Average Error: 0.6 → 0.6
Time: 24.0s
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 r4463738 = 1.0;
        double r4463739 = /* ERROR: no posit support in C */;
        double r4463740 = x;
        double r4463741 = r4463740 + r4463739;
        double r4463742 = r4463739 / r4463741;
        double r4463743 = r4463739 / r4463740;
        double r4463744 = r4463742 - r4463743;
        return r4463744;
}
↓
double f(double x) {
        double r4463745 = 1.0;
        double r4463746 = x;
        double r4463747 = r4463746 + r4463745;
        double r4463748 = r4463745 / r4463747;
        double r4463749 = r4463745 / r4463746;
        double r4463750 = r4463748 - r4463749;
        return r4463750;
}

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 2019162 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))