Average Error: 0.0 → 0.0
Time: 6.2s
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 r2029057 = x;
        double r2029058 = y;
        double r2029059 = 1.0;
        double r2029060 = r2029058 - r2029059;
        double r2029061 = r2029057 * r2029060;
        double r2029062 = 0.5;
        double r2029063 = r2029058 * r2029062;
        double r2029064 = r2029061 - r2029063;
        double r2029065 = 0.918938533204673;
        double r2029066 = r2029064 + r2029065;
        return r2029066;
}
↓
double f(double x, double y) {
        double r2029067 = y;
        double r2029068 = 1.0;
        double r2029069 = r2029067 - r2029068;
        double r2029070 = x;
        double r2029071 = 0.918938533204673;
        double r2029072 = 0.5;
        double r2029073 = r2029072 * r2029067;
        double r2029074 = r2029071 - r2029073;
        double r2029075 = fma(r2029069, r2029070, r2029074);
        return r2029075;
}

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 2019158 +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))