\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{{1}^{1}}}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\ \end{array}\]

\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}

↓

\begin{array}{l}
\mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\
\;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{{1}^{1}}}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\

\end{array}

double f(double x, double y, double z, double t, double a, double b) {
        double r100468 = x;
        double r100469 = y;
        double r100470 = z;
        double r100471 = log(r100470);
        double r100472 = r100469 * r100471;
        double r100473 = t;
        double r100474 = 1.0;
        double r100475 = r100473 - r100474;
        double r100476 = a;
        double r100477 = log(r100476);
        double r100478 = r100475 * r100477;
        double r100479 = r100472 + r100478;
        double r100480 = b;
        double r100481 = r100479 - r100480;
        double r100482 = exp(r100481);
        double r100483 = r100468 * r100482;
        double r100484 = r100483 / r100469;
        return r100484;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r100485 = t;
        double r100486 = 1.0;
        double r100487 = r100485 - r100486;
        double r100488 = a;
        double r100489 = log(r100488);
        double r100490 = r100487 * r100489;
        double r100491 = -5.036976424860008e+32;
        bool r100492 = r100490 <= r100491;
        double r100493 = 65.39440531857437;
        bool r100494 = r100490 <= r100493;
        double r100495 = !r100494;
        bool r100496 = r100492 || r100495;
        double r100497 = x;
        double r100498 = y;
        double r100499 = z;
        double r100500 = log(r100499);
        double r100501 = r100498 * r100500;
        double r100502 = r100501 + r100490;
        double r100503 = b;
        double r100504 = r100502 - r100503;
        double r100505 = exp(r100504);
        double r100506 = r100497 * r100505;
        double r100507 = r100506 / r100498;
        double r100508 = 1.0;
        double r100509 = pow(r100508, r100486);
        double r100510 = r100497 / r100509;
        double r100511 = r100503 - r100501;
        double r100512 = exp(r100511);
        double r100513 = pow(r100488, r100485);
        double r100514 = r100512 / r100513;
        double r100515 = r100508 / r100498;
        double r100516 = pow(r100488, r100486);
        double r100517 = r100515 / r100516;
        double r100518 = r100514 / r100517;
        double r100519 = r100510 / r100518;
        double r100520 = r100496 ? r100507 : r100519;
        return r100520;
}

Derivation

Split input into 2 regimes
if (* (- t 1.0) (log a)) < -5.036976424860008e+32 or 65.39440531857437 < (* (- t 1.0) (log a))
1. Initial program 0.5
  \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
if -5.036976424860008e+32 < (* (- t 1.0) (log a)) < 65.39440531857437
1. Initial program 4.7
  \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\]
2. Taylor expanded around inf 4.7
  \[\leadsto \color{blue}{\frac{x \cdot e^{1 \cdot \log \left(\frac{1}{a}\right) - \left(y \cdot \log \left(\frac{1}{z}\right) + \left(\log \left(\frac{1}{a}\right) \cdot t + b\right)\right)}}{y}}\]
3. Simplified8.5
  \[\leadsto \color{blue}{\frac{\frac{\frac{x}{y}}{{a}^{1}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}}\]
4. Using strategy rm
5. Applied *-un-lft-identity8.5
  \[\leadsto \frac{\frac{\frac{x}{y}}{{\color{blue}{\left(1 \cdot a\right)}}^{1}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
6. Applied unpow-prod-down8.5
  \[\leadsto \frac{\frac{\frac{x}{y}}{\color{blue}{{1}^{1} \cdot {a}^{1}}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
7. Applied div-inv8.5
  \[\leadsto \frac{\frac{\color{blue}{x \cdot \frac{1}{y}}}{{1}^{1} \cdot {a}^{1}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
8. Applied times-frac2.6
  \[\leadsto \frac{\color{blue}{\frac{x}{{1}^{1}} \cdot \frac{\frac{1}{y}}{{a}^{1}}}}{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}\]
9. Applied associate-/l*0.9
  \[\leadsto \color{blue}{\frac{\frac{x}{{1}^{1}}}{\frac{e^{\left(b - y \cdot \log z\right) - \log a \cdot t}}{\frac{\frac{1}{y}}{{a}^{1}}}}}\]
10. Simplified0.9
  \[\leadsto \frac{\frac{x}{{1}^{1}}}{\color{blue}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}}\]
Recombined 2 regimes into one program.
Final simplification0.6
\[\leadsto \begin{array}{l} \mathbf{if}\;\left(t - 1\right) \cdot \log a \le -5.03697642486000799 \cdot 10^{32} \lor \neg \left(\left(t - 1\right) \cdot \log a \le 65.394405318574371\right):\\ \;\;\;\;\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1\right) \cdot \log a\right) - b}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{{1}^{1}}}{\frac{\frac{e^{b - y \cdot \log z}}{{a}^{t}}}{\frac{\frac{1}{y}}{{a}^{1}}}}\\ \end{array}\]

Falling back on racket egraph because egg-herbie package not installed (more)

Error

Try it out

Derivation

`if (* (- t 1.0) (log a)) < -5.036976424860008e+32 or 65.39440531857437 < (* (- t 1.0) (log a))`

`if -5.036976424860008e+32 < (* (- t 1.0) (log a)) < 65.39440531857437`

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