Average Error: 0.6 → 0.6
Time: 27.5s
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 r5850406 = 1.0;
        double r5850407 = /* ERROR: no posit support in C */;
        double r5850408 = x;
        double r5850409 = r5850408 + r5850407;
        double r5850410 = r5850407 / r5850409;
        double r5850411 = r5850407 / r5850408;
        double r5850412 = r5850410 - r5850411;
        return r5850412;
}
↓
double f(double x) {
        double r5850413 = 1.0;
        double r5850414 = /* ERROR: no posit support in C */;
        double r5850415 = x;
        double r5850416 = r5850415 + r5850414;
        double r5850417 = r5850414 / r5850416;
        double r5850418 = r5850414 / r5850415;
        double r5850419 = r5850417 - r5850418;
        return r5850419;
}

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 2019163 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))