Average Error: 0.6 → 0.6
Time: 23.7s
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 r4592422 = 1.0;
        double r4592423 = /* ERROR: no posit support in C */;
        double r4592424 = x;
        double r4592425 = r4592424 + r4592423;
        double r4592426 = r4592423 / r4592425;
        double r4592427 = r4592423 / r4592424;
        double r4592428 = r4592426 - r4592427;
        return r4592428;
}
↓
double f(double x) {
        double r4592429 = 1.0;
        double r4592430 = x;
        double r4592431 = r4592430 + r4592429;
        double r4592432 = r4592429 / r4592431;
        double r4592433 = r4592429 / r4592430;
        double r4592434 = r4592432 - r4592433;
        return r4592434;
}

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 2019158 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))