Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)
double f(double x, double y) {
        double r37851 = x;
        double r37852 = y;
        double r37853 = 1.0;
        double r37854 = r37852 - r37853;
        double r37855 = r37851 * r37854;
        double r37856 = 0.5;
        double r37857 = r37852 * r37856;
        double r37858 = r37855 - r37857;
        double r37859 = 0.918938533204673;
        double r37860 = r37858 + r37859;
        return r37860;
}
↓
double f(double x, double y) {
        double r37861 = y;
        double r37862 = x;
        double r37863 = 0.918938533204673;
        double r37864 = fma(r37861, r37862, r37863);
        double r37865 = 1.0;
        double r37866 = 0.5;
        double r37867 = r37861 * r37866;
        double r37868 = fma(r37862, r37865, r37867);
        double r37869 = r37864 - r37868;
        return r37869;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]

Reproduce

herbie shell --seed 2020033 +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))