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 r1595507 = x;
        double r1595508 = y;
        double r1595509 = 1.0;
        double r1595510 = r1595508 - r1595509;
        double r1595511 = r1595507 * r1595510;
        double r1595512 = 0.5;
        double r1595513 = r1595508 * r1595512;
        double r1595514 = r1595511 - r1595513;
        double r1595515 = 0.918938533204673;
        double r1595516 = r1595514 + r1595515;
        return r1595516;
}
↓
double f(double x, double y) {
        double r1595517 = x;
        double r1595518 = y;
        double r1595519 = 1.0;
        double r1595520 = r1595518 - r1595519;
        double r1595521 = 0.918938533204673;
        double r1595522 = 0.5;
        double r1595523 = r1595522 * r1595518;
        double r1595524 = r1595521 - r1595523;
        double r1595525 = fma(r1595517, r1595520, r1595524);
        return r1595525;
}

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 2019171 +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))