Average Error: 0.6 → 0.6
Time: 24.4s
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 r4753433 = 1.0;
        double r4753434 = /* ERROR: no posit support in C */;
        double r4753435 = x;
        double r4753436 = r4753435 + r4753434;
        double r4753437 = r4753434 / r4753436;
        double r4753438 = r4753434 / r4753435;
        double r4753439 = r4753437 - r4753438;
        return r4753439;
}
↓
double f(double x) {
        double r4753440 = 1.0;
        double r4753441 = x;
        double r4753442 = r4753441 + r4753440;
        double r4753443 = r4753440 / r4753442;
        double r4753444 = r4753440 / r4753441;
        double r4753445 = r4753443 - r4753444;
        return r4753445;
}

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 2019162 +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)))