Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r45781 = x;
        double r45782 = y;
        double r45783 = 1.0;
        double r45784 = r45782 - r45783;
        double r45785 = r45781 * r45784;
        double r45786 = 0.5;
        double r45787 = r45782 * r45786;
        double r45788 = r45785 - r45787;
        double r45789 = 0.918938533204673;
        double r45790 = r45788 + r45789;
        return r45790;
}
↓
double f(double x, double y) {
        double r45791 = x;
        double r45792 = y;
        double r45793 = r45791 * r45792;
        double r45794 = 1.0;
        double r45795 = -r45794;
        double r45796 = r45791 * r45795;
        double r45797 = r45793 + r45796;
        double r45798 = 0.5;
        double r45799 = r45792 * r45798;
        double r45800 = r45797 - r45799;
        double r45801 = 0.918938533204673;
        double r45802 = r45800 + r45801;
        return r45802;
}

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

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto \left(x \cdot \color{blue}{\left(y + \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \left(\color{blue}{\left(x \cdot y + x \cdot \left(-1\right)\right)} - y \cdot 0.5\right) + 0.918938533204673003\]

  5. Final simplification0.0

    \[\leadsto \left(\left(x \cdot y + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003\]

Reproduce

herbie shell --seed 2020083 
(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))