Average Error: 14.7 → 0.1
Time: 25.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{-1}{x + 1}}{x}
double f(double x) {
        double r2029732 = 1.0;
        double r2029733 = x;
        double r2029734 = r2029733 + r2029732;
        double r2029735 = r2029732 / r2029734;
        double r2029736 = r2029732 / r2029733;
        double r2029737 = r2029735 - r2029736;
        return r2029737;
}
↓
double f(double x) {
        double r2029738 = -1.0;
        double r2029739 = x;
        double r2029740 = 1.0;
        double r2029741 = r2029739 + r2029740;
        double r2029742 = r2029738 / r2029741;
        double r2029743 = r2029742 / r2029739;
        return r2029743;
}

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. Simplified0.3

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

  5. Simplified0.3

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

  7. Applied distribute-lft1-in0.3

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019124 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))