Average Error: 0.0 → 0.0
Time: 1.6s
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 r301 = x;
        double r302 = y;
        double r303 = 1.0;
        double r304 = r302 - r303;
        double r305 = r301 * r304;
        double r306 = 0.5;
        double r307 = r302 * r306;
        double r308 = r305 - r307;
        double r309 = 0.918938533204673;
        double r310 = r308 + r309;
        return r310;
}
↓
double f(double x, double y) {
        double r311 = y;
        double r312 = x;
        double r313 = 0.918938533204673;
        double r314 = fma(r311, r312, r313);
        double r315 = 1.0;
        double r316 = 0.5;
        double r317 = r311 * r316;
        double r318 = fma(r312, r315, r317);
        double r319 = r314 - r318;
        return r319;
}

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 2020025 +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))