Average Error: 0.6 → 0.6
Time: 16.7s
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 r2564423 = 1.0;
        double r2564424 = /* ERROR: no posit support in C */;
        double r2564425 = x;
        double r2564426 = r2564425 + r2564424;
        double r2564427 = r2564424 / r2564426;
        double r2564428 = r2564424 / r2564425;
        double r2564429 = r2564427 - r2564428;
        return r2564429;
}
↓
double f(double x) {
        double r2564430 = 1.0;
        double r2564431 = x;
        double r2564432 = r2564431 + r2564430;
        double r2564433 = r2564430 / r2564432;
        double r2564434 = r2564430 / r2564431;
        double r2564435 = r2564433 - r2564434;
        return r2564435;
}

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 2019154 +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)))