Average Error: 1.0 → 1.0
Time: 4.6m
Precision: 64
\[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
↓
\[\left(\frac{1}{x + 1} + \frac{1}{x - 1}\right) - \frac{2}{x}\]
\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{1}{x - 1}\right) - \frac{2}{x}
double f(double x) {
        double r4529985 = 1.0;
        double r4529986 = /* ERROR: no posit support in C */;
        double r4529987 = x;
        double r4529988 = r4529987 + r4529986;
        double r4529989 = r4529986 / r4529988;
        double r4529990 = 2.0;
        double r4529991 = /* ERROR: no posit support in C */;
        double r4529992 = r4529991 / r4529987;
        double r4529993 = r4529989 - r4529992;
        double r4529994 = r4529987 - r4529986;
        double r4529995 = r4529986 / r4529994;
        double r4529996 = r4529993 + r4529995;
        return r4529996;
}
↓
double f(double x) {
        double r4529997 = 1.0;
        double r4529998 = x;
        double r4529999 = r4529998 + r4529997;
        double r4530000 = r4529997 / r4529999;
        double r4530001 = r4529998 - r4529997;
        double r4530002 = r4529997 / r4530001;
        double r4530003 = r4530000 + r4530002;
        double r4530004 = 2.0;
        double r4530005 = r4530004 / r4529998;
        double r4530006 = r4530003 - r4530005;
        return r4530006;
}

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. Using strategy rm

  3. Applied +p16-rgt-identity-expand1.0

    \[\leadsto \frac{\left(\color{blue}{\left(\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(0.0\right)}\right)} - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  4. Applied associate--l+1.0

    \[\leadsto \frac{\color{blue}{\left(\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(\left(0.0\right) - \left(\frac{\left(2\right)}{x}\right)\right)}\right)}}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  5. Applied associate-+l+1.0

    \[\leadsto \color{blue}{\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(\frac{\left(\left(0.0\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\right)}}\]

  6. Simplified1.0

    \[\leadsto \frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\color{blue}{\left(\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}}\]
  7. Using strategy rm

  8. Applied associate-+r-1.0

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

  9. Final simplification1.0

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

Reproduce

herbie shell --seed 2019165 
(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)))))