Average Error: 1.0 → 1.0
Time: 17.2s
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 r1650868 = 1.0;
        double r1650869 = /* ERROR: no posit support in C */;
        double r1650870 = x;
        double r1650871 = r1650870 + r1650869;
        double r1650872 = r1650869 / r1650871;
        double r1650873 = 2.0;
        double r1650874 = /* ERROR: no posit support in C */;
        double r1650875 = r1650874 / r1650870;
        double r1650876 = r1650872 - r1650875;
        double r1650877 = r1650870 - r1650869;
        double r1650878 = r1650869 / r1650877;
        double r1650879 = r1650876 + r1650878;
        return r1650879;
}
↓
double f(double x) {
        double r1650880 = 1.0;
        double r1650881 = x;
        double r1650882 = r1650881 + r1650880;
        double r1650883 = r1650880 / r1650882;
        double r1650884 = 2.0;
        double r1650885 = r1650884 / r1650881;
        double r1650886 = r1650883 - r1650885;
        double r1650887 = r1650881 - r1650880;
        double r1650888 = r1650880 / r1650887;
        double r1650889 = r1650886 + r1650888;
        return r1650889;
}

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 2019104 +o rules:numerics
(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)))))