Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{{\left(\frac{x + 1}{\frac{x \cdot x}{1} - 1} + \frac{x}{x + 1}\right)}^{3}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{{\left(\frac{x + 1}{\frac{x \cdot x}{1} - 1} + \frac{x}{x + 1}\right)}^{3}}
double f(double x) {
        double r74095 = 1.0;
        double r74096 = x;
        double r74097 = r74096 - r74095;
        double r74098 = r74095 / r74097;
        double r74099 = r74096 + r74095;
        double r74100 = r74096 / r74099;
        double r74101 = r74098 + r74100;
        return r74101;
}
↓
double f(double x) {
        double r74102 = x;
        double r74103 = 1.0;
        double r74104 = r74102 + r74103;
        double r74105 = r74102 * r74102;
        double r74106 = r74105 / r74103;
        double r74107 = r74106 - r74103;
        double r74108 = r74104 / r74107;
        double r74109 = r74102 / r74104;
        double r74110 = r74108 + r74109;
        double r74111 = 3.0;
        double r74112 = pow(r74110, r74111);
        double r74113 = cbrt(r74112);
        return r74113;
}

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. Applied fma-def0.0

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

  7. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\mathsf{fma}\left(\frac{1}{x \cdot x - 1 \cdot 1}, x + 1, \frac{x}{x + 1}\right) \cdot \mathsf{fma}\left(\frac{1}{x \cdot x - 1 \cdot 1}, x + 1, \frac{x}{x + 1}\right)\right) \cdot \mathsf{fma}\left(\frac{1}{x \cdot x - 1 \cdot 1}, x + 1, \frac{x}{x + 1}\right)}}\]

  8. Simplified0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x + 1}{\frac{x \cdot x}{1} - 1} + \frac{x}{x + 1}\right)}^{3}}}\]

  9. Final simplification0.0

    \[\leadsto \sqrt[3]{{\left(\frac{x + 1}{\frac{x \cdot x}{1} - 1} + \frac{x}{x + 1}\right)}^{3}}\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))