\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]

↓

\[2 \cdot \left(\frac{1}{2} \cdot \cos \left(\frac{\pi}{6} - \left(\frac{\pi}{\frac{3}{2}} + \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)\]

double f(double g, double h) {
        double r17184198 = 2.0;
        double r17184199 = atan2(1.0, 0.0);
        double r17184200 = r17184198 * r17184199;
        double r17184201 = 3.0;
        double r17184202 = r17184200 / r17184201;
        double r17184203 = g;
        double r17184204 = -r17184203;
        double r17184205 = h;
        double r17184206 = r17184204 / r17184205;
        double r17184207 = acos(r17184206);
        double r17184208 = r17184207 / r17184201;
        double r17184209 = r17184202 + r17184208;
        double r17184210 = cos(r17184209);
        double r17184211 = r17184198 * r17184210;
        return r17184211;
}

↓

double f(double g, double h) {
        double r17184212 = 2.0;
        double r17184213 = 0.5;
        double r17184214 = atan2(1.0, 0.0);
        double r17184215 = 6.0;
        double r17184216 = r17184214 / r17184215;
        double r17184217 = 1.5;
        double r17184218 = r17184214 / r17184217;
        double r17184219 = g;
        double r17184220 = h;
        double r17184221 = r17184219 / r17184220;
        double r17184222 = asin(r17184221);
        double r17184223 = 3.0;
        double r17184224 = r17184222 / r17184223;
        double r17184225 = r17184218 + r17184224;
        double r17184226 = r17184216 - r17184225;
        double r17184227 = cos(r17184226);
        double r17184228 = r17184213 * r17184227;
        double r17184229 = r17184214 / r17184223;
        double r17184230 = sin(r17184229);
        double r17184231 = acos(r17184221);
        double r17184232 = r17184231 / r17184223;
        double r17184233 = r17184232 - r17184218;
        double r17184234 = sin(r17184233);
        double r17184235 = r17184230 * r17184234;
        double r17184236 = r17184228 + r17184235;
        double r17184237 = r17184212 * r17184236;
        return r17184237;
}

2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)

↓

2 \cdot \left(\frac{1}{2} \cdot \cos \left(\frac{\pi}{6} - \left(\frac{\pi}{\frac{3}{2}} + \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)

Derivation

Initial program 1.0
\[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]
Simplified1.0
\[\leadsto \color{blue}{\cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2}\]
Using strategy rm
Applied distribute-frac-neg1.0
\[\leadsto \cos \left(\frac{\cos^{-1} \color{blue}{\left(-\frac{g}{h}\right)}}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied acos-neg1.0
\[\leadsto \cos \left(\frac{\color{blue}{\pi - \cos^{-1} \left(\frac{g}{h}\right)}}{3} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied div-sub1.0
\[\leadsto \cos \left(\color{blue}{\left(\frac{\pi}{3} - \frac{\cos^{-1} \left(\frac{g}{h}\right)}{3}\right)} + \frac{\pi}{\frac{3}{2}}\right) \cdot 2\]
Applied associate-+l-1.0
\[\leadsto \cos \color{blue}{\left(\frac{\pi}{3} - \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)} \cdot 2\]
Applied cos-diff0.1
\[\leadsto \color{blue}{\left(\cos \left(\frac{\pi}{3}\right) \cdot \cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)} \cdot 2\]
Simplified0.1
\[\leadsto \left(\color{blue}{\cos \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2}} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Using strategy rm
Applied acos-asin0.1
\[\leadsto \left(\cos \left(\frac{\color{blue}{\frac{\pi}{2} - \sin^{-1} \left(\frac{g}{h}\right)}}{3} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Applied div-sub0.1
\[\leadsto \left(\cos \left(\color{blue}{\left(\frac{\frac{\pi}{2}}{3} - \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)} - \frac{\pi}{\frac{3}{2}}\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Applied associate--l-0.0
\[\leadsto \left(\cos \color{blue}{\left(\frac{\frac{\pi}{2}}{3} - \left(\frac{\sin^{-1} \left(\frac{g}{h}\right)}{3} + \frac{\pi}{\frac{3}{2}}\right)\right)} \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Simplified0.0
\[\leadsto \left(\cos \left(\color{blue}{\frac{\pi}{6}} - \left(\frac{\sin^{-1} \left(\frac{g}{h}\right)}{3} + \frac{\pi}{\frac{3}{2}}\right)\right) \cdot \frac{1}{2} + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right) \cdot 2\]
Final simplification0.0
\[\leadsto 2 \cdot \left(\frac{1}{2} \cdot \cos \left(\frac{\pi}{6} - \left(\frac{\pi}{\frac{3}{2}} + \frac{\sin^{-1} \left(\frac{g}{h}\right)}{3}\right)\right) + \sin \left(\frac{\pi}{3}\right) \cdot \sin \left(\frac{\cos^{-1} \left(\frac{g}{h}\right)}{3} - \frac{\pi}{\frac{3}{2}}\right)\right)\]

Error

Derivation

Reproduce