Average Error: 0.6 → 0.6
Time: 25.7s
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 r9392611 = 1.0;
        double r9392612 = /* ERROR: no posit support in C */;
        double r9392613 = x;
        double r9392614 = r9392613 + r9392612;
        double r9392615 = r9392612 / r9392614;
        double r9392616 = r9392612 / r9392613;
        double r9392617 = r9392615 - r9392616;
        return r9392617;
}
↓
double f(double x) {
        double r9392618 = 1.0;
        double r9392619 = x;
        double r9392620 = r9392619 + r9392618;
        double r9392621 = r9392618 / r9392620;
        double r9392622 = r9392618 / r9392619;
        double r9392623 = r9392621 - r9392622;
        return r9392623;
}

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 2019162 +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)))