Average Error: 0.6 → 0.6
Time: 11.4s
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 r3362898 = 1.0;
        double r3362899 = /* ERROR: no posit support in C */;
        double r3362900 = x;
        double r3362901 = r3362900 + r3362899;
        double r3362902 = r3362899 / r3362901;
        double r3362903 = r3362899 / r3362900;
        double r3362904 = r3362902 - r3362903;
        return r3362904;
}
↓
double f(double x) {
        double r3362905 = 1.0;
        double r3362906 = x;
        double r3362907 = r3362906 + r3362905;
        double r3362908 = r3362905 / r3362907;
        double r3362909 = r3362905 / r3362906;
        double r3362910 = r3362908 - r3362909;
        return r3362910;
}

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 2019112 +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)))