Average Error: 0.0 → 0.0
Time: 16.1s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)
double f(double x, double y) {
        double r44976 = x;
        double r44977 = y;
        double r44978 = 1.0;
        double r44979 = r44977 - r44978;
        double r44980 = r44976 * r44979;
        double r44981 = 0.5;
        double r44982 = r44977 * r44981;
        double r44983 = r44980 - r44982;
        double r44984 = 0.918938533204673;
        double r44985 = r44983 + r44984;
        return r44985;
}
↓
double f(double x, double y) {
        double r44986 = y;
        double r44987 = 1.0;
        double r44988 = r44986 - r44987;
        double r44989 = x;
        double r44990 = 0.5;
        double r44991 = -r44986;
        double r44992 = 0.918938533204673;
        double r44993 = fma(r44990, r44991, r44992);
        double r44994 = fma(r44988, r44989, r44993);
        return r44994;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019199 +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))