Average Error: 0.0 → 0.0
Time: 19.3s
Precision: 64
\[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]
↓
\[\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]
\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673
↓
\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)
double f(double x, double y) {
        double r2427669 = x;
        double r2427670 = y;
        double r2427671 = 1.0;
        double r2427672 = r2427670 - r2427671;
        double r2427673 = r2427669 * r2427672;
        double r2427674 = 0.5;
        double r2427675 = r2427670 * r2427674;
        double r2427676 = r2427673 - r2427675;
        double r2427677 = 0.918938533204673;
        double r2427678 = r2427676 + r2427677;
        return r2427678;
}
↓
double f(double x, double y) {
        double r2427679 = y;
        double r2427680 = 1.0;
        double r2427681 = r2427679 - r2427680;
        double r2427682 = x;
        double r2427683 = 0.918938533204673;
        double r2427684 = 0.5;
        double r2427685 = r2427684 * r2427679;
        double r2427686 = r2427683 - r2427685;
        double r2427687 = fma(r2427681, r2427682, r2427686);
        return r2427687;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x \cdot \left(y - 1.0\right) - y \cdot 0.5\right) + 0.918938533204673\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - y \cdot 0.5\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1.0, x, 0.918938533204673 - 0.5 \cdot y\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, A"
  (+ (- (* x (- y 1.0)) (* y 0.5)) 0.918938533204673))