Average Error: 0.0 → 0.0
Time: 6.4s
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 r36162 = x;
        double r36163 = y;
        double r36164 = 1.0;
        double r36165 = r36163 - r36164;
        double r36166 = r36162 * r36165;
        double r36167 = 0.5;
        double r36168 = r36163 * r36167;
        double r36169 = r36166 - r36168;
        double r36170 = 0.918938533204673;
        double r36171 = r36169 + r36170;
        return r36171;
}
↓
double f(double x, double y) {
        double r36172 = x;
        double r36173 = y;
        double r36174 = 1.0;
        double r36175 = r36173 - r36174;
        double r36176 = 0.5;
        double r36177 = -r36173;
        double r36178 = 0.918938533204673;
        double r36179 = fma(r36176, r36177, r36178);
        double r36180 = fma(r36172, r36175, r36179);
        return r36180;
}

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 2020042 +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))