Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(\left(x + 1\right) \cdot \frac{1}{x - 1}\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(\left(x + 1\right) \cdot \frac{1}{x - 1}\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}
double f(double x) {
        double r151181 = 1.0;
        double r151182 = x;
        double r151183 = r151182 - r151181;
        double r151184 = r151181 / r151183;
        double r151185 = r151182 + r151181;
        double r151186 = r151182 / r151185;
        double r151187 = r151184 + r151186;
        return r151187;
}
↓
double f(double x) {
        double r151188 = 1.0;
        double r151189 = x;
        double r151190 = r151189 * r151189;
        double r151191 = r151188 * r151188;
        double r151192 = r151190 - r151191;
        double r151193 = r151188 / r151192;
        double r151194 = r151189 + r151188;
        double r151195 = r151189 - r151188;
        double r151196 = r151188 / r151195;
        double r151197 = r151194 * r151196;
        double r151198 = r151193 * r151197;
        double r151199 = r151189 / r151194;
        double r151200 = r151199 * r151199;
        double r151201 = r151198 - r151200;
        double r151202 = r151196 - r151199;
        double r151203 = r151201 / r151202;
        return r151203;
}

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 flip-+0.0

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

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Applied associate-*l*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))