Average Error: 0.0 → 0.0
Time: 16.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{\frac{1}{x - 1} \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right) + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}{\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \left(\frac{\frac{x}{x + 1}}{x - 1} - \frac{\frac{1}{x - 1}}{x - 1}\right)}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{\frac{1}{x - 1} \cdot \left(\frac{1}{x - 1} \cdot \frac{1}{x - 1}\right) + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)}{\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \left(\frac{\frac{x}{x + 1}}{x - 1} - \frac{\frac{1}{x - 1}}{x - 1}\right)}}\right)
double f(double x) {
        double r2462072 = 1.0;
        double r2462073 = x;
        double r2462074 = r2462073 - r2462072;
        double r2462075 = r2462072 / r2462074;
        double r2462076 = r2462073 + r2462072;
        double r2462077 = r2462073 / r2462076;
        double r2462078 = r2462075 + r2462077;
        return r2462078;
}
↓
double f(double x) {
        double r2462079 = 1.0;
        double r2462080 = x;
        double r2462081 = r2462080 - r2462079;
        double r2462082 = r2462079 / r2462081;
        double r2462083 = r2462082 * r2462082;
        double r2462084 = r2462082 * r2462083;
        double r2462085 = r2462080 + r2462079;
        double r2462086 = r2462080 / r2462085;
        double r2462087 = r2462086 * r2462086;
        double r2462088 = r2462086 * r2462087;
        double r2462089 = r2462084 + r2462088;
        double r2462090 = r2462086 / r2462081;
        double r2462091 = r2462082 / r2462081;
        double r2462092 = r2462090 - r2462091;
        double r2462093 = r2462087 - r2462092;
        double r2462094 = r2462089 / r2462093;
        double r2462095 = exp(r2462094);
        double r2462096 = log(r2462095);
        return r2462096;
}

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 add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)}\]
  4. Using strategy rm

  5. Applied flip3-+0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

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