Average Error: 0.6 → 1.0
Time: 54.8s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\frac{\left(\frac{1}{x + 1} + \frac{1}{x}\right) \cdot \left(\frac{1}{x + 1} - \frac{1}{x}\right)}{\frac{1}{x + 1} + \frac{1}{x}}\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\frac{\left(\frac{1}{x + 1} + \frac{1}{x}\right) \cdot \left(\frac{1}{x + 1} - \frac{1}{x}\right)}{\frac{1}{x + 1} + \frac{1}{x}}
double f(double x) {
        double r11142154 = 1.0;
        double r11142155 = /* ERROR: no posit support in C */;
        double r11142156 = x;
        double r11142157 = r11142156 + r11142155;
        double r11142158 = r11142155 / r11142157;
        double r11142159 = r11142155 / r11142156;
        double r11142160 = r11142158 - r11142159;
        return r11142160;
}
↓
double f(double x) {
        double r11142161 = 1.0;
        double r11142162 = x;
        double r11142163 = r11142162 + r11142161;
        double r11142164 = r11142161 / r11142163;
        double r11142165 = r11142161 / r11142162;
        double r11142166 = r11142164 + r11142165;
        double r11142167 = r11142164 - r11142165;
        double r11142168 = r11142166 * r11142167;
        double r11142169 = r11142168 / r11142166;
        return r11142169;
}

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. Using strategy rm

  3. Applied p16-flip--1.3

    \[\leadsto \color{blue}{\frac{\left(\left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) \cdot \left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)\right) - \left(\left(\frac{\left(1\right)}{x}\right) \cdot \left(\frac{\left(1\right)}{x}\right)\right)\right)}{\left(\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(\frac{\left(1\right)}{x}\right)}\right)}}\]
  4. Using strategy rm

  5. Applied difference-of-squares1.0

    \[\leadsto \frac{\color{blue}{\left(\left(\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(\frac{\left(1\right)}{x}\right)}\right) \cdot \left(\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\right)\right)}}{\left(\frac{\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right)}{\left(\frac{\left(1\right)}{x}\right)}\right)}\]

  6. Final simplification1.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))