Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931\]
↓
\[\mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.9189385332046730026078762421093415468931
↓
\mathsf{fma}\left(x, y - 1, 0.9189385332046730026078762421093415468931 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r1648208 = x;
        double r1648209 = y;
        double r1648210 = 1.0;
        double r1648211 = r1648209 - r1648210;
        double r1648212 = r1648208 * r1648211;
        double r1648213 = 0.5;
        double r1648214 = r1648209 * r1648213;
        double r1648215 = r1648212 - r1648214;
        double r1648216 = 0.918938533204673;
        double r1648217 = r1648215 + r1648216;
        return r1648217;
}
↓
double f(double x, double y) {
        double r1648218 = x;
        double r1648219 = y;
        double r1648220 = 1.0;
        double r1648221 = r1648219 - r1648220;
        double r1648222 = 0.918938533204673;
        double r1648223 = 0.5;
        double r1648224 = r1648223 * r1648219;
        double r1648225 = r1648222 - r1648224;
        double r1648226 = fma(r1648218, r1648221, r1648225);
        return r1648226;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 +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))