Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\left(\left(y \cdot x + \left(-1\right) \cdot x\right) - y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\left(\left(y \cdot x + \left(-1\right) \cdot x\right) - y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r49815 = x;
        double r49816 = y;
        double r49817 = 1.0;
        double r49818 = r49816 - r49817;
        double r49819 = r49815 * r49818;
        double r49820 = 0.5;
        double r49821 = r49816 * r49820;
        double r49822 = r49819 - r49821;
        double r49823 = 0.918938533204673;
        double r49824 = r49822 + r49823;
        return r49824;
}
↓
double f(double x, double y) {
        double r49825 = y;
        double r49826 = x;
        double r49827 = r49825 * r49826;
        double r49828 = 1.0;
        double r49829 = -r49828;
        double r49830 = r49829 * r49826;
        double r49831 = r49827 + r49830;
        double r49832 = 0.5;
        double r49833 = r49825 * r49832;
        double r49834 = r49831 - r49833;
        double r49835 = 0.918938533204673;
        double r49836 = r49834 + r49835;
        return r49836;
}

Error

Bits error versus x

Bits error versus y

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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. Simplified0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(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))