Average Error: 28.6 → 0.0
Time: 25.6s
Precision: 64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1}\]
↓
\[\frac{-\left(3 + \frac{1}{x}\right)}{x - \frac{1}{x}}\]
\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{-\left(3 + \frac{1}{x}\right)}{x - \frac{1}{x}}
double f(double x) {
        double r4714246 = x;
        double r4714247 = 1.0;
        double r4714248 = r4714246 + r4714247;
        double r4714249 = r4714246 / r4714248;
        double r4714250 = r4714246 - r4714247;
        double r4714251 = r4714248 / r4714250;
        double r4714252 = r4714249 - r4714251;
        return r4714252;
}
↓
double f(double x) {
        double r4714253 = 3.0;
        double r4714254 = 1.0;
        double r4714255 = x;
        double r4714256 = r4714254 / r4714255;
        double r4714257 = r4714253 + r4714256;
        double r4714258 = -r4714257;
        double r4714259 = r4714255 - r4714256;
        double r4714260 = r4714258 / r4714259;
        return r4714260;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.6

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

  3. Applied clear-num28.6

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

  4. Applied frac-sub28.3

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

  5. Taylor expanded around 0 0.0

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

  6. Taylor expanded around 0 0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x)
  :name "Asymptote C"
  (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))