Average Error: 0.6 → 0.6
Time: 9.7s
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 r3181514 = 1.0;
        double r3181515 = /* ERROR: no posit support in C */;
        double r3181516 = x;
        double r3181517 = r3181516 + r3181515;
        double r3181518 = r3181515 / r3181517;
        double r3181519 = r3181515 / r3181516;
        double r3181520 = r3181518 - r3181519;
        return r3181520;
}
↓
double f(double x) {
        double r3181521 = 1.0;
        double r3181522 = x;
        double r3181523 = r3181522 + r3181521;
        double r3181524 = r3181521 / r3181523;
        double r3181525 = r3181521 / r3181522;
        double r3181526 = r3181524 - r3181525;
        return r3181526;
}

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 2019120 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))