Average Error: 1.0 → 1.0
Time: 17.5s
Precision: 64
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
↓
\[\frac{1}{x + 1} - \left(\frac{2}{x} - \frac{1}{x - 1}\right)\]
double f(double x) {
        double r2760822 = 1.0;
        double r2760823 = x;
        double r2760824 = r2760823 + r2760822;
        double r2760825 = r2760822 / r2760824;
        double r2760826 = 2.0;
        double r2760827 = r2760826 / r2760823;
        double r2760828 = r2760825 - r2760827;
        double r2760829 = r2760823 - r2760822;
        double r2760830 = r2760822 / r2760829;
        double r2760831 = r2760828 + r2760830;
        return r2760831;
}
↓
double f(double x) {
        double r2760832 = 1.0;
        double r2760833 = x;
        double r2760834 = r2760833 + r2760832;
        double r2760835 = r2760832 / r2760834;
        double r2760836 = 2.0;
        double r2760837 = r2760836 / r2760833;
        double r2760838 = r2760833 - r2760832;
        double r2760839 = r2760832 / r2760838;
        double r2760840 = r2760837 - r2760839;
        double r2760841 = r2760835 - r2760840;
        return r2760841;
}


\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}
↓
\frac{1}{x + 1} - \left(\frac{2}{x} - \frac{1}{x - 1}\right)

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. Using strategy rm

  3. Applied associate-+l-1.0

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

  4. Final simplification1.0

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

Reproduce

herbie shell --seed 2019101 
(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)))))