Average Error: 0.0 → 0.0
Time: 13.6s
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 r88187 = 1.0;
        double r88188 = x;
        double r88189 = r88188 - r88187;
        double r88190 = r88187 / r88189;
        double r88191 = r88188 + r88187;
        double r88192 = r88188 / r88191;
        double r88193 = r88190 + r88192;
        return r88193;
}
↓
double f(double x) {
        double r88194 = 1.0;
        double r88195 = x;
        double r88196 = r88195 - r88194;
        double r88197 = r88194 / r88196;
        double r88198 = r88197 * r88197;
        double r88199 = r88195 + r88194;
        double r88200 = r88195 / r88199;
        double r88201 = r88200 * r88200;
        double r88202 = r88198 - r88201;
        double r88203 = r88197 - r88200;
        double r88204 = r88202 / r88203;
        return r88204;
}

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 2019199 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))