Average Error: 15.0 → 0.1
Time: 2.7s
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 r33612 = 1.0;
        double r33613 = x;
        double r33614 = r33613 + r33612;
        double r33615 = r33612 / r33614;
        double r33616 = r33612 / r33613;
        double r33617 = r33615 - r33616;
        return r33617;
}
↓
double f(double x) {
        double r33618 = 1.0;
        double r33619 = x;
        double r33620 = r33619 + r33618;
        double r33621 = 0.0;
        double r33622 = r33621 - r33618;
        double r33623 = r33620 / r33622;
        double r33624 = r33618 / r33623;
        double r33625 = r33624 / r33619;
        return r33625;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

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

  3. Applied frac-sub14.3

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

  4. Simplified14.3

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

  6. Applied associate-/r*14.3

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

  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 2020060 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))