\[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]

↓

\[\begin{array}{l} \mathbf{if}\;z \le 7.17401834154551376 \cdot 10^{192}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)\\ \end{array}\]

x + \left(y - z\right) \cdot \frac{t - x}{a - z}

↓

\begin{array}{l}
\mathbf{if}\;z \le 7.17401834154551376 \cdot 10^{192}:\\
\;\;\;\;\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)\\

\end{array}

double f(double x, double y, double z, double t, double a) {
        double r124813 = x;
        double r124814 = y;
        double r124815 = z;
        double r124816 = r124814 - r124815;
        double r124817 = t;
        double r124818 = r124817 - r124813;
        double r124819 = a;
        double r124820 = r124819 - r124815;
        double r124821 = r124818 / r124820;
        double r124822 = r124816 * r124821;
        double r124823 = r124813 + r124822;
        return r124823;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r124824 = z;
        double r124825 = 7.174018341545514e+192;
        bool r124826 = r124824 <= r124825;
        double r124827 = x;
        double r124828 = cbrt(r124827);
        double r124829 = r124828 * r124828;
        double r124830 = y;
        double r124831 = r124830 - r124824;
        double r124832 = cbrt(r124831);
        double r124833 = r124832 * r124832;
        double r124834 = a;
        double r124835 = r124834 - r124824;
        double r124836 = cbrt(r124835);
        double r124837 = r124833 / r124836;
        double r124838 = r124832 / r124836;
        double r124839 = t;
        double r124840 = r124839 - r124827;
        double r124841 = r124840 / r124836;
        double r124842 = r124838 * r124841;
        double r124843 = r124837 * r124842;
        double r124844 = fma(r124829, r124828, r124843);
        double r124845 = r124827 / r124824;
        double r124846 = r124839 * r124830;
        double r124847 = r124846 / r124824;
        double r124848 = r124839 - r124847;
        double r124849 = fma(r124845, r124830, r124848);
        double r124850 = r124826 ? r124844 : r124849;
        return r124850;
}

Derivation

Split input into 2 regimes
if z < 7.174018341545514e+192
1. Initial program 13.0
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Using strategy rm
3. Applied add-cube-cbrt13.6
  \[\leadsto x + \left(y - z\right) \cdot \frac{t - x}{\color{blue}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}}\]
4. Applied *-un-lft-identity13.6
  \[\leadsto x + \left(y - z\right) \cdot \frac{\color{blue}{1 \cdot \left(t - x\right)}}{\left(\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}\right) \cdot \sqrt[3]{a - z}}\]
5. Applied times-frac13.6
  \[\leadsto x + \left(y - z\right) \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]
6. Applied associate-*r*10.7
  \[\leadsto x + \color{blue}{\left(\left(y - z\right) \cdot \frac{1}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}\right) \cdot \frac{t - x}{\sqrt[3]{a - z}}}\]
7. Simplified10.7
  \[\leadsto x + \color{blue}{\frac{y - z}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
8. Using strategy rm
9. Applied add-cube-cbrt10.7
  \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}\right) \cdot \sqrt[3]{y - z}}}{\sqrt[3]{a - z} \cdot \sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
10. Applied times-frac10.7
  \[\leadsto x + \color{blue}{\left(\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}}\right)} \cdot \frac{t - x}{\sqrt[3]{a - z}}\]
11. Applied associate-*l*10.4
  \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)}\]
12. Using strategy rm
13. Applied add-cube-cbrt10.8
  \[\leadsto \color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}} + \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\]
14. Applied fma-def10.8
  \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\right)}\]
if 7.174018341545514e+192 < z
1. Initial program 29.9
  \[x + \left(y - z\right) \cdot \frac{t - x}{a - z}\]
2. Taylor expanded around inf 23.4
  \[\leadsto \color{blue}{\left(\frac{x \cdot y}{z} + t\right) - \frac{t \cdot y}{z}}\]
3. Simplified20.3
  \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)}\]
Recombined 2 regimes into one program.
Final simplification11.8
\[\leadsto \begin{array}{l} \mathbf{if}\;z \le 7.17401834154551376 \cdot 10^{192}:\\ \;\;\;\;\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x}, \frac{\sqrt[3]{y - z} \cdot \sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \left(\frac{\sqrt[3]{y - z}}{\sqrt[3]{a - z}} \cdot \frac{t - x}{\sqrt[3]{a - z}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{z}, y, t - \frac{t \cdot y}{z}\right)\\ \end{array}\]

Error

Derivation

`if z < 7.174018341545514e+192`

`if 7.174018341545514e+192 < z`

Reproduce