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 r7667291 = 1.0;
        double r7667292 = /* ERROR: no posit support in C */;
        double r7667293 = x;
        double r7667294 = r7667293 + r7667292;
        double r7667295 = r7667292 / r7667294;
        double r7667296 = 2.0;
        double r7667297 = /* ERROR: no posit support in C */;
        double r7667298 = r7667297 / r7667293;
        double r7667299 = r7667295 - r7667298;
        double r7667300 = r7667293 - r7667292;
        double r7667301 = r7667292 / r7667300;
        double r7667302 = r7667299 + r7667301;
        return r7667302;
}
↓
double f(double x) {
        double r7667303 = 1.0;
        double r7667304 = x;
        double r7667305 = r7667304 + r7667303;
        double r7667306 = r7667303 / r7667305;
        double r7667307 = 2.0;
        double r7667308 = r7667307 / r7667304;
        double r7667309 = r7667306 - r7667308;
        double r7667310 = r7667304 - r7667303;
        double r7667311 = r7667303 / r7667310;
        double r7667312 = r7667309 + r7667311;
        return r7667312;
}

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 
(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)))))