Average Error: 2.0 → 0.1
Time: 46.5s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 3.765086051784335 \cdot 10^{+91}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot a\right) \cdot 99 + \left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{\left(a \cdot 10\right) \cdot e^{m \cdot \log k}}{k \cdot \left(k \cdot k\right)}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 3.765086051784335 \cdot 10^{+91}:\\
\;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{e^{m \cdot \log k}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot a\right) \cdot 99 + \left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{\left(a \cdot 10\right) \cdot e^{m \cdot \log k}}{k \cdot \left(k \cdot k\right)}\right)\\

\end{array}
double f(double a, double k, double m) {
        double r7687898 = a;
        double r7687899 = k;
        double r7687900 = m;
        double r7687901 = pow(r7687899, r7687900);
        double r7687902 = r7687898 * r7687901;
        double r7687903 = 1.0;
        double r7687904 = 10.0;
        double r7687905 = r7687904 * r7687899;
        double r7687906 = r7687903 + r7687905;
        double r7687907 = r7687899 * r7687899;
        double r7687908 = r7687906 + r7687907;
        double r7687909 = r7687902 / r7687908;
        return r7687909;
}
↓
double f(double a, double k, double m) {
        double r7687910 = k;
        double r7687911 = 3.765086051784335e+91;
        bool r7687912 = r7687910 <= r7687911;
        double r7687913 = a;
        double r7687914 = 1.0;
        double r7687915 = 10.0;
        double r7687916 = r7687910 + r7687915;
        double r7687917 = r7687916 * r7687910;
        double r7687918 = r7687914 + r7687917;
        double r7687919 = m;
        double r7687920 = pow(r7687910, r7687919);
        double r7687921 = r7687918 / r7687920;
        double r7687922 = r7687913 / r7687921;
        double r7687923 = log(r7687910);
        double r7687924 = r7687919 * r7687923;
        double r7687925 = exp(r7687924);
        double r7687926 = r7687910 * r7687910;
        double r7687927 = r7687926 * r7687926;
        double r7687928 = r7687925 / r7687927;
        double r7687929 = r7687928 * r7687913;
        double r7687930 = 99.0;
        double r7687931 = r7687929 * r7687930;
        double r7687932 = r7687913 / r7687910;
        double r7687933 = r7687925 / r7687910;
        double r7687934 = r7687932 * r7687933;
        double r7687935 = r7687913 * r7687915;
        double r7687936 = r7687935 * r7687925;
        double r7687937 = r7687910 * r7687926;
        double r7687938 = r7687936 / r7687937;
        double r7687939 = r7687934 - r7687938;
        double r7687940 = r7687931 + r7687939;
        double r7687941 = r7687912 ? r7687922 : r7687940;
        return r7687941;
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if k < 3.765086051784335e+91

    1. Initial program 0.1

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    2. Simplified0.1

      \[\leadsto \color{blue}{\frac{a}{\frac{\left(k + 10\right) \cdot k + 1}{{k}^{m}}}}\]

    if 3.765086051784335e+91 < k

    1. Initial program 6.9

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    2. Simplified6.9

      \[\leadsto \color{blue}{\frac{a}{\frac{\left(k + 10\right) \cdot k + 1}{{k}^{m}}}}\]

    3. Taylor expanded around inf 6.9

      \[\leadsto \color{blue}{\left(99 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{4}} + \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{2}}\right) - 10 \cdot \frac{e^{-1 \cdot \left(\log \left(\frac{1}{k}\right) \cdot m\right)} \cdot a}{{k}^{3}}}\]

    4. Simplified0.1

      \[\leadsto \color{blue}{99 \cdot \left(\frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot a\right) + \left(\frac{a}{k} \cdot \frac{e^{\left(-m\right) \cdot \left(-\log k\right)}}{k} - \frac{\left(10 \cdot a\right) \cdot e^{\left(-m\right) \cdot \left(-\log k\right)}}{\left(k \cdot k\right) \cdot k}\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 3.765086051784335 \cdot 10^{+91}:\\ \;\;\;\;\frac{a}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m}}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{e^{m \cdot \log k}}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} \cdot a\right) \cdot 99 + \left(\frac{a}{k} \cdot \frac{e^{m \cdot \log k}}{k} - \frac{\left(a \cdot 10\right) \cdot e^{m \cdot \log k}}{k \cdot \left(k \cdot k\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))