Average Error: 0.6 → 0.6
Time: 25.2s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
double f(double x) {
        double r4646689 = 1.0;
        double r4646690 = /* ERROR: no posit support in C */;
        double r4646691 = x;
        double r4646692 = r4646691 + r4646690;
        double r4646693 = r4646690 / r4646692;
        double r4646694 = r4646690 / r4646691;
        double r4646695 = r4646693 - r4646694;
        return r4646695;
}
↓
double f(double x) {
        double r4646696 = 1.0;
        double r4646697 = /* ERROR: no posit support in C */;
        double r4646698 = x;
        double r4646699 = r4646698 + r4646697;
        double r4646700 = r4646697 / r4646699;
        double r4646701 = r4646697 / r4646698;
        double r4646702 = r4646700 - r4646701;
        return r4646702;
}

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

    \[\leadsto \left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]

Reproduce

herbie shell --seed 2019164 +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)))