Average Error: 1.9 → 0.2
Time: 23.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 4.210367473372475 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m} \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{e^{m \cdot \log k} \cdot a}{k}}{k} + \frac{\frac{e^{m \cdot \log k} \cdot a}{k}}{k} \cdot \left(\frac{99}{k \cdot k} - \frac{10}{k}\right)\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 4.210367473372475 \cdot 10^{+145}:\\
\;\;\;\;\frac{1}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m} \cdot a}}\\

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

\end{array}
double f(double a, double k, double m) {
        double r6422955 = a;
        double r6422956 = k;
        double r6422957 = m;
        double r6422958 = pow(r6422956, r6422957);
        double r6422959 = r6422955 * r6422958;
        double r6422960 = 1.0;
        double r6422961 = 10.0;
        double r6422962 = r6422961 * r6422956;
        double r6422963 = r6422960 + r6422962;
        double r6422964 = r6422956 * r6422956;
        double r6422965 = r6422963 + r6422964;
        double r6422966 = r6422959 / r6422965;
        return r6422966;
}
↓
double f(double a, double k, double m) {
        double r6422967 = k;
        double r6422968 = 4.210367473372475e+145;
        bool r6422969 = r6422967 <= r6422968;
        double r6422970 = 1.0;
        double r6422971 = 10.0;
        double r6422972 = r6422967 + r6422971;
        double r6422973 = r6422972 * r6422967;
        double r6422974 = r6422970 + r6422973;
        double r6422975 = m;
        double r6422976 = pow(r6422967, r6422975);
        double r6422977 = a;
        double r6422978 = r6422976 * r6422977;
        double r6422979 = r6422974 / r6422978;
        double r6422980 = r6422970 / r6422979;
        double r6422981 = log(r6422967);
        double r6422982 = r6422975 * r6422981;
        double r6422983 = exp(r6422982);
        double r6422984 = r6422983 * r6422977;
        double r6422985 = r6422984 / r6422967;
        double r6422986 = r6422985 / r6422967;
        double r6422987 = 99.0;
        double r6422988 = r6422967 * r6422967;
        double r6422989 = r6422987 / r6422988;
        double r6422990 = r6422971 / r6422967;
        double r6422991 = r6422989 - r6422990;
        double r6422992 = r6422986 * r6422991;
        double r6422993 = r6422986 + r6422992;
        double r6422994 = r6422969 ? r6422980 : r6422993;
        return r6422994;
}

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 < 4.210367473372475e+145

    1. Initial program 0.1

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

    2. Simplified0.1

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

    4. Applied clear-num0.2

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

    if 4.210367473372475e+145 < k

    1. Initial program 9.0

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

    2. Simplified9.0

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

    4. Applied add-cube-cbrt9.1

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

    5. Applied associate-*r*9.1

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

    6. Taylor expanded around -inf 63.0

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

    7. Simplified0.0

      \[\leadsto \color{blue}{\frac{\frac{a \cdot e^{\left(0 + \log k\right) \cdot m}}{k}}{k} \cdot \left(\frac{99}{k \cdot k} - \frac{10}{k}\right) + \frac{\frac{a \cdot e^{\left(0 + \log k\right) \cdot m}}{k}}{k}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 4.210367473372475 \cdot 10^{+145}:\\ \;\;\;\;\frac{1}{\frac{1 + \left(k + 10\right) \cdot k}{{k}^{m} \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{e^{m \cdot \log k} \cdot a}{k}}{k} + \frac{\frac{e^{m \cdot \log k} \cdot a}{k}}{k} \cdot \left(\frac{99}{k \cdot k} - \frac{10}{k}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))