Average Error: 0.0 → 0.0
Time: 7.4s
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 r2440854 = x;
        double r2440855 = y;
        double r2440856 = 1.0;
        double r2440857 = r2440855 - r2440856;
        double r2440858 = r2440854 * r2440857;
        double r2440859 = 0.5;
        double r2440860 = r2440855 * r2440859;
        double r2440861 = r2440858 - r2440860;
        double r2440862 = 0.918938533204673;
        double r2440863 = r2440861 + r2440862;
        return r2440863;
}
↓
double f(double x, double y) {
        double r2440864 = y;
        double r2440865 = 1.0;
        double r2440866 = r2440864 - r2440865;
        double r2440867 = x;
        double r2440868 = 0.918938533204673;
        double r2440869 = 0.5;
        double r2440870 = r2440869 * r2440864;
        double r2440871 = r2440868 - r2440870;
        double r2440872 = fma(r2440866, r2440867, r2440871);
        return r2440872;
}

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 2019168 +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))