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

↓

\[\begin{array}{l} \mathbf{if}\;k \le 1.442302470468942821043172495313077911614 \cdot 10^{138}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{k}, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}, \mathsf{fma}\left(99, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}, \left(-10\right) \cdot \left(\frac{a}{{k}^{3}} \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}\right)\right)\right)\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;k \le 1.442302470468942821043172495313077911614 \cdot 10^{138}:\\
\;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{a}{k}, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}, \mathsf{fma}\left(99, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}, \left(-10\right) \cdot \left(\frac{a}{{k}^{3}} \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}\right)\right)\right)\\

\end{array}

double f(double a, double k, double m) {
        double r206998 = a;
        double r206999 = k;
        double r207000 = m;
        double r207001 = pow(r206999, r207000);
        double r207002 = r206998 * r207001;
        double r207003 = 1.0;
        double r207004 = 10.0;
        double r207005 = r207004 * r206999;
        double r207006 = r207003 + r207005;
        double r207007 = r206999 * r206999;
        double r207008 = r207006 + r207007;
        double r207009 = r207002 / r207008;
        return r207009;
}

↓

double f(double a, double k, double m) {
        double r207010 = k;
        double r207011 = 1.4423024704689428e+138;
        bool r207012 = r207010 <= r207011;
        double r207013 = a;
        double r207014 = m;
        double r207015 = pow(r207010, r207014);
        double r207016 = r207013 * r207015;
        double r207017 = 1.0;
        double r207018 = 10.0;
        double r207019 = r207018 * r207010;
        double r207020 = r207017 + r207019;
        double r207021 = r207010 * r207010;
        double r207022 = r207020 + r207021;
        double r207023 = r207016 / r207022;
        double r207024 = r207013 / r207010;
        double r207025 = 1.0;
        double r207026 = r207025 / r207010;
        double r207027 = -r207014;
        double r207028 = pow(r207026, r207027);
        double r207029 = r207028 / r207010;
        double r207030 = 99.0;
        double r207031 = 4.0;
        double r207032 = pow(r207010, r207031);
        double r207033 = r207032 / r207013;
        double r207034 = r207028 / r207033;
        double r207035 = -r207018;
        double r207036 = 3.0;
        double r207037 = pow(r207010, r207036);
        double r207038 = r207013 / r207037;
        double r207039 = r207038 * r207028;
        double r207040 = r207035 * r207039;
        double r207041 = fma(r207030, r207034, r207040);
        double r207042 = fma(r207024, r207029, r207041);
        double r207043 = r207012 ? r207023 : r207042;
        return r207043;
}

Derivation

Split input into 2 regimes
if k < 1.4423024704689428e+138
1. Initial program 0.1
  \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
if 1.4423024704689428e+138 < k
1. Initial program 8.9
  \[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
2. Using strategy rm
3. Applied add-sqr-sqrt8.9
  \[\leadsto \frac{a \cdot {k}^{m}}{\color{blue}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k} \cdot \sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}\]
4. Applied associate-/r*8.9
  \[\leadsto \color{blue}{\frac{\frac{a \cdot {k}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}\]
5. Simplified8.9
  \[\leadsto \frac{\color{blue}{\frac{a \cdot {k}^{m}}{\sqrt{\mathsf{fma}\left(k, 10 + k, 1\right)}}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]
6. Using strategy rm
7. Applied add-cbrt-cube11.3
  \[\leadsto \frac{\frac{a \cdot {k}^{m}}{\color{blue}{\sqrt[3]{\left(\sqrt{\mathsf{fma}\left(k, 10 + k, 1\right)} \cdot \sqrt{\mathsf{fma}\left(k, 10 + k, 1\right)}\right) \cdot \sqrt{\mathsf{fma}\left(k, 10 + k, 1\right)}}}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]
8. Simplified11.3
  \[\leadsto \frac{\frac{a \cdot {k}^{m}}{\sqrt[3]{\color{blue}{{\left(\sqrt{\mathsf{fma}\left(k, 10 + k, 1\right)}\right)}^{3}}}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]
9. Taylor expanded around inf 8.9
  \[\leadsto \color{blue}{\left(\frac{a \cdot e^{-1 \cdot \left(m \cdot \log \left(\frac{1}{k}\right)\right)}}{{k}^{2}} + 99 \cdot \frac{a \cdot e^{-1 \cdot \left(m \cdot \log \left(\frac{1}{k}\right)\right)}}{{k}^{4}}\right) - 10 \cdot \frac{a \cdot e^{-1 \cdot \left(m \cdot \log \left(\frac{1}{k}\right)\right)}}{{k}^{3}}}\]
10. Simplified0.1
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{a}{k}, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}, \mathsf{fma}\left(99, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}, \left(-10\right) \cdot \left(\frac{a}{{k}^{3}} \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}\right)\right)\right)}\]
Recombined 2 regimes into one program.
Final simplification0.1
\[\leadsto \begin{array}{l} \mathbf{if}\;k \le 1.442302470468942821043172495313077911614 \cdot 10^{138}:\\ \;\;\;\;\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{a}{k}, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{k}, \mathsf{fma}\left(99, \frac{{\left(\frac{1}{k}\right)}^{\left(-m\right)}}{\frac{{k}^{4}}{a}}, \left(-10\right) \cdot \left(\frac{a}{{k}^{3}} \cdot {\left(\frac{1}{k}\right)}^{\left(-m\right)}\right)\right)\right)\\ \end{array}\]

Error

Derivation

`if k < 1.4423024704689428e+138`

`if 1.4423024704689428e+138 < k`

Reproduce