Average Error: 14.3 → 0.1
Time: 10.3s
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 r45505 = 1.0;
        double r45506 = x;
        double r45507 = r45506 + r45505;
        double r45508 = r45505 / r45507;
        double r45509 = r45505 / r45506;
        double r45510 = r45508 - r45509;
        return r45510;
}
↓
double f(double x) {
        double r45511 = 1.0;
        double r45512 = -r45511;
        double r45513 = r45512 * r45511;
        double r45514 = x;
        double r45515 = r45514 + r45511;
        double r45516 = r45513 / r45515;
        double r45517 = r45516 / r45514;
        return r45517;
}

Error

Bits error versus x

Try it out

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. Simplified0.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 x)))