Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.9189385332046730026078762421093415468931\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.9189385332046730026078762421093415468931\right)\right)
double f(double x, double y) {
        double r34632 = x;
        double r34633 = y;
        double r34634 = 1.0;
        double r34635 = r34633 - r34634;
        double r34636 = r34632 * r34635;
        double r34637 = 0.5;
        double r34638 = r34633 * r34637;
        double r34639 = r34636 - r34638;
        double r34640 = 0.918938533204673;
        double r34641 = r34639 + r34640;
        return r34641;
}
↓
double f(double x, double y) {
        double r34642 = y;
        double r34643 = 1.0;
        double r34644 = r34642 - r34643;
        double r34645 = x;
        double r34646 = 0.5;
        double r34647 = -r34642;
        double r34648 = 0.918938533204673;
        double r34649 = fma(r34646, r34647, r34648);
        double r34650 = fma(r34644, r34645, r34649);
        return r34650;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019351 +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))