Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)
double f(double x, double y) {
        double r36302 = x;
        double r36303 = y;
        double r36304 = 1.0;
        double r36305 = r36303 - r36304;
        double r36306 = r36302 * r36305;
        double r36307 = 0.5;
        double r36308 = r36303 * r36307;
        double r36309 = r36306 - r36308;
        double r36310 = 0.918938533204673;
        double r36311 = r36309 + r36310;
        return r36311;
}
↓
double f(double x, double y) {
        double r36312 = y;
        double r36313 = 1.0;
        double r36314 = r36312 - r36313;
        double r36315 = x;
        double r36316 = 0.5;
        double r36317 = -r36312;
        double r36318 = 0.918938533204673;
        double r36319 = fma(r36316, r36317, r36318);
        double r36320 = fma(r36314, r36315, r36319);
        return r36320;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - 1, x, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]

Reproduce

herbie shell --seed 2019198 +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))