Average Error: 14.8 → 0.1
Time: 2.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
1 \cdot \frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r98663 = 1.0;
        double r98664 = x;
        double r98665 = r98664 + r98663;
        double r98666 = r98663 / r98665;
        double r98667 = r98664 - r98663;
        double r98668 = r98663 / r98667;
        double r98669 = r98666 - r98668;
        return r98669;
}
↓
double f(double x) {
        double r98670 = 1.0;
        double r98671 = 2.0;
        double r98672 = -r98671;
        double r98673 = x;
        double r98674 = r98673 + r98670;
        double r98675 = r98672 / r98674;
        double r98676 = r98673 - r98670;
        double r98677 = r98675 / r98676;
        double r98678 = r98670 * r98677;
        return r98678;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

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

  3. Applied flip--29.7

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

  4. Applied associate-/r/29.7

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

  5. Applied flip-+14.9

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

  6. Applied associate-/r/14.8

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

  7. Applied distribute-lft-out--14.3

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

  8. Taylor expanded around 0 0.4

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

  10. Applied div-inv0.4

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

  11. Applied associate-*l*0.4

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))