Average Error: 0.0 → 0.0
Time: 7.7s
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 r1003175 = x;
        double r1003176 = y;
        double r1003177 = 1.0;
        double r1003178 = r1003176 - r1003177;
        double r1003179 = r1003175 * r1003178;
        double r1003180 = 0.5;
        double r1003181 = r1003176 * r1003180;
        double r1003182 = r1003179 - r1003181;
        double r1003183 = 0.918938533204673;
        double r1003184 = r1003182 + r1003183;
        return r1003184;
}
↓
double f(double x, double y) {
        double r1003185 = y;
        double r1003186 = 1.0;
        double r1003187 = r1003185 - r1003186;
        double r1003188 = x;
        double r1003189 = 0.918938533204673;
        double r1003190 = 0.5;
        double r1003191 = r1003190 * r1003185;
        double r1003192 = r1003189 - r1003191;
        double r1003193 = fma(r1003187, r1003188, r1003192);
        return r1003193;
}

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 2019170 +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))