Average Error: 14.1 → 0.1
Time: 11.3s
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 r41448 = 1.0;
        double r41449 = x;
        double r41450 = r41449 + r41448;
        double r41451 = r41448 / r41450;
        double r41452 = r41448 / r41449;
        double r41453 = r41451 - r41452;
        return r41453;
}
↓
double f(double x) {
        double r41454 = 1.0;
        double r41455 = x;
        double r41456 = r41455 + r41454;
        double r41457 = -r41454;
        double r41458 = r41456 / r41457;
        double r41459 = r41454 / r41458;
        double r41460 = r41459 / r41455;
        return r41460;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

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

  3. Applied frac-sub13.5

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

  4. Simplified13.5

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

  6. Applied associate-/r*13.5

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))