Average Error: 0.6 → 0.6
Time: 8.2s
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 r2921064 = 1.0;
        double r2921065 = /* ERROR: no posit support in C */;
        double r2921066 = x;
        double r2921067 = r2921066 + r2921065;
        double r2921068 = r2921065 / r2921067;
        double r2921069 = r2921065 / r2921066;
        double r2921070 = r2921068 - r2921069;
        return r2921070;
}
↓
double f(double x) {
        double r2921071 = 1.0;
        double r2921072 = x;
        double r2921073 = r2921072 + r2921071;
        double r2921074 = r2921071 / r2921073;
        double r2921075 = r2921071 / r2921072;
        double r2921076 = r2921074 - r2921075;
        return r2921076;
}

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 2019119 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))