Average Error: 0.0 → 0.0
Time: 5.3s
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 r15670 = x;
        double r15671 = y;
        double r15672 = 1.0;
        double r15673 = r15671 - r15672;
        double r15674 = r15670 * r15673;
        double r15675 = 0.5;
        double r15676 = r15671 * r15675;
        double r15677 = r15674 - r15676;
        double r15678 = 0.918938533204673;
        double r15679 = r15677 + r15678;
        return r15679;
}
↓
double f(double x, double y) {
        double r15680 = y;
        double r15681 = 1.0;
        double r15682 = r15680 - r15681;
        double r15683 = x;
        double r15684 = 0.5;
        double r15685 = -r15680;
        double r15686 = 0.918938533204673;
        double r15687 = fma(r15684, r15685, r15686);
        double r15688 = fma(r15682, r15683, r15687);
        return r15688;
}

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 2019310 +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)) 0.918938533204673003))