Average Error: 0.0 → 0.0
Time: 7.6s
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 r51428 = x;
        double r51429 = y;
        double r51430 = 1.0;
        double r51431 = r51429 - r51430;
        double r51432 = r51428 * r51431;
        double r51433 = 0.5;
        double r51434 = r51429 * r51433;
        double r51435 = r51432 - r51434;
        double r51436 = 0.918938533204673;
        double r51437 = r51435 + r51436;
        return r51437;
}
↓
double f(double x, double y) {
        double r51438 = x;
        double r51439 = y;
        double r51440 = 1.0;
        double r51441 = r51439 - r51440;
        double r51442 = 0.5;
        double r51443 = -r51439;
        double r51444 = 0.918938533204673;
        double r51445 = fma(r51442, r51443, r51444);
        double r51446 = fma(r51438, r51441, r51445);
        return r51446;
}

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 2020043 +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))