Average Error: 0.0 → 0.0
Time: 33.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{\frac{x + 1}{x}} + \frac{1}{x \cdot x - 1} \cdot \left(x + 1\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{\frac{x + 1}{x}} + \frac{1}{x \cdot x - 1} \cdot \left(x + 1\right)
double f(double x) {
        double r10408919 = 1.0;
        double r10408920 = x;
        double r10408921 = r10408920 - r10408919;
        double r10408922 = r10408919 / r10408921;
        double r10408923 = r10408920 + r10408919;
        double r10408924 = r10408920 / r10408923;
        double r10408925 = r10408922 + r10408924;
        return r10408925;
}
↓
double f(double x) {
        double r10408926 = 1.0;
        double r10408927 = x;
        double r10408928 = r10408927 + r10408926;
        double r10408929 = r10408928 / r10408927;
        double r10408930 = r10408926 / r10408929;
        double r10408931 = r10408927 * r10408927;
        double r10408932 = r10408931 - r10408926;
        double r10408933 = r10408926 / r10408932;
        double r10408934 = r10408933 * r10408928;
        double r10408935 = r10408930 + r10408934;
        return r10408935;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied *-un-lft-identity0.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  5. Using strategy rm

  6. Applied flip--0.0

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

  7. Applied associate-/r/0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019112 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))