Average Error: 0.0 → 0.0
Time: 3.4s
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 r28229 = x;
        double r28230 = y;
        double r28231 = 1.0;
        double r28232 = r28230 - r28231;
        double r28233 = r28229 * r28232;
        double r28234 = 0.5;
        double r28235 = r28230 * r28234;
        double r28236 = r28233 - r28235;
        double r28237 = 0.918938533204673;
        double r28238 = r28236 + r28237;
        return r28238;
}
↓
double f(double x, double y) {
        double r28239 = y;
        double r28240 = 1.0;
        double r28241 = r28239 - r28240;
        double r28242 = x;
        double r28243 = 0.5;
        double r28244 = -r28239;
        double r28245 = 0.918938533204673;
        double r28246 = fma(r28243, r28244, r28245);
        double r28247 = fma(r28241, r28242, r28246);
        return r28247;
}

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 2019326 +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))