Average Error: 0.6 → 0.6
Time: 24.4s
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 r6508909 = 1.0;
        double r6508910 = /* ERROR: no posit support in C */;
        double r6508911 = x;
        double r6508912 = r6508911 + r6508910;
        double r6508913 = r6508910 / r6508912;
        double r6508914 = r6508910 / r6508911;
        double r6508915 = r6508913 - r6508914;
        return r6508915;
}
↓
double f(double x) {
        double r6508916 = 1.0;
        double r6508917 = x;
        double r6508918 = r6508917 + r6508916;
        double r6508919 = r6508916 / r6508918;
        double r6508920 = r6508916 / r6508917;
        double r6508921 = r6508919 - r6508920;
        return r6508921;
}

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 2019163 +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)))