Average Error: 0.6 → 0.6
Time: 8.7s
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 r3171666 = 1.0;
        double r3171667 = /* ERROR: no posit support in C */;
        double r3171668 = x;
        double r3171669 = r3171668 + r3171667;
        double r3171670 = r3171667 / r3171669;
        double r3171671 = r3171667 / r3171668;
        double r3171672 = r3171670 - r3171671;
        return r3171672;
}
↓
double f(double x) {
        double r3171673 = 1.0;
        double r3171674 = x;
        double r3171675 = r3171674 + r3171673;
        double r3171676 = r3171673 / r3171675;
        double r3171677 = r3171673 / r3171674;
        double r3171678 = r3171676 - r3171677;
        return r3171678;
}

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 2019121 +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)))