Average Error: 29.0 → 0.2
Time: 3.4s
Precision: 64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{\frac{-\left(3 \cdot x + 1\right)}{x + 1}}{x - 1}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{\frac{-\left(3 \cdot x + 1\right)}{x + 1}}{x - 1}
double f(double x) {
        double r155642 = x;
        double r155643 = 1.0;
        double r155644 = r155642 + r155643;
        double r155645 = r155642 / r155644;
        double r155646 = r155642 - r155643;
        double r155647 = r155644 / r155646;
        double r155648 = r155645 - r155647;
        return r155648;
}
↓
double f(double x) {
        double r155649 = 3.0;
        double r155650 = x;
        double r155651 = r155649 * r155650;
        double r155652 = 1.0;
        double r155653 = r155651 + r155652;
        double r155654 = -r155653;
        double r155655 = r155650 + r155652;
        double r155656 = r155654 / r155655;
        double r155657 = r155650 - r155652;
        double r155658 = r155656 / r155657;
        return r155658;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.0

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

  3. Applied frac-sub30.1

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

  4. Simplified30.1

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

  5. Taylor expanded around 0 14.8

    \[\leadsto \frac{\color{blue}{-\left(3 \cdot x + 1\right)}}{x \cdot x - 1 \cdot 1}\]
  6. Using strategy rm

  7. Applied difference-of-squares14.9

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

  8. Applied associate-/r*0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))