Average Error: 1.0 → 1.0
Time: 25.8s
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 r3775785 = 1.0;
        double r3775786 = /* ERROR: no posit support in C */;
        double r3775787 = x;
        double r3775788 = r3775787 + r3775786;
        double r3775789 = r3775786 / r3775788;
        double r3775790 = 2.0;
        double r3775791 = /* ERROR: no posit support in C */;
        double r3775792 = r3775791 / r3775787;
        double r3775793 = r3775789 - r3775792;
        double r3775794 = r3775787 - r3775786;
        double r3775795 = r3775786 / r3775794;
        double r3775796 = r3775793 + r3775795;
        return r3775796;
}
↓
double f(double x) {
        double r3775797 = 1.0;
        double r3775798 = x;
        double r3775799 = r3775798 + r3775797;
        double r3775800 = r3775797 / r3775799;
        double r3775801 = 2.0;
        double r3775802 = r3775801 / r3775798;
        double r3775803 = r3775800 - r3775802;
        double r3775804 = r3775798 - r3775797;
        double r3775805 = r3775797 / r3775804;
        double r3775806 = r3775803 + r3775805;
        return r3775806;
}

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 2019128 +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)))))