Average Error: 14.7 → 0.1
Time: 10.4s
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 r42356 = 1.0;
        double r42357 = x;
        double r42358 = r42357 + r42356;
        double r42359 = r42356 / r42358;
        double r42360 = r42356 / r42357;
        double r42361 = r42359 - r42360;
        return r42361;
}
↓
double f(double x) {
        double r42362 = 1.0;
        double r42363 = -r42362;
        double r42364 = x;
        double r42365 = r42364 / r42362;
        double r42366 = r42363 / r42365;
        double r42367 = r42362 + r42364;
        double r42368 = r42366 / r42367;
        return r42368;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  5. Simplified14.1

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

  7. Applied associate-/r*14.1

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

  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 2019179 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 x)))