Average Error: 1.0 → 1.0
Time: 18.6s
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 r1557213 = 1.0;
        double r1557214 = /* ERROR: no posit support in C */;
        double r1557215 = x;
        double r1557216 = r1557215 + r1557214;
        double r1557217 = r1557214 / r1557216;
        double r1557218 = 2.0;
        double r1557219 = /* ERROR: no posit support in C */;
        double r1557220 = r1557219 / r1557215;
        double r1557221 = r1557217 - r1557220;
        double r1557222 = r1557215 - r1557214;
        double r1557223 = r1557214 / r1557222;
        double r1557224 = r1557221 + r1557223;
        return r1557224;
}
↓
double f(double x) {
        double r1557225 = 1.0;
        double r1557226 = x;
        double r1557227 = r1557226 + r1557225;
        double r1557228 = r1557225 / r1557227;
        double r1557229 = 2.0;
        double r1557230 = r1557229 / r1557226;
        double r1557231 = r1557228 - r1557230;
        double r1557232 = r1557226 - r1557225;
        double r1557233 = r1557225 / r1557232;
        double r1557234 = r1557231 + r1557233;
        return r1557234;
}

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 2019119 
(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)))))