Average Error: 0.6 → 0.6
Time: 36.4s
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 r1923414 = 1.0;
        double r1923415 = /* ERROR: no posit support in C */;
        double r1923416 = x;
        double r1923417 = r1923416 + r1923415;
        double r1923418 = r1923415 / r1923417;
        double r1923419 = r1923415 / r1923416;
        double r1923420 = r1923418 - r1923419;
        return r1923420;
}
↓
double f(double x) {
        double r1923421 = 1.0;
        double r1923422 = x;
        double r1923423 = r1923422 + r1923421;
        double r1923424 = r1923421 / r1923423;
        double r1923425 = r1923421 / r1923422;
        double r1923426 = r1923424 - r1923425;
        return r1923426;
}

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