Average Error: 14.5 → 0.1
Time: 10.0s
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 r3532653 = 1.0;
        double r3532654 = x;
        double r3532655 = r3532654 + r3532653;
        double r3532656 = r3532653 / r3532655;
        double r3532657 = r3532654 - r3532653;
        double r3532658 = r3532653 / r3532657;
        double r3532659 = r3532656 - r3532658;
        return r3532659;
}
↓
double f(double x) {
        double r3532660 = -2.0;
        double r3532661 = 1.0;
        double r3532662 = x;
        double r3532663 = r3532661 + r3532662;
        double r3532664 = r3532660 / r3532663;
        double r3532665 = r3532662 - r3532661;
        double r3532666 = r3532664 / r3532665;
        return r3532666;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

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

  3. Applied frac-sub13.9

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

  4. Simplified13.8

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

  5. Simplified13.8

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

  7. Applied difference-of-sqr--113.8

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

  8. Applied associate-/r*13.8

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

  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 2019133 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))