Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)
double f(double x, double y) {
        double r37434 = x;
        double r37435 = y;
        double r37436 = 1.0;
        double r37437 = r37435 - r37436;
        double r37438 = r37434 * r37437;
        double r37439 = 0.5;
        double r37440 = r37435 * r37439;
        double r37441 = r37438 - r37440;
        double r37442 = 0.918938533204673;
        double r37443 = r37441 + r37442;
        return r37443;
}
↓
double f(double x, double y) {
        double r37444 = x;
        double r37445 = y;
        double r37446 = 1.0;
        double r37447 = r37445 - r37446;
        double r37448 = 0.5;
        double r37449 = -r37445;
        double r37450 = 0.918938533204673;
        double r37451 = fma(r37448, r37449, r37450);
        double r37452 = fma(r37444, r37447, r37451);
        return r37452;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]

Reproduce

herbie shell --seed 2020045 +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))