Average Error: 1.0 → 1.0
Time: 19.0s
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 r4965877 = 1.0;
        double r4965878 = /* ERROR: no posit support in C */;
        double r4965879 = x;
        double r4965880 = r4965879 + r4965878;
        double r4965881 = r4965878 / r4965880;
        double r4965882 = 2.0;
        double r4965883 = /* ERROR: no posit support in C */;
        double r4965884 = r4965883 / r4965879;
        double r4965885 = r4965881 - r4965884;
        double r4965886 = r4965879 - r4965878;
        double r4965887 = r4965878 / r4965886;
        double r4965888 = r4965885 + r4965887;
        return r4965888;
}
↓
double f(double x) {
        double r4965889 = 1.0;
        double r4965890 = x;
        double r4965891 = r4965890 + r4965889;
        double r4965892 = r4965889 / r4965891;
        double r4965893 = 2.0;
        double r4965894 = r4965893 / r4965890;
        double r4965895 = r4965892 - r4965894;
        double r4965896 = r4965890 - r4965889;
        double r4965897 = r4965889 / r4965896;
        double r4965898 = r4965895 + r4965897;
        return r4965898;
}

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 2019125 +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)))))