Average Error: 0.6 → 0.6
Time: 15.7s
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 r1705032 = 1.0;
        double r1705033 = /* ERROR: no posit support in C */;
        double r1705034 = x;
        double r1705035 = r1705034 + r1705033;
        double r1705036 = r1705033 / r1705035;
        double r1705037 = r1705033 / r1705034;
        double r1705038 = r1705036 - r1705037;
        return r1705038;
}
↓
double f(double x) {
        double r1705039 = 1.0;
        double r1705040 = x;
        double r1705041 = r1705040 + r1705039;
        double r1705042 = r1705039 / r1705041;
        double r1705043 = r1705039 / r1705040;
        double r1705044 = r1705042 - r1705043;
        return r1705044;
}

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 2019156 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))