Average Error: 0.0 → 0.0
Time: 760.0ms
Precision: 64
\[\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003\]
↓
\[\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right) + 0.918938533204673003\]
\left(x \cdot \left(y - 1\right) - y \cdot 0.5\right) + 0.918938533204673003
↓
\mathsf{fma}\left(x, y - 1, -y \cdot 0.5\right) + 0.918938533204673003
double f(double x, double y) {
        double r32300 = x;
        double r32301 = y;
        double r32302 = 1.0;
        double r32303 = r32301 - r32302;
        double r32304 = r32300 * r32303;
        double r32305 = 0.5;
        double r32306 = r32301 * r32305;
        double r32307 = r32304 - r32306;
        double r32308 = 0.918938533204673;
        double r32309 = r32307 + r32308;
        return r32309;
}
↓
double f(double x, double y) {
        double r32310 = x;
        double r32311 = y;
        double r32312 = 1.0;
        double r32313 = r32311 - r32312;
        double r32314 = 0.5;
        double r32315 = r32311 * r32314;
        double r32316 = -r32315;
        double r32317 = fma(r32310, r32313, r32316);
        double r32318 = 0.918938533204673;
        double r32319 = r32317 + r32318;
        return r32319;
}

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. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +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))