Average Error: 0.6 → 0.6
Time: 9.9s
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 r3328049 = 1.0;
        double r3328050 = /* ERROR: no posit support in C */;
        double r3328051 = x;
        double r3328052 = r3328051 + r3328050;
        double r3328053 = r3328050 / r3328052;
        double r3328054 = r3328050 / r3328051;
        double r3328055 = r3328053 - r3328054;
        return r3328055;
}
↓
double f(double x) {
        double r3328056 = 1.0;
        double r3328057 = x;
        double r3328058 = r3328057 + r3328056;
        double r3328059 = r3328056 / r3328058;
        double r3328060 = r3328056 / r3328057;
        double r3328061 = r3328059 - r3328060;
        return r3328061;
}

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 +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)))