Average Error: 0.0 → 0.0
Time: 754.0ms
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 r59147 = x;
        double r59148 = y;
        double r59149 = 1.0;
        double r59150 = r59148 - r59149;
        double r59151 = r59147 * r59150;
        double r59152 = 0.5;
        double r59153 = r59148 * r59152;
        double r59154 = r59151 - r59153;
        double r59155 = 0.918938533204673;
        double r59156 = r59154 + r59155;
        return r59156;
}
↓
double f(double x, double y) {
        double r59157 = x;
        double r59158 = y;
        double r59159 = 1.0;
        double r59160 = r59158 - r59159;
        double r59161 = 0.5;
        double r59162 = r59158 * r59161;
        double r59163 = -r59162;
        double r59164 = fma(r59157, r59160, r59163);
        double r59165 = 0.918938533204673;
        double r59166 = r59164 + r59165;
        return r59166;
}

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))