Average Error: 14.3 → 0.1
Time: 10.1s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}\]
\frac{1}{x + 1} - \frac{1}{x}
↓
\frac{\frac{\left(-1\right) \cdot 1}{x + 1}}{x}
double f(double x) {
        double r39663 = 1.0;
        double r39664 = x;
        double r39665 = r39664 + r39663;
        double r39666 = r39663 / r39665;
        double r39667 = r39663 / r39664;
        double r39668 = r39666 - r39667;
        return r39668;
}
↓
double f(double x) {
        double r39669 = 1.0;
        double r39670 = -r39669;
        double r39671 = r39670 * r39669;
        double r39672 = x;
        double r39673 = r39672 + r39669;
        double r39674 = r39671 / r39673;
        double r39675 = r39674 / r39672;
        return r39675;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  6. Applied associate-/r*13.7

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))