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 r1940072 = 1.0;
        double r1940073 = /* ERROR: no posit support in C */;
        double r1940074 = x;
        double r1940075 = r1940074 + r1940073;
        double r1940076 = r1940073 / r1940075;
        double r1940077 = r1940073 / r1940074;
        double r1940078 = r1940076 - r1940077;
        return r1940078;
}
↓
double f(double x) {
        double r1940079 = 1.0;
        double r1940080 = x;
        double r1940081 = r1940080 + r1940079;
        double r1940082 = r1940079 / r1940081;
        double r1940083 = r1940079 / r1940080;
        double r1940084 = r1940082 - r1940083;
        return r1940084;
}

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 2019104 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))