Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}
double f(double x) {
        double r98089 = 1.0;
        double r98090 = x;
        double r98091 = r98090 - r98089;
        double r98092 = r98089 / r98091;
        double r98093 = r98090 + r98089;
        double r98094 = r98090 / r98093;
        double r98095 = r98092 + r98094;
        return r98095;
}
↓
double f(double x) {
        double r98096 = 1.0;
        double r98097 = x;
        double r98098 = r98097 - r98096;
        double r98099 = r98096 / r98098;
        double r98100 = 3.0;
        double r98101 = pow(r98099, r98100);
        double r98102 = r98097 + r98096;
        double r98103 = r98097 / r98102;
        double r98104 = pow(r98103, r98100);
        double r98105 = r98101 + r98104;
        double r98106 = r98099 * r98099;
        double r98107 = r98103 - r98099;
        double r98108 = r98103 * r98107;
        double r98109 = r98106 + r98108;
        double r98110 = r98105 / r98109;
        return r98110;
}

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 flip3-+0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))