double r32690 = y;
        double r32691 = x;
        double r32692 = r32690 * r32691;
        double r32693 = 0.918938533204673;
        double r32694 = r32692 + r32693;
        double r32695 = 1.0;
        double r32696 = r32695 * r32691;
        double r32697 = 0.5;
        double r32698 = r32697 * r32690;
        double r32699 = r32696 + r32698;
        double r32700 = r32694 - r32699;
        return r32700;
}

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-rgt-in0.0

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

  5. Applied associate--l+0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  9. Applied associate-+r-0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(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))