Average Error: 14.0 → 0.1
Time: 3.5s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{x + 1}}{x - 1} \cdot \left(-2\right)\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{x + 1}}{x - 1} \cdot \left(-2\right)
double f(double x) {
        double r115408 = 1.0;
        double r115409 = x;
        double r115410 = r115409 + r115408;
        double r115411 = r115408 / r115410;
        double r115412 = r115409 - r115408;
        double r115413 = r115408 / r115412;
        double r115414 = r115411 - r115413;
        return r115414;
}
↓
double f(double x) {
        double r115415 = 1.0;
        double r115416 = x;
        double r115417 = r115416 + r115415;
        double r115418 = r115415 / r115417;
        double r115419 = r115416 - r115415;
        double r115420 = r115418 / r115419;
        double r115421 = 2.0;
        double r115422 = -r115421;
        double r115423 = r115420 * r115422;
        return r115423;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  3. Applied flip--28.8

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

  4. Applied associate-/r/28.9

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

  5. Applied flip-+14.1

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

  6. Applied associate-/r/14.0

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

  7. Applied distribute-lft-out--13.4

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

  9. Applied difference-of-squares13.4

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

  10. Applied associate-/r*13.4

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

  11. Taylor expanded around 0 0.1

    \[\leadsto \frac{\frac{1}{x + 1}}{x - 1} \cdot \color{blue}{\left(-2\right)}\]

  12. Final simplification0.1

    \[\leadsto \frac{\frac{1}{x + 1}}{x - 1} \cdot \left(-2\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))