Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]
↓
\[\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r856077 = x;
        double r856078 = y;
        double r856079 = 1.0;
        double r856080 = r856078 - r856079;
        double r856081 = r856077 * r856080;
        double r856082 = 0.5;
        double r856083 = r856078 * r856082;
        double r856084 = r856081 - r856083;
        double r856085 = 0.918938533204673;
        double r856086 = r856084 + r856085;
        return r856086;
}
↓
double f(double x, double y) {
        double r856087 = y;
        double r856088 = 1.0;
        double r856089 = r856087 - r856088;
        double r856090 = x;
        double r856091 = 0.918938533204673;
        double r856092 = 0.5;
        double r856093 = r856092 * r856087;
        double r856094 = r856091 - r856093;
        double r856095 = fma(r856089, r856090, r856094);
        return r856095;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - y \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019156 +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))