Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\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}}
double f(double x) {
        double r173234 = 1.0;
        double r173235 = x;
        double r173236 = r173235 - r173234;
        double r173237 = r173234 / r173236;
        double r173238 = r173235 + r173234;
        double r173239 = r173235 / r173238;
        double r173240 = r173237 + r173239;
        return r173240;
}
↓
double f(double x) {
        double r173241 = 1.0;
        double r173242 = x;
        double r173243 = r173242 - r173241;
        double r173244 = r173241 / r173243;
        double r173245 = r173244 * r173244;
        double r173246 = r173242 + r173241;
        double r173247 = r173242 / r173246;
        double r173248 = r173247 * r173247;
        double r173249 = r173245 - r173248;
        double r173250 = r173244 - r173247;
        double r173251 = r173249 / r173250;
        return r173251;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))