Average Error: 0.0 → 0.0
Time: 7.4s
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 r37595 = x;
        double r37596 = y;
        double r37597 = 1.0;
        double r37598 = r37596 - r37597;
        double r37599 = r37595 * r37598;
        double r37600 = 0.5;
        double r37601 = r37596 * r37600;
        double r37602 = r37599 - r37601;
        double r37603 = 0.918938533204673;
        double r37604 = r37602 + r37603;
        return r37604;
}
↓
double f(double x, double y) {
        double r37605 = x;
        double r37606 = y;
        double r37607 = r37605 * r37606;
        double r37608 = 1.0;
        double r37609 = -r37608;
        double r37610 = r37605 * r37609;
        double r37611 = r37607 + r37610;
        double r37612 = 0.5;
        double r37613 = r37606 * r37612;
        double r37614 = r37611 - r37613;
        double r37615 = 0.918938533204673;
        double r37616 = r37614 + r37615;
        return r37616;
}

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 2019323 
(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))