Average Error: 0.0 → 0.0
Time: 5.1s
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 r60409 = x;
        double r60410 = y;
        double r60411 = 1.0;
        double r60412 = r60410 - r60411;
        double r60413 = r60409 * r60412;
        double r60414 = 0.5;
        double r60415 = r60410 * r60414;
        double r60416 = r60413 - r60415;
        double r60417 = 0.918938533204673;
        double r60418 = r60416 + r60417;
        return r60418;
}
↓
double f(double x, double y) {
        double r60419 = x;
        double r60420 = y;
        double r60421 = 1.0;
        double r60422 = r60420 - r60421;
        double r60423 = 0.5;
        double r60424 = -r60420;
        double r60425 = 0.918938533204673;
        double r60426 = fma(r60423, r60424, r60425);
        double r60427 = fma(r60419, r60422, r60426);
        return r60427;
}

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))