Average Error: 0.0 → 0.0
Time: 18.3s
Precision: 64
\[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]
↓
\[\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r3552887 = x;
        double r3552888 = y;
        double r3552889 = 1.0;
        double r3552890 = r3552888 - r3552889;
        double r3552891 = r3552887 * r3552890;
        double r3552892 = 0.5;
        double r3552893 = r3552888 * r3552892;
        double r3552894 = r3552891 - r3552893;
        double r3552895 = 0.918938533204673;
        double r3552896 = r3552894 + r3552895;
        return r3552896;
}
↓
double f(double x, double y) {
        double r3552897 = y;
        double r3552898 = 1.0;
        double r3552899 = r3552897 - r3552898;
        double r3552900 = x;
        double r3552901 = 0.918938533204673;
        double r3552902 = 0.5;
        double r3552903 = r3552902 * r3552897;
        double r3552904 = r3552901 - r3552903;
        double r3552905 = fma(r3552899, r3552900, r3552904);
        return r3552905;
}

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

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

  3. Final simplification0.0

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

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))