Average Error: 0.0 → 0.0
Time: 4.3s
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 r47669 = x;
        double r47670 = y;
        double r47671 = 1.0;
        double r47672 = r47670 - r47671;
        double r47673 = r47669 * r47672;
        double r47674 = 0.5;
        double r47675 = r47670 * r47674;
        double r47676 = r47673 - r47675;
        double r47677 = 0.918938533204673;
        double r47678 = r47676 + r47677;
        return r47678;
}
↓
double f(double x, double y) {
        double r47679 = x;
        double r47680 = y;
        double r47681 = 1.0;
        double r47682 = r47680 - r47681;
        double r47683 = 0.5;
        double r47684 = -r47680;
        double r47685 = 0.918938533204673;
        double r47686 = fma(r47683, r47684, r47685);
        double r47687 = fma(r47679, r47682, r47686);
        return r47687;
}

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 2020047 +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))