Average Error: 0.6 → 0.6
Time: 25.6s
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 r6640261 = 1.0;
        double r6640262 = /* ERROR: no posit support in C */;
        double r6640263 = x;
        double r6640264 = r6640263 + r6640262;
        double r6640265 = r6640262 / r6640264;
        double r6640266 = r6640262 / r6640263;
        double r6640267 = r6640265 - r6640266;
        return r6640267;
}
↓
double f(double x) {
        double r6640268 = 1.0;
        double r6640269 = x;
        double r6640270 = r6640269 + r6640268;
        double r6640271 = r6640268 / r6640270;
        double r6640272 = r6640268 / r6640269;
        double r6640273 = r6640271 - r6640272;
        return r6640273;
}

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 2019163 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))