Average Error: 1.0 → 1.0
Time: 17.7s
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 r1594450 = 1.0;
        double r1594451 = /* ERROR: no posit support in C */;
        double r1594452 = x;
        double r1594453 = r1594452 + r1594451;
        double r1594454 = r1594451 / r1594453;
        double r1594455 = 2.0;
        double r1594456 = /* ERROR: no posit support in C */;
        double r1594457 = r1594456 / r1594452;
        double r1594458 = r1594454 - r1594457;
        double r1594459 = r1594452 - r1594451;
        double r1594460 = r1594451 / r1594459;
        double r1594461 = r1594458 + r1594460;
        return r1594461;
}
↓
double f(double x) {
        double r1594462 = 1.0;
        double r1594463 = x;
        double r1594464 = r1594463 + r1594462;
        double r1594465 = r1594462 / r1594464;
        double r1594466 = 2.0;
        double r1594467 = r1594466 / r1594463;
        double r1594468 = r1594465 - r1594467;
        double r1594469 = r1594463 - r1594462;
        double r1594470 = r1594462 / r1594469;
        double r1594471 = r1594468 + r1594470;
        return r1594471;
}

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 2019104 
(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)))))