Average Error: 0.0 → 0.0
Time: 1.8s
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 r41327 = x;
        double r41328 = y;
        double r41329 = 1.0;
        double r41330 = r41328 - r41329;
        double r41331 = r41327 * r41330;
        double r41332 = 0.5;
        double r41333 = r41328 * r41332;
        double r41334 = r41331 - r41333;
        double r41335 = 0.918938533204673;
        double r41336 = r41334 + r41335;
        return r41336;
}
↓
double f(double x, double y) {
        double r41337 = x;
        double r41338 = y;
        double r41339 = r41337 * r41338;
        double r41340 = 1.0;
        double r41341 = -r41340;
        double r41342 = r41341 * r41337;
        double r41343 = 0.5;
        double r41344 = r41338 * r41343;
        double r41345 = r41342 - r41344;
        double r41346 = r41339 + r41345;
        double r41347 = 0.918938533204673;
        double r41348 = r41346 + r41347;
        return r41348;
}

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 2019347 
(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))