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

↓

\[\begin{array}{l} \mathbf{if}\;x \le -3.639623849017884427727010081959901910409 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1} \cdot \frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{1 \cdot \left(1 - e^{x}\right) + e^{2 \cdot x}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 + x \cdot \left(0.5 \cdot x + 1\right)}\\ \end{array}\]

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

↓

\begin{array}{l}
\mathbf{if}\;x \le -3.639623849017884427727010081959901910409 \cdot 10^{-7}:\\
\;\;\;\;\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1} \cdot \frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{1 \cdot \left(1 - e^{x}\right) + e^{2 \cdot x}}}\\

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

\end{array}

double f(double x) {
        double r20075 = 2.0;
        double r20076 = x;
        double r20077 = r20075 * r20076;
        double r20078 = exp(r20077);
        double r20079 = 1.0;
        double r20080 = r20078 - r20079;
        double r20081 = exp(r20076);
        double r20082 = r20081 - r20079;
        double r20083 = r20080 / r20082;
        double r20084 = sqrt(r20083);
        return r20084;
}

↓

double f(double x) {
        double r20085 = x;
        double r20086 = -3.6396238490178844e-07;
        bool r20087 = r20085 <= r20086;
        double r20088 = 2.0;
        double r20089 = r20088 * r20085;
        double r20090 = exp(r20089);
        double r20091 = 1.0;
        double r20092 = r20090 - r20091;
        double r20093 = r20085 + r20085;
        double r20094 = exp(r20093);
        double r20095 = r20091 * r20091;
        double r20096 = r20094 - r20095;
        double r20097 = r20092 / r20096;
        double r20098 = exp(r20085);
        double r20099 = 3.0;
        double r20100 = pow(r20098, r20099);
        double r20101 = pow(r20091, r20099);
        double r20102 = r20100 + r20101;
        double r20103 = r20091 - r20098;
        double r20104 = r20091 * r20103;
        double r20105 = 2.0;
        double r20106 = r20105 * r20085;
        double r20107 = exp(r20106);
        double r20108 = r20104 + r20107;
        double r20109 = r20102 / r20108;
        double r20110 = r20097 * r20109;
        double r20111 = sqrt(r20110);
        double r20112 = 0.5;
        double r20113 = r20112 * r20085;
        double r20114 = r20113 + r20091;
        double r20115 = r20085 * r20114;
        double r20116 = r20088 + r20115;
        double r20117 = sqrt(r20116);
        double r20118 = r20087 ? r20111 : r20117;
        return r20118;
}

Derivation

Split input into 2 regimes
if x < -3.6396238490178844e-07
1. Initial program 0.2
  \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
2. Using strategy rm
3. Applied flip--0.1
  \[\leadsto \sqrt{\frac{e^{2 \cdot x} - 1}{\color{blue}{\frac{e^{x} \cdot e^{x} - 1 \cdot 1}{e^{x} + 1}}}}\]
4. Applied associate-/r/0.1
  \[\leadsto \sqrt{\color{blue}{\frac{e^{2 \cdot x} - 1}{e^{x} \cdot e^{x} - 1 \cdot 1} \cdot \left(e^{x} + 1\right)}}\]
5. Simplified0.0
  \[\leadsto \sqrt{\color{blue}{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1}} \cdot \left(e^{x} + 1\right)}\]
6. Using strategy rm
7. Applied flip3-+0.0
  \[\leadsto \sqrt{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1} \cdot \color{blue}{\frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{e^{x} \cdot e^{x} + \left(1 \cdot 1 - e^{x} \cdot 1\right)}}}\]
8. Simplified0.0
  \[\leadsto \sqrt{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1} \cdot \frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{\color{blue}{1 \cdot \left(1 - e^{x}\right) + e^{2 \cdot x}}}}\]
if -3.6396238490178844e-07 < x
1. Initial program 34.4
  \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
2. Taylor expanded around 0 6.6
  \[\leadsto \sqrt{\color{blue}{0.5 \cdot {x}^{2} + \left(1 \cdot x + 2\right)}}\]
3. Simplified6.6
  \[\leadsto \sqrt{\color{blue}{2 + x \cdot \left(0.5 \cdot x + 1\right)}}\]
Recombined 2 regimes into one program.
Final simplification0.8
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.639623849017884427727010081959901910409 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x + x} - 1 \cdot 1} \cdot \frac{{\left(e^{x}\right)}^{3} + {1}^{3}}{1 \cdot \left(1 - e^{x}\right) + e^{2 \cdot x}}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{2 + x \cdot \left(0.5 \cdot x + 1\right)}\\ \end{array}\]

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

Error

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Derivation

`if x < -3.6396238490178844e-07`

`if -3.6396238490178844e-07 < x`

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