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

↓

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

double f(double g, double h) {
        double r14721315 = 2.0;
        double r14721316 = atan2(1.0, 0.0);
        double r14721317 = r14721315 * r14721316;
        double r14721318 = 3.0;
        double r14721319 = r14721317 / r14721318;
        double r14721320 = g;
        double r14721321 = -r14721320;
        double r14721322 = h;
        double r14721323 = r14721321 / r14721322;
        double r14721324 = acos(r14721323);
        double r14721325 = r14721324 / r14721318;
        double r14721326 = r14721319 + r14721325;
        double r14721327 = cos(r14721326);
        double r14721328 = r14721315 * r14721327;
        return r14721328;
}

↓

double f(double g, double h) {
        double r14721329 = 2.0;
        double r14721330 = 0.5;
        double r14721331 = atan2(1.0, 0.0);
        double r14721332 = 6.0;
        double r14721333 = r14721331 / r14721332;
        double r14721334 = 1.5;
        double r14721335 = r14721331 / r14721334;
        double r14721336 = g;
        double r14721337 = h;
        double r14721338 = r14721336 / r14721337;
        double r14721339 = asin(r14721338);
        double r14721340 = 3.0;
        double r14721341 = r14721339 / r14721340;
        double r14721342 = r14721335 + r14721341;
        double r14721343 = r14721333 - r14721342;
        double r14721344 = cos(r14721343);
        double r14721345 = r14721330 * r14721344;
        double r14721346 = r14721331 / r14721340;
        double r14721347 = sin(r14721346);
        double r14721348 = acos(r14721338);
        double r14721349 = r14721348 / r14721340;
        double r14721350 = r14721349 - r14721335;
        double r14721351 = sin(r14721350);
        double r14721352 = r14721347 * r14721351;
        double r14721353 = r14721345 + r14721352;
        double r14721354 = r14721329 * r14721353;
        return r14721354;
}

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