Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\left(x \cdot y + \left(\left(-1\right) \cdot x - y \cdot 0.5\right)\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\left(x \cdot y + \left(\left(-1\right) \cdot x - y \cdot 0.5\right)\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r67471 = x;
        double r67472 = y;
        double r67473 = 1.0;
        double r67474 = r67472 - r67473;
        double r67475 = r67471 * r67474;
        double r67476 = 0.5;
        double r67477 = r67472 * r67476;
        double r67478 = r67475 - r67477;
        double r67479 = 0.918938533204673;
        double r67480 = r67478 + r67479;
        return r67480;
}
↓
double f(double x, double y) {
        double r67481 = x;
        double r67482 = y;
        double r67483 = r67481 * r67482;
        double r67484 = 1.0;
        double r67485 = -r67484;
        double r67486 = r67485 * r67481;
        double r67487 = 0.5;
        double r67488 = r67482 * r67487;
        double r67489 = r67486 - r67488;
        double r67490 = r67483 + r67489;
        double r67491 = 0.918938533204673;
        double r67492 = r67490 + r67491;
        return r67492;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019362 
(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))