Average Error: 0.0 → 0.0
Time: 1.0s
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 r50437 = x;
        double r50438 = y;
        double r50439 = 1.0;
        double r50440 = r50438 - r50439;
        double r50441 = r50437 * r50440;
        double r50442 = 0.5;
        double r50443 = r50438 * r50442;
        double r50444 = r50441 - r50443;
        double r50445 = 0.918938533204673;
        double r50446 = r50444 + r50445;
        return r50446;
}
↓
double f(double x, double y) {
        double r50447 = y;
        double r50448 = x;
        double r50449 = 0.918938533204673;
        double r50450 = fma(r50447, r50448, r50449);
        double r50451 = 1.0;
        double r50452 = 0.5;
        double r50453 = r50447 * r50452;
        double r50454 = fma(r50448, r50451, r50453);
        double r50455 = r50450 - r50454;
        return r50455;
}

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 2020081 +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))