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

↓

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

double f(double g, double h) {
        double r24817831 = 2.0;
        double r24817832 = atan2(1.0, 0.0);
        double r24817833 = r24817831 * r24817832;
        double r24817834 = 3.0;
        double r24817835 = r24817833 / r24817834;
        double r24817836 = g;
        double r24817837 = -r24817836;
        double r24817838 = h;
        double r24817839 = r24817837 / r24817838;
        double r24817840 = acos(r24817839);
        double r24817841 = r24817840 / r24817834;
        double r24817842 = r24817835 + r24817841;
        double r24817843 = cos(r24817842);
        double r24817844 = r24817831 * r24817843;
        return r24817844;
}

↓

double f(double g, double h) {
        double r24817845 = 2.0;
        double r24817846 = 0.6666666666666666;
        double r24817847 = atan2(1.0, 0.0);
        double r24817848 = g;
        double r24817849 = -r24817848;
        double r24817850 = h;
        double r24817851 = r24817849 / r24817850;
        double r24817852 = acos(r24817851);
        double r24817853 = 3.0;
        double r24817854 = r24817852 / r24817853;
        double r24817855 = fma(r24817846, r24817847, r24817854);
        double r24817856 = cos(r24817855);
        double r24817857 = expm1(r24817856);
        double r24817858 = log1p(r24817857);
        double r24817859 = r24817845 * r24817858;
        return r24817859;
}

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

↓

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

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
\[\leadsto \color{blue}{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right) \cdot 2}\]
Using strategy rm
Applied log1p-expm1-u1.0
\[\leadsto \color{blue}{\log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right)} - 1)^*)} \cdot 2\]
Final simplification1.0
\[\leadsto 2 \cdot \log_* (1 + (e^{\cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right)} - 1)^*)\]

Error

Derivation

Reproduce