Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r3565323 = 1.0;
        double r3565324 = x;
        double r3565325 = r3565324 - r3565323;
        double r3565326 = r3565323 / r3565325;
        double r3565327 = r3565324 + r3565323;
        double r3565328 = r3565324 / r3565327;
        double r3565329 = r3565326 + r3565328;
        return r3565329;
}
↓
double f(double x) {
        double r3565330 = 1.0;
        double r3565331 = x;
        double r3565332 = r3565331 * r3565331;
        double r3565333 = r3565330 * r3565330;
        double r3565334 = r3565332 - r3565333;
        double r3565335 = r3565330 / r3565334;
        double r3565336 = r3565331 + r3565330;
        double r3565337 = r3565335 * r3565336;
        double r3565338 = 1.0;
        double r3565339 = r3565336 / r3565331;
        double r3565340 = r3565338 / r3565339;
        double r3565341 = r3565337 + r3565340;
        return r3565341;
}

Error

Bits error versus x

Try it out

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 clear-num0.0

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

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))