\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

↓

\[J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U\]

double f(double J, double l, double K, double U) {
        double r12207454 = J;
        double r12207455 = l;
        double r12207456 = exp(r12207455);
        double r12207457 = -r12207455;
        double r12207458 = exp(r12207457);
        double r12207459 = r12207456 - r12207458;
        double r12207460 = r12207454 * r12207459;
        double r12207461 = K;
        double r12207462 = 2.0;
        double r12207463 = r12207461 / r12207462;
        double r12207464 = cos(r12207463);
        double r12207465 = r12207460 * r12207464;
        double r12207466 = U;
        double r12207467 = r12207465 + r12207466;
        return r12207467;
}

↓

double f(double J, double l, double K, double U) {
        double r12207468 = J;
        double r12207469 = K;
        double r12207470 = 2.0;
        double r12207471 = r12207469 / r12207470;
        double r12207472 = cos(r12207471);
        double r12207473 = l;
        double r12207474 = 5.0;
        double r12207475 = pow(r12207473, r12207474);
        double r12207476 = 0.016666666666666666;
        double r12207477 = r12207475 * r12207476;
        double r12207478 = 0.3333333333333333;
        double r12207479 = r12207478 * r12207473;
        double r12207480 = r12207479 * r12207473;
        double r12207481 = r12207470 + r12207480;
        double r12207482 = r12207481 * r12207473;
        double r12207483 = r12207477 + r12207482;
        double r12207484 = r12207472 * r12207483;
        double r12207485 = r12207468 * r12207484;
        double r12207486 = U;
        double r12207487 = r12207485 + r12207486;
        return r12207487;
}

\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U

↓

J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U

Derivation

Initial program 16.5
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Taylor expanded around 0 0.3
\[\leadsto \left(J \cdot \color{blue}{\left(2 \cdot \ell + \left(\frac{1}{3} \cdot {\ell}^{3} + \frac{1}{60} \cdot {\ell}^{5}\right)\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Simplified0.3
\[\leadsto \left(J \cdot \color{blue}{\left(\ell \cdot \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) + {\ell}^{5} \cdot \frac{1}{60}\right)}\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
Using strategy rm
Applied associate-*l*0.3
\[\leadsto \color{blue}{J \cdot \left(\left(\ell \cdot \left(\ell \cdot \left(\frac{1}{3} \cdot \ell\right) + 2\right) + {\ell}^{5} \cdot \frac{1}{60}\right) \cdot \cos \left(\frac{K}{2}\right)\right)} + U\]
Final simplification0.3
\[\leadsto J \cdot \left(\cos \left(\frac{K}{2}\right) \cdot \left({\ell}^{5} \cdot \frac{1}{60} + \left(2 + \left(\frac{1}{3} \cdot \ell\right) \cdot \ell\right) \cdot \ell\right)\right) + U\]

Error

Derivation

Reproduce