Average Error: 0.6 → 0.6
Time: 41.3s
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 r8081867 = 1.0;
        double r8081868 = /* ERROR: no posit support in C */;
        double r8081869 = x;
        double r8081870 = r8081869 + r8081868;
        double r8081871 = r8081868 / r8081870;
        double r8081872 = r8081868 / r8081869;
        double r8081873 = r8081871 - r8081872;
        return r8081873;
}
↓
double f(double x) {
        double r8081874 = 1.0;
        double r8081875 = x;
        double r8081876 = r8081875 + r8081874;
        double r8081877 = r8081874 / r8081876;
        double r8081878 = r8081874 / r8081875;
        double r8081879 = r8081877 - r8081878;
        return r8081879;
}

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 2019133 +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)))