Average Error: 14.3 → 0.1
Time: 3.3s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{1}{\frac{x + 1}{0 - 1}}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{1}{\frac{x + 1}{0 - 1}}}{x}
double f(double x) {
        double r41901 = 1.0;
        double r41902 = x;
        double r41903 = r41902 + r41901;
        double r41904 = r41901 / r41903;
        double r41905 = r41901 / r41902;
        double r41906 = r41904 - r41905;
        return r41906;
}
↓
double f(double x) {
        double r41907 = 1.0;
        double r41908 = x;
        double r41909 = r41908 + r41907;
        double r41910 = 0.0;
        double r41911 = r41910 - r41907;
        double r41912 = r41909 / r41911;
        double r41913 = r41907 / r41912;
        double r41914 = r41913 / r41908;
        return r41914;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x + 1}{0 - 1}}}}{x}\]

  8. Final simplification0.1

    \[\leadsto \frac{\frac{1}{\frac{x + 1}{0 - 1}}}{x}\]

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))