Average Error: 1.0 → 1.0
Time: 20.1s
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 r5631570 = 1.0;
        double r5631571 = /* ERROR: no posit support in C */;
        double r5631572 = x;
        double r5631573 = r5631572 + r5631571;
        double r5631574 = r5631571 / r5631573;
        double r5631575 = 2.0;
        double r5631576 = /* ERROR: no posit support in C */;
        double r5631577 = r5631576 / r5631572;
        double r5631578 = r5631574 - r5631577;
        double r5631579 = r5631572 - r5631571;
        double r5631580 = r5631571 / r5631579;
        double r5631581 = r5631578 + r5631580;
        return r5631581;
}
↓
double f(double x) {
        double r5631582 = 1.0;
        double r5631583 = x;
        double r5631584 = r5631583 + r5631582;
        double r5631585 = r5631582 / r5631584;
        double r5631586 = 2.0;
        double r5631587 = r5631586 / r5631583;
        double r5631588 = r5631585 - r5631587;
        double r5631589 = r5631583 - r5631582;
        double r5631590 = r5631582 / r5631589;
        double r5631591 = r5631588 + r5631590;
        return r5631591;
}

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 2019125 
(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)))))