Average Error: 0.6 → 0.6
Time: 16.4s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\frac{1}{x + 1} - \frac{1}{x}\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\frac{1}{x + 1} - \frac{1}{x}
double f(double x) {
        double r4420979 = 1.0;
        double r4420980 = /* ERROR: no posit support in C */;
        double r4420981 = x;
        double r4420982 = r4420981 + r4420980;
        double r4420983 = r4420980 / r4420982;
        double r4420984 = r4420980 / r4420981;
        double r4420985 = r4420983 - r4420984;
        return r4420985;
}
↓
double f(double x) {
        double r4420986 = 1.0;
        double r4420987 = x;
        double r4420988 = r4420987 + r4420986;
        double r4420989 = r4420986 / r4420988;
        double r4420990 = r4420986 / r4420987;
        double r4420991 = r4420989 - r4420990;
        return r4420991;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

    \[\leadsto \frac{1}{x + 1} - \frac{1}{x}\]

Reproduce

herbie shell --seed 2019125 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))