Average Error: 1.0 → 1.0
Time: 5.8m
Precision: 64
\[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
↓
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}
↓
\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}
double f(double x) {
        double r6810346 = 1.0;
        double r6810347 = /* ERROR: no posit support in C */;
        double r6810348 = x;
        double r6810349 = r6810348 + r6810347;
        double r6810350 = r6810347 / r6810349;
        double r6810351 = 2.0;
        double r6810352 = /* ERROR: no posit support in C */;
        double r6810353 = r6810352 / r6810348;
        double r6810354 = r6810350 - r6810353;
        double r6810355 = r6810348 - r6810347;
        double r6810356 = r6810347 / r6810355;
        double r6810357 = r6810354 + r6810356;
        return r6810357;
}
↓
double f(double x) {
        double r6810358 = 1.0;
        double r6810359 = x;
        double r6810360 = r6810359 + r6810358;
        double r6810361 = r6810358 / r6810360;
        double r6810362 = 2.0;
        double r6810363 = r6810362 / r6810359;
        double r6810364 = r6810361 - r6810363;
        double r6810365 = r6810359 - r6810358;
        double r6810366 = r6810358 / r6810365;
        double r6810367 = r6810364 + r6810366;
        return r6810367;
}

Error

Bits error versus x

Derivation

  1. Initial program 1.0

    \[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  2. Final simplification1.0

    \[\leadsto \left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  (+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))