Average Error: 14.9 → 0.1
Time: 9.0s
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 r2509663 = 1.0;
        double r2509664 = x;
        double r2509665 = r2509664 + r2509663;
        double r2509666 = r2509663 / r2509665;
        double r2509667 = r2509663 / r2509664;
        double r2509668 = r2509666 - r2509667;
        return r2509668;
}
↓
double f(double x) {
        double r2509669 = -1.0;
        double r2509670 = x;
        double r2509671 = 1.0;
        double r2509672 = r2509670 + r2509671;
        double r2509673 = r2509669 / r2509672;
        double r2509674 = r2509673 / r2509670;
        return r2509674;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.9

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

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

  5. Taylor expanded around 0 0.4

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))