Average Error: 2.1 → 0.1
Time: 25.2s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 1.21824748075500874323673407969583515157 \cdot 10^{154}:\\ \;\;\;\;\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{{\left(\sqrt[3]{k}\right)}^{m}}{\left(10 \cdot k + 1\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \left(a \cdot 99\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{{\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}}{k} \cdot \frac{a}{k}\right) - \left(\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \frac{a}{k \cdot \left(k \cdot k\right)}\right) \cdot 10\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 1.21824748075500874323673407969583515157 \cdot 10^{154}:\\
\;\;\;\;\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{{\left(\sqrt[3]{k}\right)}^{m}}{\left(10 \cdot k + 1\right) + k \cdot k}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \left(a \cdot 99\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{{\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}}{k} \cdot \frac{a}{k}\right) - \left(\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \frac{a}{k \cdot \left(k \cdot k\right)}\right) \cdot 10\\

\end{array}
double f(double a, double k, double m) {
        double r9653865 = a;
        double r9653866 = k;
        double r9653867 = m;
        double r9653868 = pow(r9653866, r9653867);
        double r9653869 = r9653865 * r9653868;
        double r9653870 = 1.0;
        double r9653871 = 10.0;
        double r9653872 = r9653871 * r9653866;
        double r9653873 = r9653870 + r9653872;
        double r9653874 = r9653866 * r9653866;
        double r9653875 = r9653873 + r9653874;
        double r9653876 = r9653869 / r9653875;
        return r9653876;
}
↓
double f(double a, double k, double m) {
        double r9653877 = k;
        double r9653878 = 1.2182474807550087e+154;
        bool r9653879 = r9653877 <= r9653878;
        double r9653880 = a;
        double r9653881 = cbrt(r9653877);
        double r9653882 = r9653881 * r9653881;
        double r9653883 = m;
        double r9653884 = pow(r9653882, r9653883);
        double r9653885 = r9653880 * r9653884;
        double r9653886 = pow(r9653881, r9653883);
        double r9653887 = 10.0;
        double r9653888 = r9653887 * r9653877;
        double r9653889 = 1.0;
        double r9653890 = r9653888 + r9653889;
        double r9653891 = r9653877 * r9653877;
        double r9653892 = r9653890 + r9653891;
        double r9653893 = r9653886 / r9653892;
        double r9653894 = r9653885 * r9653893;
        double r9653895 = 1.0;
        double r9653896 = r9653895 / r9653877;
        double r9653897 = -0.3333333333333333;
        double r9653898 = pow(r9653896, r9653897);
        double r9653899 = r9653898 * r9653898;
        double r9653900 = pow(r9653899, r9653883);
        double r9653901 = pow(r9653898, r9653883);
        double r9653902 = r9653900 * r9653901;
        double r9653903 = 99.0;
        double r9653904 = r9653880 * r9653903;
        double r9653905 = r9653902 * r9653904;
        double r9653906 = r9653891 * r9653891;
        double r9653907 = r9653905 / r9653906;
        double r9653908 = r9653902 / r9653877;
        double r9653909 = r9653880 / r9653877;
        double r9653910 = r9653908 * r9653909;
        double r9653911 = r9653907 + r9653910;
        double r9653912 = r9653877 * r9653891;
        double r9653913 = r9653880 / r9653912;
        double r9653914 = r9653902 * r9653913;
        double r9653915 = r9653914 * r9653887;
        double r9653916 = r9653911 - r9653915;
        double r9653917 = r9653879 ? r9653894 : r9653916;
        return r9653917;
}

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 < 1.2182474807550087e+154

    1. Initial program 0.1

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt0.1

      \[\leadsto \frac{a \cdot {\color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    4. Applied unpow-prod-down0.1

      \[\leadsto \frac{a \cdot \color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot {\left(\sqrt[3]{k}\right)}^{m}\right)}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    5. Applied associate-*r*0.1

      \[\leadsto \frac{\color{blue}{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity0.1

      \[\leadsto \frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\color{blue}{1 \cdot \left(\left(1 + 10 \cdot k\right) + k \cdot k\right)}}\]

    8. Applied times-frac0.1

      \[\leadsto \color{blue}{\frac{a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}{1} \cdot \frac{{\left(\sqrt[3]{k}\right)}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}}\]

    9. Simplified0.1

      \[\leadsto \color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot a\right)} \cdot \frac{{\left(\sqrt[3]{k}\right)}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    if 1.2182474807550087e+154 < k

    1. Initial program 10.5

      \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
    2. Using strategy rm

    3. Applied add-cube-cbrt10.5

      \[\leadsto \frac{a \cdot {\color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    4. Applied unpow-prod-down10.5

      \[\leadsto \frac{a \cdot \color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot {\left(\sqrt[3]{k}\right)}^{m}\right)}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    5. Applied associate-*r*10.5

      \[\leadsto \frac{\color{blue}{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

    6. Taylor expanded around inf 10.5

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

    7. Simplified0.4

      \[\leadsto \color{blue}{\left(\frac{\left(99 \cdot a\right) \cdot \left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{{\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}}{k} \cdot \frac{a}{k}\right) - 10 \cdot \left(\frac{a}{k \cdot \left(k \cdot k\right)} \cdot \left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right)\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.21824748075500874323673407969583515157 \cdot 10^{154}:\\ \;\;\;\;\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{{\left(\sqrt[3]{k}\right)}^{m}}{\left(10 \cdot k + 1\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \left(a \cdot 99\right)}{\left(k \cdot k\right) \cdot \left(k \cdot k\right)} + \frac{{\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}}{k} \cdot \frac{a}{k}\right) - \left(\left({\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}} \cdot {\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m} \cdot {\left({\left(\frac{1}{k}\right)}^{\frac{-1}{3}}\right)}^{m}\right) \cdot \frac{a}{k \cdot \left(k \cdot k\right)}\right) \cdot 10\\ \end{array}\]

Reproduce

herbie shell --seed 2019169 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))