Average Error: 0.0 → 0.0
Time: 29.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\frac{\left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right) \cdot \left(\left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right)\right)}{\left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right) \cdot \left(\left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right) \cdot \left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right)\right)}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\frac{\left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right) \cdot \left(\left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1}\right)\right)\right)}{\left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right) \cdot \left(\left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right) \cdot \left(\frac{\frac{1}{x - 1}}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right)\right)}}
double f(double x) {
        double r3636943 = 1.0;
        double r3636944 = x;
        double r3636945 = r3636944 - r3636943;
        double r3636946 = r3636943 / r3636945;
        double r3636947 = r3636944 + r3636943;
        double r3636948 = r3636944 / r3636947;
        double r3636949 = r3636946 + r3636948;
        return r3636949;
}
↓
double f(double x) {
        double r3636950 = 1.0;
        double r3636951 = x;
        double r3636952 = r3636951 - r3636950;
        double r3636953 = r3636950 / r3636952;
        double r3636954 = r3636953 / r3636952;
        double r3636955 = r3636953 * r3636954;
        double r3636956 = r3636951 + r3636950;
        double r3636957 = r3636951 / r3636956;
        double r3636958 = r3636957 * r3636957;
        double r3636959 = r3636957 * r3636958;
        double r3636960 = r3636955 + r3636959;
        double r3636961 = r3636960 * r3636960;
        double r3636962 = r3636960 * r3636961;
        double r3636963 = r3636957 - r3636953;
        double r3636964 = r3636957 * r3636963;
        double r3636965 = r3636954 + r3636964;
        double r3636966 = r3636965 * r3636965;
        double r3636967 = r3636965 * r3636966;
        double r3636968 = r3636962 / r3636967;
        double r3636969 = cbrt(r3636968);
        return r3636969;
}

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-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}}\]
  4. Using strategy rm

  5. Applied flip3-+0.0

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

  6. Applied flip3-+0.0

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

  7. Applied flip3-+0.0

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

  8. Applied frac-times0.0

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

  9. Applied frac-times0.0

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

  10. Simplified0.0

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

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))