Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]
↓
\[\mathsf{fma}\left(y, x - 0.5, 0.918938533204673 - 1.0 \cdot x\right)\]
\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(y, x - 0.5, 0.918938533204673 - 1.0 \cdot x\right)
double f(double x, double y) {
        double r2268837 = x;
        double r2268838 = y;
        double r2268839 = 1.0;
        double r2268840 = r2268838 - r2268839;
        double r2268841 = r2268837 * r2268840;
        double r2268842 = 0.5;
        double r2268843 = r2268838 * r2268842;
        double r2268844 = r2268841 - r2268843;
        double r2268845 = 0.918938533204673;
        double r2268846 = r2268844 + r2268845;
        return r2268846;
}
↓
double f(double x, double y) {
        double r2268847 = y;
        double r2268848 = x;
        double r2268849 = 0.5;
        double r2268850 = r2268848 - r2268849;
        double r2268851 = 0.918938533204673;
        double r2268852 = 1.0;
        double r2268853 = r2268852 * r2268848;
        double r2268854 = r2268851 - r2268853;
        double r2268855 = fma(r2268847, r2268850, r2268854);
        return r2268855;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - 0.5, 0.918938533204673 - 1.0 \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - 0.5, 0.918938533204673 - 1.0 \cdot x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))