Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y, x, 0.918938533204673003\right) - \mathsf{fma}\left(x, 1, y \cdot 0.5\right)
double f(double x, double y) {
        double r62690 = x;
        double r62691 = y;
        double r62692 = 1.0;
        double r62693 = r62691 - r62692;
        double r62694 = r62690 * r62693;
        double r62695 = 0.5;
        double r62696 = r62691 * r62695;
        double r62697 = r62694 - r62696;
        double r62698 = 0.918938533204673;
        double r62699 = r62697 + r62698;
        return r62699;
}
↓
double f(double x, double y) {
        double r62700 = y;
        double r62701 = x;
        double r62702 = 0.918938533204673;
        double r62703 = fma(r62700, r62701, r62702);
        double r62704 = 1.0;
        double r62705 = 0.5;
        double r62706 = r62700 * r62705;
        double r62707 = fma(r62701, r62704, r62706);
        double r62708 = r62703 - r62707;
        return r62708;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +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))