Average Error: 14.7 → 0.1
Time: 14.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{-\frac{1}{1 + x} \cdot 2}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{-\frac{1}{1 + x} \cdot 2}{x - 1}
double f(double x) {
        double r93051 = 1.0;
        double r93052 = x;
        double r93053 = r93052 + r93051;
        double r93054 = r93051 / r93053;
        double r93055 = r93052 - r93051;
        double r93056 = r93051 / r93055;
        double r93057 = r93054 - r93056;
        return r93057;
}
↓
double f(double x) {
        double r93058 = 1.0;
        double r93059 = x;
        double r93060 = r93058 + r93059;
        double r93061 = r93058 / r93060;
        double r93062 = 2.0;
        double r93063 = r93061 * r93062;
        double r93064 = -r93063;
        double r93065 = r93059 - r93058;
        double r93066 = r93064 / r93065;
        return r93066;
}

Error

Bits error versus x

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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 flip--29.1

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

  4. Applied associate-/r/29.1

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

  5. Applied flip-+14.7

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

  6. Applied associate-/r/14.7

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

  7. Applied distribute-lft-out--14.1

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

  8. Simplified14.1

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

  9. Taylor expanded around 0 0.3

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

  11. Applied difference-of-squares0.3

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

  12. Applied associate-/r*0.1

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

  13. Simplified0.1

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

  15. Applied associate-*l/0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))