Average Error: 2.3 → 0.1
Time: 21.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\begin{array}{l} \mathbf{if}\;k \le 5.413206367433749081791782278643320672943 \cdot 10^{73}:\\ \;\;\;\;\frac{\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}{\left(k + 10\right) \cdot k + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{a \cdot e^{m \cdot \log k}}{k}}{k} - \frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot k}{a}} \cdot 10\right) + \frac{\frac{\left(99 \cdot e^{m \cdot \log k}\right) \cdot a}{k \cdot k}}{k \cdot k}\\ \end{array}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\begin{array}{l}
\mathbf{if}\;k \le 5.413206367433749081791782278643320672943 \cdot 10^{73}:\\
\;\;\;\;\frac{\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}{\left(k + 10\right) \cdot k + 1}\\

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

\end{array}
double f(double a, double k, double m) {
        double r7838080 = a;
        double r7838081 = k;
        double r7838082 = m;
        double r7838083 = pow(r7838081, r7838082);
        double r7838084 = r7838080 * r7838083;
        double r7838085 = 1.0;
        double r7838086 = 10.0;
        double r7838087 = r7838086 * r7838081;
        double r7838088 = r7838085 + r7838087;
        double r7838089 = r7838081 * r7838081;
        double r7838090 = r7838088 + r7838089;
        double r7838091 = r7838084 / r7838090;
        return r7838091;
}
↓
double f(double a, double k, double m) {
        double r7838092 = k;
        double r7838093 = 5.413206367433749e+73;
        bool r7838094 = r7838092 <= r7838093;
        double r7838095 = cbrt(r7838092);
        double r7838096 = m;
        double r7838097 = pow(r7838095, r7838096);
        double r7838098 = a;
        double r7838099 = r7838097 * r7838098;
        double r7838100 = r7838095 * r7838095;
        double r7838101 = pow(r7838100, r7838096);
        double r7838102 = r7838099 * r7838101;
        double r7838103 = 10.0;
        double r7838104 = r7838092 + r7838103;
        double r7838105 = r7838104 * r7838092;
        double r7838106 = 1.0;
        double r7838107 = r7838105 + r7838106;
        double r7838108 = r7838102 / r7838107;
        double r7838109 = log(r7838092);
        double r7838110 = r7838096 * r7838109;
        double r7838111 = exp(r7838110);
        double r7838112 = r7838098 * r7838111;
        double r7838113 = r7838112 / r7838092;
        double r7838114 = r7838113 / r7838092;
        double r7838115 = r7838092 * r7838092;
        double r7838116 = r7838115 * r7838092;
        double r7838117 = r7838116 / r7838098;
        double r7838118 = r7838111 / r7838117;
        double r7838119 = r7838118 * r7838103;
        double r7838120 = r7838114 - r7838119;
        double r7838121 = 99.0;
        double r7838122 = r7838121 * r7838111;
        double r7838123 = r7838122 * r7838098;
        double r7838124 = r7838123 / r7838115;
        double r7838125 = r7838124 / r7838115;
        double r7838126 = r7838120 + r7838125;
        double r7838127 = r7838094 ? r7838108 : r7838126;
        return r7838127;
}

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 < 5.413206367433749e+73

    1. Initial program 0.1

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

    2. Simplified0.0

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

    4. Applied associate-*l/0.0

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

    6. Applied add-cube-cbrt0.0

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

    7. Applied unpow-prod-down0.0

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

    8. Applied associate-*l*0.0

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

    if 5.413206367433749e+73 < k

    1. Initial program 7.8

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

    2. Simplified7.8

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

    4. Applied associate-*l/7.8

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

    5. Taylor expanded around inf 7.8

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

    6. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;k \le 5.413206367433749081791782278643320672943 \cdot 10^{73}:\\ \;\;\;\;\frac{\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}}{\left(k + 10\right) \cdot k + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\frac{a \cdot e^{m \cdot \log k}}{k}}{k} - \frac{e^{m \cdot \log k}}{\frac{\left(k \cdot k\right) \cdot k}{a}} \cdot 10\right) + \frac{\frac{\left(99 \cdot e^{m \cdot \log k}\right) \cdot a}{k \cdot k}}{k \cdot k}\\ \end{array}\]

Reproduce

herbie shell --seed 2019171 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))