Average Error: 0.1 → 0.1
Time: 54.7s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[\left(y + x\right) - \mathsf{fma}\left(\log y, y + 0.5, z\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
\left(y + x\right) - \mathsf{fma}\left(\log y, y + 0.5, z\right)
double f(double x, double y, double z) {
        double r341885 = x;
        double r341886 = y;
        double r341887 = 0.5;
        double r341888 = r341886 + r341887;
        double r341889 = log(r341886);
        double r341890 = r341888 * r341889;
        double r341891 = r341885 - r341890;
        double r341892 = r341891 + r341886;
        double r341893 = z;
        double r341894 = r341892 - r341893;
        return r341894;
}
↓
double f(double x, double y, double z) {
        double r341895 = y;
        double r341896 = x;
        double r341897 = r341895 + r341896;
        double r341898 = log(r341895);
        double r341899 = 0.5;
        double r341900 = r341895 + r341899;
        double r341901 = z;
        double r341902 = fma(r341898, r341900, r341901);
        double r341903 = r341897 - r341902;
        return r341903;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

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

  3. Final simplification0.1

    \[\leadsto \left(y + x\right) - \mathsf{fma}\left(\log y, y + 0.5, z\right)\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))