Average Error: 0.0 → 0.0
Time: 37.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1}}{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) + \frac{\frac{1}{x - 1}}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1}}{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) + \frac{\frac{1}{x - 1}}{x - 1}}
double f(double x) {
        double r4420145 = 1.0;
        double r4420146 = x;
        double r4420147 = r4420146 - r4420145;
        double r4420148 = r4420145 / r4420147;
        double r4420149 = r4420146 + r4420145;
        double r4420150 = r4420146 / r4420149;
        double r4420151 = r4420148 + r4420150;
        return r4420151;
}
↓
double f(double x) {
        double r4420152 = x;
        double r4420153 = 1.0;
        double r4420154 = r4420153 + r4420152;
        double r4420155 = r4420152 / r4420154;
        double r4420156 = r4420155 * r4420155;
        double r4420157 = r4420155 * r4420156;
        double r4420158 = r4420152 - r4420153;
        double r4420159 = r4420153 / r4420158;
        double r4420160 = r4420159 / r4420158;
        double r4420161 = r4420159 * r4420160;
        double r4420162 = r4420157 + r4420161;
        double r4420163 = r4420155 - r4420159;
        double r4420164 = r4420155 * r4420163;
        double r4420165 = r4420164 + r4420160;
        double r4420166 = r4420162 / r4420165;
        return r4420166;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019151 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))