Average Error: 14.6 → 0.1
Time: 10.8s
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 r1022734 = 1.0;
        double r1022735 = x;
        double r1022736 = r1022735 + r1022734;
        double r1022737 = r1022734 / r1022736;
        double r1022738 = r1022734 / r1022735;
        double r1022739 = r1022737 - r1022738;
        return r1022739;
}
↓
double f(double x) {
        double r1022740 = -1.0;
        double r1022741 = x;
        double r1022742 = 1.0;
        double r1022743 = r1022741 + r1022742;
        double r1022744 = r1022740 / r1022743;
        double r1022745 = r1022744 / r1022741;
        return r1022745;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub13.9

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

  4. Simplified13.9

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

  6. Applied associate-/r*13.9

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019152 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))