Average Error: 1.0 → 1.0
Time: 17.5s
Precision: 64
\[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]
↓
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}
↓
\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}
double f(double x) {
        double r2964157 = 1.0;
        double r2964158 = /* ERROR: no posit support in C */;
        double r2964159 = x;
        double r2964160 = r2964159 + r2964158;
        double r2964161 = r2964158 / r2964160;
        double r2964162 = 2.0;
        double r2964163 = /* ERROR: no posit support in C */;
        double r2964164 = r2964163 / r2964159;
        double r2964165 = r2964161 - r2964164;
        double r2964166 = r2964159 - r2964158;
        double r2964167 = r2964158 / r2964166;
        double r2964168 = r2964165 + r2964167;
        return r2964168;
}
↓
double f(double x) {
        double r2964169 = 1.0;
        double r2964170 = x;
        double r2964171 = r2964170 + r2964169;
        double r2964172 = r2964169 / r2964171;
        double r2964173 = 2.0;
        double r2964174 = r2964173 / r2964170;
        double r2964175 = r2964172 - r2964174;
        double r2964176 = r2964170 - r2964169;
        double r2964177 = r2964169 / r2964176;
        double r2964178 = r2964175 + r2964177;
        return r2964178;
}

Error

Bits error versus x

Derivation

  1. Initial program 1.0

    \[\frac{\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(2\right)}{x}\right)\right)}{\left(\frac{\left(1\right)}{\left(x - \left(1\right)\right)}\right)}\]

  2. Final simplification1.0

    \[\leadsto \left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  (+.p16 (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 2) x)) (/.p16 (real->posit16 1) (-.p16 x (real->posit16 1)))))