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

↓

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

\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 r1331494 = 2.0;
        double r1331495 = x;
        double r1331496 = r1331494 * r1331495;
        double r1331497 = exp(r1331496);
        double r1331498 = 1.0;
        double r1331499 = r1331497 - r1331498;
        double r1331500 = exp(r1331495);
        double r1331501 = r1331500 - r1331498;
        double r1331502 = r1331499 / r1331501;
        double r1331503 = sqrt(r1331502);
        return r1331503;
}

↓

double f(double x) {
        double r1331504 = x;
        double r1331505 = -9.471958066473225e-06;
        bool r1331506 = r1331504 <= r1331505;
        double r1331507 = 1.0;
        double r1331508 = sqrt(r1331507);
        double r1331509 = 2.0;
        double r1331510 = r1331509 * r1331504;
        double r1331511 = exp(r1331510);
        double r1331512 = sqrt(r1331511);
        double r1331513 = r1331508 + r1331512;
        double r1331514 = sqrt(r1331513);
        double r1331515 = r1331514 * r1331514;
        double r1331516 = exp(r1331504);
        double r1331517 = r1331516 - r1331507;
        double r1331518 = r1331512 - r1331508;
        double r1331519 = r1331517 / r1331518;
        double r1331520 = r1331515 / r1331519;
        double r1331521 = sqrt(r1331520);
        double r1331522 = 0.5;
        double r1331523 = r1331504 * r1331522;
        double r1331524 = r1331507 + r1331523;
        double r1331525 = r1331504 * r1331524;
        double r1331526 = r1331509 + r1331525;
        double r1331527 = sqrt(r1331526);
        double r1331528 = r1331506 ? r1331521 : r1331527;
        return r1331528;
}

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

Try it out

Derivation

`if x < -9.471958066473225e-06`

`if -9.471958066473225e-06 < x`

Reproduce

In
Out