\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]

↓

\[\sqrt{\frac{\frac{1}{2}}{\log \left(e^{\sqrt{\left(\left(\frac{2}{Om} \cdot \ell\right) \cdot \left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right)\right) \cdot \left(\frac{2}{Om} \cdot \ell\right) + 1}}\right)} + \frac{1}{2}}\]

double f(double l, double Om, double kx, double ky) {
        double r17430176 = 1.0;
        double r17430177 = 2.0;
        double r17430178 = r17430176 / r17430177;
        double r17430179 = l;
        double r17430180 = r17430177 * r17430179;
        double r17430181 = Om;
        double r17430182 = r17430180 / r17430181;
        double r17430183 = pow(r17430182, r17430177);
        double r17430184 = kx;
        double r17430185 = sin(r17430184);
        double r17430186 = pow(r17430185, r17430177);
        double r17430187 = ky;
        double r17430188 = sin(r17430187);
        double r17430189 = pow(r17430188, r17430177);
        double r17430190 = r17430186 + r17430189;
        double r17430191 = r17430183 * r17430190;
        double r17430192 = r17430176 + r17430191;
        double r17430193 = sqrt(r17430192);
        double r17430194 = r17430176 / r17430193;
        double r17430195 = r17430176 + r17430194;
        double r17430196 = r17430178 * r17430195;
        double r17430197 = sqrt(r17430196);
        return r17430197;
}

↓

double f(double l, double Om, double kx, double ky) {
        double r17430198 = 0.5;
        double r17430199 = 2.0;
        double r17430200 = Om;
        double r17430201 = r17430199 / r17430200;
        double r17430202 = l;
        double r17430203 = r17430201 * r17430202;
        double r17430204 = ky;
        double r17430205 = sin(r17430204);
        double r17430206 = r17430205 * r17430205;
        double r17430207 = kx;
        double r17430208 = sin(r17430207);
        double r17430209 = r17430208 * r17430208;
        double r17430210 = r17430206 + r17430209;
        double r17430211 = r17430203 * r17430210;
        double r17430212 = r17430211 * r17430203;
        double r17430213 = 1.0;
        double r17430214 = r17430212 + r17430213;
        double r17430215 = sqrt(r17430214);
        double r17430216 = exp(r17430215);
        double r17430217 = log(r17430216);
        double r17430218 = r17430198 / r17430217;
        double r17430219 = r17430218 + r17430198;
        double r17430220 = sqrt(r17430219);
        return r17430220;
}

\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}

↓

\sqrt{\frac{\frac{1}{2}}{\log \left(e^{\sqrt{\left(\left(\frac{2}{Om} \cdot \ell\right) \cdot \left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right)\right) \cdot \left(\frac{2}{Om} \cdot \ell\right) + 1}}\right)} + \frac{1}{2}}

Derivation

Initial program 1.7
\[\sqrt{\frac{1}{2} \cdot \left(1 + \frac{1}{\sqrt{1 + {\left(\frac{2 \cdot \ell}{Om}\right)}^{2} \cdot \left({\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}\right)}}\right)}\]
Simplified1.7
\[\leadsto \color{blue}{\sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{\left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right) \cdot \left(\left(\ell \cdot \frac{2}{Om}\right) \cdot \left(\ell \cdot \frac{2}{Om}\right)\right) + 1}}}}\]
Using strategy rm
Applied associate-*r*1.3
\[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\sqrt{\color{blue}{\left(\left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right) \cdot \left(\ell \cdot \frac{2}{Om}\right)\right) \cdot \left(\ell \cdot \frac{2}{Om}\right)} + 1}}}\]
Using strategy rm
Applied add-log-exp1.5
\[\leadsto \sqrt{\frac{1}{2} + \frac{\frac{1}{2}}{\color{blue}{\log \left(e^{\sqrt{\left(\left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right) \cdot \left(\ell \cdot \frac{2}{Om}\right)\right) \cdot \left(\ell \cdot \frac{2}{Om}\right) + 1}}\right)}}}\]
Final simplification1.5
\[\leadsto \sqrt{\frac{\frac{1}{2}}{\log \left(e^{\sqrt{\left(\left(\frac{2}{Om} \cdot \ell\right) \cdot \left(\sin ky \cdot \sin ky + \sin kx \cdot \sin kx\right)\right) \cdot \left(\frac{2}{Om} \cdot \ell\right) + 1}}\right)} + \frac{1}{2}}\]

Error

Derivation

Reproduce