Average Error: 0.6 → 0.6
Time: 23.9s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\frac{1}{x + 1} - \frac{1}{x}\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\frac{1}{x + 1} - \frac{1}{x}
double f(double x) {
        double r4697304 = 1.0;
        double r4697305 = /* ERROR: no posit support in C */;
        double r4697306 = x;
        double r4697307 = r4697306 + r4697305;
        double r4697308 = r4697305 / r4697307;
        double r4697309 = r4697305 / r4697306;
        double r4697310 = r4697308 - r4697309;
        return r4697310;
}
↓
double f(double x) {
        double r4697311 = 1.0;
        double r4697312 = x;
        double r4697313 = r4697312 + r4697311;
        double r4697314 = r4697311 / r4697313;
        double r4697315 = r4697311 / r4697312;
        double r4697316 = r4697314 - r4697315;
        return r4697316;
}

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

    \[\leadsto \frac{1}{x + 1} - \frac{1}{x}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))