Average Error: 0.6 → 0.6
Time: 9.4s
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 r2918692 = 1.0;
        double r2918693 = /* ERROR: no posit support in C */;
        double r2918694 = x;
        double r2918695 = r2918694 + r2918693;
        double r2918696 = r2918693 / r2918695;
        double r2918697 = r2918693 / r2918694;
        double r2918698 = r2918696 - r2918697;
        return r2918698;
}
↓
double f(double x) {
        double r2918699 = 1.0;
        double r2918700 = x;
        double r2918701 = r2918700 + r2918699;
        double r2918702 = r2918699 / r2918701;
        double r2918703 = r2918699 / r2918700;
        double r2918704 = r2918702 - r2918703;
        return r2918704;
}

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 2019104 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))