Average Error: 14.8 → 0.1
Time: 10.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{\frac{x}{1}}}{1 + x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{\frac{x}{1}}}{1 + x}
double f(double x) {
        double r37966 = 1.0;
        double r37967 = x;
        double r37968 = r37967 + r37966;
        double r37969 = r37966 / r37968;
        double r37970 = r37966 / r37967;
        double r37971 = r37969 - r37970;
        return r37971;
}
↓
double f(double x) {
        double r37972 = 1.0;
        double r37973 = -r37972;
        double r37974 = x;
        double r37975 = r37974 / r37972;
        double r37976 = r37973 / r37975;
        double r37977 = r37972 + r37974;
        double r37978 = r37976 / r37977;
        return r37978;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied frac-sub14.2

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

  4. Simplified14.2

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

  5. Simplified14.2

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

  7. Applied associate-/r*14.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))