Average Error: 0.0 → 0.0
Time: 22.3s
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 r685056 = x;
        double r685057 = y;
        double r685058 = 1.0;
        double r685059 = r685057 - r685058;
        double r685060 = r685056 * r685059;
        double r685061 = 0.5;
        double r685062 = r685057 * r685061;
        double r685063 = r685060 - r685062;
        double r685064 = 0.918938533204673;
        double r685065 = r685063 + r685064;
        return r685065;
}
↓
double f(double x, double y) {
        double r685066 = y;
        double r685067 = 1.0;
        double r685068 = r685066 - r685067;
        double r685069 = x;
        double r685070 = 0.918938533204673;
        double r685071 = 0.5;
        double r685072 = r685071 * r685066;
        double r685073 = r685070 - r685072;
        double r685074 = fma(r685068, r685069, r685073);
        return r685074;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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))