Average Error: 0.6 → 0.6
Time: 26.4s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
double f(double x) {
        double r6926519 = 1.0;
        double r6926520 = /* ERROR: no posit support in C */;
        double r6926521 = x;
        double r6926522 = r6926521 + r6926520;
        double r6926523 = r6926520 / r6926522;
        double r6926524 = r6926520 / r6926521;
        double r6926525 = r6926523 - r6926524;
        return r6926525;
}
↓
double f(double x) {
        double r6926526 = 1.0;
        double r6926527 = /* ERROR: no posit support in C */;
        double r6926528 = x;
        double r6926529 = r6926528 + r6926527;
        double r6926530 = r6926527 / r6926529;
        double r6926531 = r6926527 / r6926528;
        double r6926532 = r6926530 - r6926531;
        return r6926532;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))