Average Error: 0.6 → 0.6
Time: 12.9s
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 r4726798 = 1.0;
        double r4726799 = /* ERROR: no posit support in C */;
        double r4726800 = x;
        double r4726801 = r4726800 + r4726799;
        double r4726802 = r4726799 / r4726801;
        double r4726803 = r4726799 / r4726800;
        double r4726804 = r4726802 - r4726803;
        return r4726804;
}
↓
double f(double x) {
        double r4726805 = 1.0;
        double r4726806 = x;
        double r4726807 = r4726806 + r4726805;
        double r4726808 = r4726805 / r4726807;
        double r4726809 = r4726805 / r4726806;
        double r4726810 = r4726808 - r4726809;
        return r4726810;
}

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 2019125 +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)))