Average Error: 14.4 → 0.1
Time: 7.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{\frac{2 \cdot \left(-{1}^{4}\right)}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{\frac{2 \cdot \left(-{1}^{4}\right)}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}
double f(double x) {
        double r94355 = 1.0;
        double r94356 = x;
        double r94357 = r94356 + r94355;
        double r94358 = r94355 / r94357;
        double r94359 = r94356 - r94355;
        double r94360 = r94355 / r94359;
        double r94361 = r94358 - r94360;
        return r94361;
}
↓
double f(double x) {
        double r94362 = 2.0;
        double r94363 = 1.0;
        double r94364 = 4.0;
        double r94365 = pow(r94363, r94364);
        double r94366 = -r94365;
        double r94367 = r94362 * r94366;
        double r94368 = x;
        double r94369 = r94363 + r94368;
        double r94370 = r94367 / r94369;
        double r94371 = r94368 - r94363;
        double r94372 = r94370 / r94371;
        double r94373 = r94363 * r94363;
        double r94374 = -r94363;
        double r94375 = r94374 * r94363;
        double r94376 = r94375 + r94373;
        double r94377 = r94373 + r94376;
        double r94378 = r94372 / r94377;
        return r94378;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied flip--28.5

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

  4. Applied associate-/r/28.5

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

  5. Applied flip-+14.5

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

  6. Applied associate-/r/14.4

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

  7. Applied distribute-lft-out--13.9

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

  8. Simplified0.3

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\left(\left(0 - 1\right) - 1\right)}\]
  9. Using strategy rm

  10. Applied flip3--0.3

    \[\leadsto \frac{1}{x \cdot x - 1 \cdot 1} \cdot \color{blue}{\frac{{\left(0 - 1\right)}^{3} - {1}^{3}}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}}\]

  11. Applied associate-*r/0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left({\left(0 - 1\right)}^{3} - {1}^{3}\right)}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}}\]

  12. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{\frac{2 \cdot \left(-{1}^{4}\right)}{1 + x}}{x - 1}}}{\left(0 - 1\right) \cdot \left(0 - 1\right) + \left(1 \cdot 1 + \left(0 - 1\right) \cdot 1\right)}\]

  13. Final simplification0.1

    \[\leadsto \frac{\frac{\frac{2 \cdot \left(-{1}^{4}\right)}{1 + x}}{x - 1}}{1 \cdot 1 + \left(\left(-1\right) \cdot 1 + 1 \cdot 1\right)}\]

Reproduce

herbie shell --seed 2019350 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))