Average Error: 0.6 → 0.6
Time: 31.7s
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 r1699957 = 1.0;
        double r1699958 = /* ERROR: no posit support in C */;
        double r1699959 = x;
        double r1699960 = r1699959 + r1699958;
        double r1699961 = r1699958 / r1699960;
        double r1699962 = r1699958 / r1699959;
        double r1699963 = r1699961 - r1699962;
        return r1699963;
}
↓
double f(double x) {
        double r1699964 = 1.0;
        double r1699965 = x;
        double r1699966 = r1699965 + r1699964;
        double r1699967 = r1699964 / r1699966;
        double r1699968 = r1699964 / r1699965;
        double r1699969 = r1699967 - r1699968;
        return r1699969;
}

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 2019152 +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)))