Average Error: 0.0 → 0.0
Time: 6.9s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r1927589 = x;
        double r1927590 = y;
        double r1927591 = 1.0;
        double r1927592 = r1927590 - r1927591;
        double r1927593 = r1927589 * r1927592;
        double r1927594 = 0.5;
        double r1927595 = r1927590 * r1927594;
        double r1927596 = r1927593 - r1927595;
        double r1927597 = 0.918938533204673;
        double r1927598 = r1927596 + r1927597;
        return r1927598;
}
↓
double f(double x, double y) {
        double r1927599 = y;
        double r1927600 = 1.0;
        double r1927601 = r1927599 - r1927600;
        double r1927602 = x;
        double r1927603 = 0.918938533204673;
        double r1927604 = 0.5;
        double r1927605 = r1927604 * r1927599;
        double r1927606 = r1927603 - r1927605;
        double r1927607 = fma(r1927601, r1927602, r1927606);
        return r1927607;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - y \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1, x, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019172 +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))