Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[\frac{x}{1 - x}\]
↓
\[\frac{x}{1 - x}\]
\frac{x}{1 - x}
↓
\frac{x}{1 - x}
double f(double x) {
        double r133794 = x;
        double r133795 = 1.0;
        double r133796 = r133795 - r133794;
        double r133797 = r133794 / r133796;
        return r133797;
}
↓
double f(double x) {
        double r133798 = x;
        double r133799 = 1.0;
        double r133800 = r133799 - r133798;
        double r133801 = r133798 / r133800;
        return r133801;
}

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

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

  3. Applied clear-num0.1

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

  5. Applied *-un-lft-identity0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{1 - x}{x}}}\]

  10. Simplified0.1

    \[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{1 - x}{x}}\]

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1 x)))