Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y - 1, \mathsf{fma}\left(0.5, -y, 0.918938533204673003\right)\right)
double f(double x, double y) {
        double r34310 = x;
        double r34311 = y;
        double r34312 = 1.0;
        double r34313 = r34311 - r34312;
        double r34314 = r34310 * r34313;
        double r34315 = 0.5;
        double r34316 = r34311 * r34315;
        double r34317 = r34314 - r34316;
        double r34318 = 0.918938533204673;
        double r34319 = r34317 + r34318;
        return r34319;
}
↓
double f(double x, double y) {
        double r34320 = x;
        double r34321 = y;
        double r34322 = 1.0;
        double r34323 = r34321 - r34322;
        double r34324 = 0.5;
        double r34325 = -r34321;
        double r34326 = 0.918938533204673;
        double r34327 = fma(r34324, r34325, r34326);
        double r34328 = fma(r34320, r34323, r34327);
        return r34328;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +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))