Average Error: 28.7 → 0.3
Time: 13.2s
Precision: 64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{-1}{x + 1} \cdot \frac{1 + 3 \cdot x}{x - 1}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{-1}{x + 1} \cdot \frac{1 + 3 \cdot x}{x - 1}
double f(double x) {
        double r185876 = x;
        double r185877 = 1.0;
        double r185878 = r185876 + r185877;
        double r185879 = r185876 / r185878;
        double r185880 = r185876 - r185877;
        double r185881 = r185878 / r185880;
        double r185882 = r185879 - r185881;
        return r185882;
}
↓
double f(double x) {
        double r185883 = -1.0;
        double r185884 = x;
        double r185885 = 1.0;
        double r185886 = r185884 + r185885;
        double r185887 = r185883 / r185886;
        double r185888 = 3.0;
        double r185889 = r185888 * r185884;
        double r185890 = r185885 + r185889;
        double r185891 = r185884 - r185885;
        double r185892 = r185890 / r185891;
        double r185893 = r185887 * r185892;
        return r185893;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.7

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

  2. Simplified28.7

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

  4. Applied frac-sub29.8

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

  5. Simplified29.8

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

  6. Taylor expanded around 0 14.6

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

  7. Simplified14.6

    \[\leadsto \frac{\color{blue}{-\left(1 + 3 \cdot x\right)}}{\left(1 + x\right) \cdot \left(x - 1\right)}\]
  8. Using strategy rm

  9. Applied neg-mul-114.6

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

  10. Applied times-frac0.3

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

  11. Simplified0.3

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

  12. Simplified0.3

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

  13. Final simplification0.3

    \[\leadsto \frac{-1}{x + 1} \cdot \frac{1 + 3 \cdot x}{x - 1}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))