Average Error: 0.0 → 0.0
Time: 9.3s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(\left(y \cdot x + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\left(\left(y \cdot x + x \cdot \left(-1\right)\right) - y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r33767 = x;
        double r33768 = y;
        double r33769 = 1.0;
        double r33770 = r33768 - r33769;
        double r33771 = r33767 * r33770;
        double r33772 = 0.5;
        double r33773 = r33768 * r33772;
        double r33774 = r33771 - r33773;
        double r33775 = 0.918938533204673;
        double r33776 = r33774 + r33775;
        return r33776;
}
↓
double f(double x, double y) {
        double r33777 = y;
        double r33778 = x;
        double r33779 = r33777 * r33778;
        double r33780 = 1.0;
        double r33781 = -r33780;
        double r33782 = r33778 * r33781;
        double r33783 = r33779 + r33782;
        double r33784 = 0.5;
        double r33785 = r33777 * r33784;
        double r33786 = r33783 - r33785;
        double r33787 = 0.918938533204673;
        double r33788 = r33786 + r33787;
        return r33788;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))