Average Error: 0.6 → 0.6
Time: 16.1s
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 r2458562 = 1.0;
        double r2458563 = /* ERROR: no posit support in C */;
        double r2458564 = x;
        double r2458565 = r2458564 + r2458563;
        double r2458566 = r2458563 / r2458565;
        double r2458567 = r2458563 / r2458564;
        double r2458568 = r2458566 - r2458567;
        return r2458568;
}
↓
double f(double x) {
        double r2458569 = 1.0;
        double r2458570 = x;
        double r2458571 = r2458570 + r2458569;
        double r2458572 = r2458569 / r2458571;
        double r2458573 = r2458569 / r2458570;
        double r2458574 = r2458572 - r2458573;
        return r2458574;
}

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 2019154 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))