Average Error: 0.6 → 0.6
Time: 23.2s
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 r4117410 = 1.0;
        double r4117411 = /* ERROR: no posit support in C */;
        double r4117412 = x;
        double r4117413 = r4117412 + r4117411;
        double r4117414 = r4117411 / r4117413;
        double r4117415 = r4117411 / r4117412;
        double r4117416 = r4117414 - r4117415;
        return r4117416;
}
↓
double f(double x) {
        double r4117417 = 1.0;
        double r4117418 = x;
        double r4117419 = r4117418 + r4117417;
        double r4117420 = r4117417 / r4117419;
        double r4117421 = r4117417 / r4117418;
        double r4117422 = r4117420 - r4117421;
        return r4117422;
}

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 2019165 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))