Average Error: 0.0 → 0.0
Time: 8.1s
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 r37204 = x;
        double r37205 = y;
        double r37206 = 1.0;
        double r37207 = r37205 - r37206;
        double r37208 = r37204 * r37207;
        double r37209 = 0.5;
        double r37210 = r37205 * r37209;
        double r37211 = r37208 - r37210;
        double r37212 = 0.918938533204673;
        double r37213 = r37211 + r37212;
        return r37213;
}
↓
double f(double x, double y) {
        double r37214 = y;
        double r37215 = 1.0;
        double r37216 = r37214 - r37215;
        double r37217 = x;
        double r37218 = 0.5;
        double r37219 = -r37214;
        double r37220 = 0.918938533204673;
        double r37221 = fma(r37218, r37219, r37220);
        double r37222 = fma(r37216, r37217, r37221);
        return r37222;
}

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 2019303 +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))