Average Error: 0.0 → 0.0
Time: 42.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{x}{x + 1} + \frac{1}{x \cdot x - 1} \cdot \left(x + 1\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{x}{x + 1} + \frac{1}{x \cdot x - 1} \cdot \left(x + 1\right)
double f(double x) {
        double r15130761 = 1.0;
        double r15130762 = x;
        double r15130763 = r15130762 - r15130761;
        double r15130764 = r15130761 / r15130763;
        double r15130765 = r15130762 + r15130761;
        double r15130766 = r15130762 / r15130765;
        double r15130767 = r15130764 + r15130766;
        return r15130767;
}
↓
double f(double x) {
        double r15130768 = x;
        double r15130769 = 1.0;
        double r15130770 = r15130768 + r15130769;
        double r15130771 = r15130768 / r15130770;
        double r15130772 = r15130768 * r15130768;
        double r15130773 = r15130772 - r15130769;
        double r15130774 = r15130769 / r15130773;
        double r15130775 = r15130774 * r15130770;
        double r15130776 = r15130771 + r15130775;
        return r15130776;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied flip--0.0

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

  4. Applied associate-/r/0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))