Average Error: 0.6 → 0.6
Time: 10.6s
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 r4171230 = 1.0;
        double r4171231 = /* ERROR: no posit support in C */;
        double r4171232 = x;
        double r4171233 = r4171232 + r4171231;
        double r4171234 = r4171231 / r4171233;
        double r4171235 = r4171231 / r4171232;
        double r4171236 = r4171234 - r4171235;
        return r4171236;
}
↓
double f(double x) {
        double r4171237 = 1.0;
        double r4171238 = x;
        double r4171239 = r4171238 + r4171237;
        double r4171240 = r4171237 / r4171239;
        double r4171241 = r4171237 / r4171238;
        double r4171242 = r4171240 - r4171241;
        return r4171242;
}

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 2019120 +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)))