\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \le -9.47195806647322485446235246220325620925 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{\frac{\sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}} \cdot \sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}}}{\frac{e^{x} - 1}{\sqrt{e^{2 \cdot x}} - \sqrt{1}}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 + x \cdot \left(1 + x \cdot 0.5\right)}\\ \end{array}\]

\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}

↓

\begin{array}{l}
\mathbf{if}\;x \le -9.47195806647322485446235246220325620925 \cdot 10^{-6}:\\
\;\;\;\;\sqrt{\frac{\sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}} \cdot \sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}}}{\frac{e^{x} - 1}{\sqrt{e^{2 \cdot x}} - \sqrt{1}}}}\\

\mathbf{else}:\\
\;\;\;\;\sqrt{2 + x \cdot \left(1 + x \cdot 0.5\right)}\\

\end{array}

double f(double x) {
        double r1207455 = 2.0;
        double r1207456 = x;
        double r1207457 = r1207455 * r1207456;
        double r1207458 = exp(r1207457);
        double r1207459 = 1.0;
        double r1207460 = r1207458 - r1207459;
        double r1207461 = exp(r1207456);
        double r1207462 = r1207461 - r1207459;
        double r1207463 = r1207460 / r1207462;
        double r1207464 = sqrt(r1207463);
        return r1207464;
}

↓

double f(double x) {
        double r1207465 = x;
        double r1207466 = -9.471958066473225e-06;
        bool r1207467 = r1207465 <= r1207466;
        double r1207468 = 1.0;
        double r1207469 = sqrt(r1207468);
        double r1207470 = 2.0;
        double r1207471 = r1207470 * r1207465;
        double r1207472 = exp(r1207471);
        double r1207473 = sqrt(r1207472);
        double r1207474 = r1207469 + r1207473;
        double r1207475 = sqrt(r1207474);
        double r1207476 = r1207475 * r1207475;
        double r1207477 = exp(r1207465);
        double r1207478 = r1207477 - r1207468;
        double r1207479 = r1207473 - r1207469;
        double r1207480 = r1207478 / r1207479;
        double r1207481 = r1207476 / r1207480;
        double r1207482 = sqrt(r1207481);
        double r1207483 = 0.5;
        double r1207484 = r1207465 * r1207483;
        double r1207485 = r1207468 + r1207484;
        double r1207486 = r1207465 * r1207485;
        double r1207487 = r1207470 + r1207486;
        double r1207488 = sqrt(r1207487);
        double r1207489 = r1207467 ? r1207482 : r1207488;
        return r1207489;
}

Derivation

Split input into 2 regimes
if x < -9.471958066473225e-06
1. Initial program 0.1
  \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
2. Using strategy rm
3. Applied add-sqr-sqrt0.1
  \[\leadsto \sqrt{\frac{e^{2 \cdot x} - \color{blue}{\sqrt{1} \cdot \sqrt{1}}}{e^{x} - 1}}\]
4. Applied add-sqr-sqrt0.1
  \[\leadsto \sqrt{\frac{\color{blue}{\sqrt{e^{2 \cdot x}} \cdot \sqrt{e^{2 \cdot x}}} - \sqrt{1} \cdot \sqrt{1}}{e^{x} - 1}}\]
5. Applied difference-of-squares0.0
  \[\leadsto \sqrt{\frac{\color{blue}{\left(\sqrt{e^{2 \cdot x}} + \sqrt{1}\right) \cdot \left(\sqrt{e^{2 \cdot x}} - \sqrt{1}\right)}}{e^{x} - 1}}\]
6. Applied associate-/l*0.0
  \[\leadsto \sqrt{\color{blue}{\frac{\sqrt{e^{2 \cdot x}} + \sqrt{1}}{\frac{e^{x} - 1}{\sqrt{e^{2 \cdot x}} - \sqrt{1}}}}}\]
7. Using strategy rm
8. Applied add-sqr-sqrt0.0
  \[\leadsto \sqrt{\frac{\color{blue}{\sqrt{\sqrt{e^{2 \cdot x}} + \sqrt{1}} \cdot \sqrt{\sqrt{e^{2 \cdot x}} + \sqrt{1}}}}{\frac{e^{x} - 1}{\sqrt{e^{2 \cdot x}} - \sqrt{1}}}}\]
if -9.471958066473225e-06 < x
1. Initial program 34.5
  \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
2. Taylor expanded around 0 6.5
  \[\leadsto \sqrt{\color{blue}{1 \cdot x + \left(0.5 \cdot {x}^{2} + 2\right)}}\]
3. Simplified6.5
  \[\leadsto \sqrt{\color{blue}{2 + x \cdot \left(1 + x \cdot 0.5\right)}}\]
Recombined 2 regimes into one program.
Final simplification0.8
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.47195806647322485446235246220325620925 \cdot 10^{-6}:\\ \;\;\;\;\sqrt{\frac{\sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}} \cdot \sqrt{\sqrt{1} + \sqrt{e^{2 \cdot x}}}}{\frac{e^{x} - 1}{\sqrt{e^{2 \cdot x}} - \sqrt{1}}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 + x \cdot \left(1 + x \cdot 0.5\right)}\\ \end{array}\]

could not determine a ground truth for program body (more)

Error

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Derivation

`if x < -9.471958066473225e-06`

`if -9.471958066473225e-06 < x`

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