Average Error: 14.7 → 0.1
Time: 10.9s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{1 + x}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{1 + x}}{x - 1}
double f(double x) {
        double r3920490 = 1.0;
        double r3920491 = x;
        double r3920492 = r3920491 + r3920490;
        double r3920493 = r3920490 / r3920492;
        double r3920494 = r3920491 - r3920490;
        double r3920495 = r3920490 / r3920494;
        double r3920496 = r3920493 - r3920495;
        return r3920496;
}
↓
double f(double x) {
        double r3920497 = -2.0;
        double r3920498 = 1.0;
        double r3920499 = x;
        double r3920500 = r3920498 + r3920499;
        double r3920501 = r3920497 / r3920500;
        double r3920502 = r3920499 - r3920498;
        double r3920503 = r3920501 / r3920502;
        return r3920503;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.7

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

  3. Applied frac-sub14.1

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

  4. Simplified14.1

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

  5. Simplified14.1

    \[\leadsto \frac{x + \left(-2 - x\right)}{\color{blue}{x \cdot x + -1}}\]
  6. Using strategy rm

  7. Applied difference-of-sqr--114.1

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

  8. Applied associate-/r*14.1

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

  9. Simplified0.1

    \[\leadsto \frac{\color{blue}{\frac{-2}{1 + x}}}{x - 1}\]

  10. Final simplification0.1

    \[\leadsto \frac{\frac{-2}{1 + x}}{x - 1}\]

Reproduce

herbie shell --seed 2019129 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))