Average Error: 1.0 → 1.0
Time: 52.1s
Precision: 64
\[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
↓
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}
↓
\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}
double f(double x) {
        double r1228908 = 1.0;
        double r1228909 = /* ERROR: no posit support in C */;
        double r1228910 = x;
        double r1228911 = r1228910 + r1228909;
        double r1228912 = r1228909 / r1228911;
        double r1228913 = 2.0;
        double r1228914 = /* ERROR: no posit support in C */;
        double r1228915 = r1228914 / r1228910;
        double r1228916 = r1228912 - r1228915;
        double r1228917 = r1228910 - r1228909;
        double r1228918 = r1228909 / r1228917;
        double r1228919 = r1228916 + r1228918;
        return r1228919;
}
↓
double f(double x) {
        double r1228920 = 1.0;
        double r1228921 = x;
        double r1228922 = r1228921 + r1228920;
        double r1228923 = r1228920 / r1228922;
        double r1228924 = 2.0;
        double r1228925 = r1228924 / r1228921;
        double r1228926 = r1228923 - r1228925;
        double r1228927 = r1228921 - r1228920;
        double r1228928 = r1228920 / r1228927;
        double r1228929 = r1228926 + r1228928;
        return r1228929;
}

Error

Bits error versus x

Derivation

  1. Initial program 1.0

    \[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  2. Final simplification1.0

    \[\leadsto \left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  (+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))