Average Error: 0.6 → 0.6
Time: 25.1s
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 r8876519 = 1.0;
        double r8876520 = /* ERROR: no posit support in C */;
        double r8876521 = x;
        double r8876522 = r8876521 + r8876520;
        double r8876523 = r8876520 / r8876522;
        double r8876524 = r8876520 / r8876521;
        double r8876525 = r8876523 - r8876524;
        return r8876525;
}
↓
double f(double x) {
        double r8876526 = 1.0;
        double r8876527 = x;
        double r8876528 = r8876527 + r8876526;
        double r8876529 = r8876526 / r8876528;
        double r8876530 = r8876526 / r8876527;
        double r8876531 = r8876529 - r8876530;
        return r8876531;
}

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