Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
double f(double x, double y) {
        double r57984 = x;
        double r57985 = y;
        double r57986 = 1.0;
        double r57987 = r57985 - r57986;
        double r57988 = r57984 * r57987;
        double r57989 = 0.5;
        double r57990 = r57985 * r57989;
        double r57991 = r57988 - r57990;
        double r57992 = 0.918938533204673;
        double r57993 = r57991 + r57992;
        return r57993;
}
↓
double f(double x, double y) {
        double r57994 = x;
        double r57995 = y;
        double r57996 = 1.0;
        double r57997 = r57995 - r57996;
        double r57998 = 0.5;
        double r57999 = r57995 * r57998;
        double r58000 = -r57999;
        double r58001 = fma(r57994, r57997, r58000);
        double r58002 = 0.918938533204673;
        double r58003 = r58001 + r58002;
        return r58003;
}

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. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +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))