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

↓

\[\begin{array}{l} \mathbf{if}\;k \le 4.473155123819974 \cdot 10^{+17}:\\ \;\;\;\;\left(\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{1}{(\left(10 + k\right) \cdot k + 1)_*}\\ \mathbf{else}:\\ \;\;\;\;(\left(\frac{99}{k \cdot k}\right) \cdot \left(\frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}\right) + \left(\frac{\frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}}{k} \cdot -10\right))_* + \frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}\\ \end{array}\]

double f(double a, double k, double m) {
        double r54509606 = a;
        double r54509607 = k;
        double r54509608 = m;
        double r54509609 = pow(r54509607, r54509608);
        double r54509610 = r54509606 * r54509609;
        double r54509611 = 1.0;
        double r54509612 = 10.0;
        double r54509613 = r54509612 * r54509607;
        double r54509614 = r54509611 + r54509613;
        double r54509615 = r54509607 * r54509607;
        double r54509616 = r54509614 + r54509615;
        double r54509617 = r54509610 / r54509616;
        return r54509617;
}

↓

double f(double a, double k, double m) {
        double r54509618 = k;
        double r54509619 = 4.473155123819974e+17;
        bool r54509620 = r54509618 <= r54509619;
        double r54509621 = cbrt(r54509618);
        double r54509622 = m;
        double r54509623 = pow(r54509621, r54509622);
        double r54509624 = a;
        double r54509625 = r54509623 * r54509624;
        double r54509626 = r54509621 * r54509621;
        double r54509627 = pow(r54509626, r54509622);
        double r54509628 = r54509625 * r54509627;
        double r54509629 = 1.0;
        double r54509630 = 10.0;
        double r54509631 = r54509630 + r54509618;
        double r54509632 = fma(r54509631, r54509618, r54509629);
        double r54509633 = r54509629 / r54509632;
        double r54509634 = r54509628 * r54509633;
        double r54509635 = 99.0;
        double r54509636 = r54509618 * r54509618;
        double r54509637 = r54509635 / r54509636;
        double r54509638 = log(r54509618);
        double r54509639 = r54509638 * r54509622;
        double r54509640 = exp(r54509639);
        double r54509641 = r54509624 / r54509618;
        double r54509642 = r54509640 * r54509641;
        double r54509643 = r54509642 / r54509618;
        double r54509644 = r54509643 / r54509618;
        double r54509645 = -10.0;
        double r54509646 = r54509644 * r54509645;
        double r54509647 = fma(r54509637, r54509643, r54509646);
        double r54509648 = r54509647 + r54509643;
        double r54509649 = r54509620 ? r54509634 : r54509648;
        return r54509649;
}

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

↓

\begin{array}{l}
\mathbf{if}\;k \le 4.473155123819974 \cdot 10^{+17}:\\
\;\;\;\;\left(\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{1}{(\left(10 + k\right) \cdot k + 1)_*}\\

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

\end{array}

Derivation

Split input into 2 regimes
if k < 4.473155123819974e+17
1. Initial program 0.1
  \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
2. Simplified0.0
  \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{(\left(k + 10\right) \cdot k + 1)_*}}\]
3. Using strategy rm
4. Applied add-cube-cbrt0.0
  \[\leadsto \frac{{\color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}}^{m} \cdot a}{(\left(k + 10\right) \cdot k + 1)_*}\]
5. Applied unpow-prod-down0.0
  \[\leadsto \frac{\color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot {\left(\sqrt[3]{k}\right)}^{m}\right)} \cdot a}{(\left(k + 10\right) \cdot k + 1)_*}\]
6. Applied associate-*l*0.0
  \[\leadsto \frac{\color{blue}{{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot \left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right)}}{(\left(k + 10\right) \cdot k + 1)_*}\]
7. Using strategy rm
8. Applied div-inv0.0
  \[\leadsto \color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot \left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right)\right) \cdot \frac{1}{(\left(k + 10\right) \cdot k + 1)_*}}\]
if 4.473155123819974e+17 < k
1. Initial program 5.3
  \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
2. Simplified5.3
  \[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{(\left(k + 10\right) \cdot k + 1)_*}}\]
3. Taylor expanded around -inf 63.0
  \[\leadsto \color{blue}{\left(99 \cdot \frac{a \cdot e^{m \cdot \left(\log -1 - \log \left(\frac{-1}{k}\right)\right)}}{{k}^{4}} + \frac{a \cdot e^{m \cdot \left(\log -1 - \log \left(\frac{-1}{k}\right)\right)}}{{k}^{2}}\right) - 10 \cdot \frac{a \cdot e^{m \cdot \left(\log -1 - \log \left(\frac{-1}{k}\right)\right)}}{{k}^{3}}}\]
4. Simplified0.1
  \[\leadsto \color{blue}{(\left(\frac{99}{k \cdot k}\right) \cdot \left(\frac{\frac{a}{k} \cdot e^{m \cdot \left(0 + \log k\right)}}{k}\right) + \left(-10 \cdot \frac{\frac{\frac{a}{k} \cdot e^{m \cdot \left(0 + \log k\right)}}{k}}{k}\right))_* + \frac{\frac{a}{k} \cdot e^{m \cdot \left(0 + \log k\right)}}{k}}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;k \le 4.473155123819974 \cdot 10^{+17}:\\ \;\;\;\;\left(\left({\left(\sqrt[3]{k}\right)}^{m} \cdot a\right) \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot \frac{1}{(\left(10 + k\right) \cdot k + 1)_*}\\ \mathbf{else}:\\ \;\;\;\;(\left(\frac{99}{k \cdot k}\right) \cdot \left(\frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}\right) + \left(\frac{\frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}}{k} \cdot -10\right))_* + \frac{e^{\log k \cdot m} \cdot \frac{a}{k}}{k}\\ \end{array}\]

Error

Derivation

`if k < 4.473155123819974e+17`

`if 4.473155123819974e+17 < k`

Reproduce