Average Error: 15.1 → 0.1
Time: 14.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r4125723 = 1.0;
        double r4125724 = x;
        double r4125725 = r4125724 + r4125723;
        double r4125726 = r4125723 / r4125725;
        double r4125727 = r4125724 - r4125723;
        double r4125728 = r4125723 / r4125727;
        double r4125729 = r4125726 - r4125728;
        return r4125729;
}
↓
double f(double x) {
        double r4125730 = -2.0;
        double r4125731 = x;
        double r4125732 = 1.0;
        double r4125733 = r4125731 + r4125732;
        double r4125734 = r4125730 / r4125733;
        double r4125735 = r4125731 - r4125732;
        double r4125736 = r4125734 / r4125735;
        return r4125736;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

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

  3. Applied frac-sub14.5

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

  4. Simplified14.5

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

  5. Simplified14.5

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

  7. Applied difference-of-sqr--114.5

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

  8. Applied associate-/r*14.5

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019139 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))