Average Error: 0.0 → 0.0
Time: 16.9s
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 r2573001 = x;
        double r2573002 = y;
        double r2573003 = 1.0;
        double r2573004 = r2573002 - r2573003;
        double r2573005 = r2573001 * r2573004;
        double r2573006 = 0.5;
        double r2573007 = r2573002 * r2573006;
        double r2573008 = r2573005 - r2573007;
        double r2573009 = 0.918938533204673;
        double r2573010 = r2573008 + r2573009;
        return r2573010;
}
↓
double f(double x, double y) {
        double r2573011 = y;
        double r2573012 = 1.0;
        double r2573013 = r2573011 - r2573012;
        double r2573014 = x;
        double r2573015 = 0.918938533204673;
        double r2573016 = 0.5;
        double r2573017 = r2573016 * r2573011;
        double r2573018 = r2573015 - r2573017;
        double r2573019 = fma(r2573013, r2573014, r2573018);
        return r2573019;
}

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 2019163 +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))